UNIVERSITY OF CALIFORNIA, SAN DIEGO The Significance of Spatial

UNIVERSITY OF CALIFORNIA, SAN DIEGO

The Significance of Spatial Representation

A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Cognitive Science and Philosophy

by

Aarre Laakso

Committee in charge: Professor Patricia S. Churchland, Chair Professor Garrison Cottrell, Co-Chair Professor Paul M. Churchland Professor Georgios Anagnastopoulos Professor V. S. Ramachandran

1999

Copyright Aarre Laakso, 1999 All rights reserved

The dissertation of Aarre Laakso is approved, and it is acceptable in quality and form for publication on microfilm:

1999

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Table of Contents Signature Page............................................................................. iii Table of Contents ........................................................................ iv List of Figures ............................................................................ vii List of Tables............................................................................... ix Preface ......................................................................................... x Acknowledgements ..................................................................... xi Vita ........................................................................................... xiii Abstract of the Dissertation......................................................... xv Chapter 1 Introduction ......................................................................................... 1 1.1

Motivation.................................................................................... 1

1.2

Related Work ............................................................................... 3

1.3

Overview of the Dissertation ...................................................... 19

Chapter 2 Philosophical Context........................................................................ 22 2.1

Abstract...................................................................................... 22

2.2

The Mind/Body Problem and Intentionality ................................ 23

2.3

The Problem of Objectivity......................................................... 30

2.4

The Problem of Naturalizing Epistemology ................................ 39

2.5

Physicalism ................................................................................ 42

2.6

Sketch of the Solution................................................................. 49

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Chapter 3 Historical Background ....................................................................... 52 3.1

Abstract...................................................................................... 52

3.2

The Ancients .............................................................................. 52

3.3

The Moderns .............................................................................. 63

3.4

Kant ........................................................................................... 77

3.5

The Twentieth Century ............................................................... 97

3.6

Conclusion ............................................................................... 104

Chapter 4 Strawson.......................................................................................... 105 4.1

Abstract.................................................................................... 105

4.2

The Importance of Mathematical Space .................................... 106

4.3

Conclusions .............................................................................. 155

Chapter 5 Strawson’s Critics............................................................................ 157 5.1

Abstract.................................................................................... 157

5.2

Bennett..................................................................................... 157

5.3

Wiggins .................................................................................... 162

5.4

Pears......................................................................................... 163

5.5

Rorty ........................................................................................ 174

5.6

Conclusion ............................................................................... 199

Chapter 6 Representational Similarity.............................................................. 201 6.1

Abstract.................................................................................... 201

6.2

Introduction.............................................................................. 201

6.3

A Modest Proposal ................................................................... 218

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6.4

Experiment One........................................................................ 223 6.4.1 Procedure...................................................................... 224 6.4.2 Results .......................................................................... 228 6.4.3 Discussion..................................................................... 238

6.5

Experiment Two....................................................................... 240 6.5.1 Procedure...................................................................... 240 6.5.2 Results .......................................................................... 241

6.6

Discussion ................................................................................ 245

6.7

Conclusions .............................................................................. 254

6.8

Acknowledgement.................................................................... 254

Chapter 7 Conclusion ...................................................................................... 255 7.1

Summary .................................................................................. 255

7.2

Directions for Future Research ................................................. 256 References................................................................................ 258

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List of Figures Figure 1

The physical world: a place without error ................................... 35

Figure 2

The representational world: a place where error is possible......... 35

Figure 3

The person as object ................................................................... 36

Figure 4

A one-dimensional vector coding.............................................. 219

Figure 5

A two-dimensional vector coding ............................................. 220

Figure 6

Representative clustering of input patterns in the “real” encoding (31 of 627 patterns shown). ....................................... 229

Figure 7

Hinton diagram showing correlation among input patterns. The areas of the boxes are proportional to the values. ............... 230

Figure 8

Hinton diagram showing mean correlations of the different input pattern encodings with the hidden unit activations of 5 networks trained on each encoding. The area of each box is proportional to its value. The input patterns are represented in the columns; the hidden unit patterns are represented in the rows. ............................................................ 232

Figure 9

Hinton diagram showing mean correlation between hidden unit activations. Shows mean correlation between hidden unit activations of 5 networks trained on each encoding and hidden unit activations of 5 networks trained on each other encoding (e.g., binary vs. real), as well as mean correlation between hidden unit activations among the 5 networks trained on each encoding (e.g., binary vs. binary). The area of each box is proportional to its value...................................... 234

Figure 10

Representative clustering of hidden-unit activations in one of the five networks trained on the “real” encoding (31 of 627 patterns shown).................................................................. 235

Figure 11

Representative clustering of hidden-unit activations in another of the five networks trained on the “real” encoding (31 of 627 patterns shown). ...................................................... 236

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Figure 12

Representative clustering of hidden-unit activations of one of the five networks trained on the “sequential” encoding (31 of 627 patterns shown). ...................................................... 238

Figure 13

Percent correct on the test set versus number of hidden units. ........................................................................................ 242

Figure 14

Number of hidden units versus correlation to input patterns and average correlation to networks with different numbers of hidden units for networks trained on the “real” encoding. ..... 243

Figure 15

Number of hidden units versus correlation to input patterns and average correlation to networks with different numbers of hidden units for networks trained on the “sequential” encoding................................................................................... 244

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List of Tables Table 1

Comparison of distances between points in two different vector encodings....................................................................... 220

Table 2

Target output patterns for the 5 color categories........................ 225

Table 3

Mean value of each element in the gaussian encoding............... 226

Table 4

Some examples of gaussian encodings...................................... 226

Table 5

Some examples of sequential encodings. .................................. 227

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Preface This work is the product of two separate projects whose true relation only became clear after both had been nearly completed. The first was a study of spatial representation, especially as it had been treated in the philosophical literature but also with some attention to the psychological and neuroscientific literature. The second was a defense of “state-space semantics”, Paul Churchland’s theory that the contents of representations in connectionist networks are mirrored by the proximities of those representations in the networks’ activation spaces. Obviously, both projects are about “spatial representation” in some sense. However, at least in the early stages of both projects, I thought that the similarities ended there – that combining them would have meant equivocating about the meanings of the key terms “space” and “representation”. The two projects became one when I realized two things. The first was that there was, in fact, a pervasive equivocation about the meaning of “space” in the philosophical literature on “spatial representation”. The second was that this equivocation was a result of confusion between two different but related problems. This led to the discovery that became the thesis of this dissertation: while neither of the senses of “spatial representation” is relevant to both problems, each of the two senses is relevant to one of them. Indeed, distinguishing the senses of “spatial representation” from each other, and applying each to the problem to which it is relevant, leads to a solution to both problems.

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Acknowledgements I first want to thank my co-chairs, Patricia Churchland and Garrison Cottrell. Pat brought the fundamental importance of spatial representation to my attention at a time when I was despairing of making any further progress in the analysis of representation in general. In many meetings and through many drafts, Gary and I together worked out the theory of representational similarity that I present in Chapter 6. Also, they have both, in their own ways, supported and encouraged me, not to mention tolerated my considerable shortcomings. In addition, I owe a particular debt to Paul Churchland, whose work on state-space semantics was the catalyst for most of my own thinking about representation in neural systems. Thanks also to the other members of my committee – Georgios Anagnastopoulos and V. S. Ramachandran – for their interest in and support of my work. I would be remiss if I did not thank all of the past and present members of Pat’s Experimental Philosophy Lab and Gary’s Unbelievable Research Unit for invaluable feedback on my work. Oron Shagrir, Rick Grush, Mark Collier, Joe Ramsey, Ilya Farber, Willie Wheeler, Brian Keeley, David Noelle and Dan Clouse were particularly helpful.

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Many other individuals have also helped me along the way, both personally and intellectually, especially Michael Selgelid, Jason Frye, Kyle Stanford, Adrian Cussins and, most of all, Nitya Sethuraman.

The text of Chapter 6 is joint work with Garrison Cottrell. The dissertation author was the primary author, and the co-author (Garrison Cottrell) directed and supervised the research that forms the basis for this chapter.

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Vita September 15, 1969 Born, Lynn, Massachusetts 1991

B.A., Philosophy, University of North Carolina, Chapel Hill, North Carolina

1991-1997

Teaching Assistant, Department of Philosophy and Revelle College Humanities Writing Program, University of California, San Diego

1997

Associate in Philosophy, Department of Philosophy, University of California, San Diego

1997-1999

Senior Application Developer, Silicon Space, Inc., San Diego, California

1999

Ph.D., Philosophy and Cognitive Science, University of California, San Diego

Publications Laakso, A. and G. Cottrell (1998) “How can I know what You think?: Assessing representational similarity in neural systems.” In Proceedings of the Twentieth Annual Cognitive Science Conference, Madison, WI, Mahwah: Lawrence Erlbaum (pp. 591-596). Laakso, A. (1996) “Has Hardcastle Located Consciousness?” (Review of Valerie Gray Hardcastle (1995) Locating Consciousness Philadelphia: John Benjamins Publishing Company) Psycoloquy 7(42). Laakso, A. (1994a) “Review of Cultivating Consciousness by K. Ramakrishna Rao (ed.)” Canadian Philosophical Reviews 14(3): 206-8. Laakso, A. (1994b) “Review of The Body/Mind Conceptual Framework and the Problem of Personal Identity by Albert Shalom” Canadian Philosophical Reviews 14(2): 137-9.

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Laakso, A. (1993a) “Pigeons and the Problem of Other Minds” Behavioral and Brain Sciences 16(4): 652-3. Laakso, A. (1993b) “Language Equals Mimesis Plus Speech” Behavioral and Brain Sciences 16(4): 765-6.

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Abstract of the Dissertation

The Significance of Spatial Representation

by

Aarre Laakso Doctor of Philosophy in Cognitive Science and Philosophy University of California, San Diego, 1999 Professor Patricia S. Churchland, Chair Professor Garrison Cottrell, Co-Chair

This dissertation explores the fundamental role of spatial representation in constituting thought. The thesis of this dissertation is that spatial representation is a fundamental constituent of thought in two ways. First, reference is a metaphorical extension of grasping material objects located in physical space. Second, predication is the relative placement of representations of these referents in a high-dimensional neural activation space. Hence, spatial representation, albeit in two different senses, is fundamental to both reference and predication, which are themselves the fundamental constituents of thought. In other words, “spatial

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representation” actually plays two fundamental roles in thought: the representation of objects as located in physical space allows us to refer to them, and the representation of objects in activation space allows us to conceptualize them. After a brief introduction in Chapter 1, the first part of this dissertation situates the problem of spatial representation in philosophical context, both synchronically (Chapter 2) and diachronically (Chapter 3). The second part (Chapter 4 and Chapter 5) considers in detail Strawson’s “Kantian” arguments for the fundamental importance of spatial representation. It concludes that, although Strawson does not carefully distinguish the importance of physical space for reference from the importance of activation space for predication, his arguments ultimately pertain to both. The final part of this dissertation (Chapter 6) presents an argument for the fundamental importance of neural activation space in categorizing stimuli and defends this “state-space semantics” (owing to Paul Churchland) against the charge that it cannot support any notion of identity of content. In addition to a method for comparing the similarity of representations across neural networks, the chapter contains the results of empirical studies with artificial neural networks demonstrating that internal representations are often remarkably similar in “speakers” of the same artificial language, despite differences in inputs and architectures. The conclusion (Chapter 7) contains a summary of the dissertation and suggestions for future research.

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Chapter 1 Introduction 1.1

Motivation Analysis of the nature of representation is an essential part of cognitive

science. In order to understand how we think, we must understand how we represent things and, more fundamentally, how it is possible for anything to “represent” anything else. Most psychological theorizing takes the idioms of representation (belief, desire, etc.) for granted and merely attempts to relate sets of mental states to behaviors. For the most part, psychology has not taken upon itself the task of analyzing what thought itself is. Cognitive science has brought the resources of many diverse fields to bear on the problem of understanding thought, but most of the central work in cognitive science is no better grounded than that in traditional psychology. Many computer models, including connectionist models, take some (often inchoate if not incoherent) notion of “representation” for granted and run with it. Only the discipline of philosophy has taken responsibility for grappling with the difficult issue of how representation is possible at all. For most of this century, the dominant trend in Anglo-American analytic philosophy (the only sort of philosophy that one usually finds associated with cognitive science) has been toward a linguistic analysis of representation. This trend is the origin of Jerry Fodor’s Language of Thought hypothesis (Fodor 1975), the theory that thoughts are “sentences in the head”.

1

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The Language of Thought hypothesis is an appealing theory for researchers in the field that has come to be known as “Good Old-Fashioned Artificial Intelligence” (GOFAI). It is but a short step from postulating that thoughts are sentences in the head to postulating that sentences in the head are symbols manipulated by rule-governed processes (i.e., computer programs). Whence comes the mantra of the last thirty years: thinking is computing. There are, however, some gaps in this explanation, some of which have been made prominent by research in cognitive science. Perhaps most important is the fact that there has never been a satisfactory analysis of representation in computation. Hence, the “thinking is computing” theory only drives the problem down a level. It substitutes the problem of analyzing representation in computers for the problem of analyzing representation in human beings. One problem with the “thinking is computing” theory that has been elicited by cognitive science is the remarkable continuity in cognitive abilities between non-linguistic species and human beings. A second problem is the empirical inadequacy of GOFAI models in their handling of exceptions, especially in reproducing the error patterns and robustness in the face of damage that are characteristic of biological cognizers. A third problem that cognitive science, especially neuroscience, has raised for the “thinking is computing” theory is that it is not biologically plausible: real brains are simply not built like von Neumann machines.

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A final problem with the “thinking is computing” theory is the lack of an adequate analysis of language. While the disciplines of logic and linguistics have done an admirable job of separating linguistic constructions into categories (such as logical connectives, quantifiers, singular terms, and predicates) that perform different functions, the most fundamental functions (reference and predication) have never been adequately explained. This dissertation was motivated by these problems with the dominant “thinking is computing” explanation of representation. The goal of the dissertation is to provide an alternative theory of representation that is both better grounded on its own terms and also more adequate to the task of grounding empirical research in cognitive science. Instead of grounding representation in linguistic abilities, the theory grounds representation in spatial abilities, and explains linguistic abilities in terms of these spatial abilities. 1.2

Related Work Although the early part of the dissertation discusses related philosophical

work in some depth, it would be impossible to adequately treat all of the related philosophical work, let alone all of the related work from other disciplines, in a work of any length. In this section, I merely mention some of the related research that this dissertation does not treat in depth, especially that from fields other than philosophy. My argument depends on claims about certain alleged features of perception (e.g., object identification) and spatial representation (especially

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spatial frames of reference) that have been investigated in great detail by psychophysicists and neurophysiologists. To begin with, developmental studies show that perception of unified, permanent objects does not develop until at least several months after birth (Bower 1967; Bower 1982; Baillargeon 1987b; Baillargeon 1987a; Baillargeon and Graber 1987; Kestenbaum, Termine et al. 1987; Baillargeon, Graber et al. 1990), although infants can apparently recognize objects and other features of the world earlier than that. For example, infants recognize sounds (Clifton, Perris et al. 1991) and shapes (Schwartz and Day 1979; Streri 1987) extremely early in development and apparently recognize facial gestures immediately after birth (Meltzoff and Moore 1983; Meltzoff and Moore 1989; Meltzoff and Moore 1992). Moreover, it is clear that object identification is dependent on prior perception of form, depth, orientation, motion, and color (Novick and Arnold 1988; Shepherd 1988; Gray, König et al. 1989; Bradley, Daroff et al. 1991; Kandel, Schwartz et al. 1991; Braddick 1993). The consideration of Strawson’s arguments in Chapter 4 and Chapter 5 of this dissertation lead to the claim that particular identification (reference) must be based on material body identification. In order to identify material bodies, we must be able to represent spatial relations in an absolute way (i.e., from an allocentric frame of reference, or by a “cognitive map”). The literature on the subject of development of spatial representation is enormous (e.g. Eliot and Salkind 1975; Siegel and White 1975; Bremner 1978a; Bremner 1978b; Hazen, Lockman et al. 1978; Pick and Lockman 1981; Cohen 1982; Pick and Lockman

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1982; Cohen 1985; Wellman 1985; Willatts 1985; Birns 1986; Kellman, Spelke et al. 1986; Ellen and Thinus-Blanc 1987; Kestenbaum, Termine et al. 1987; Pick, Montello et al. 1988; Spelke 1988; Stiles-Davis, Kritchevsky et al. 1988; Liben and Downs 1989; Streri and Spelke 1989; Craton, Elicker et al. 1990; Slater, Morison et al. 1990; Hatwell and Sayettat 1991; Denney, Dew et al. 1992; Schumannhengsteler 1992; Atkinson 1993; Hoben and Lohaus 1993; Liben and Downs 1993; Pick 1993; O'Keefe 1994). John O’Keefe’s data on the hippocampus as a cognitive map is also clearly relevant (O'Keefe and Dostrovsky 1971; O'Keefe, Nadel et al. 1975; O'Keefe 1976; O'Keefe and Nadel 1978; Nadel 1979; O'Keefe 1979; O'Keefe 1983; O'Keefe 1989; O'Keefe 1990; O'Keefe 1991; O'Keefe 1993; O'Keefe 1994). O’Keefe’s hypothesis has also been investigated by others, not only in rats (Morris, Hagan et al. 1986; Rasmussen, Barnes et al. 1989; Muller, Kubie et al. 1991), but also, for example, in monkeys (Feignebaum and Rolls 1991). Also relevant are computational models such as those described by McNaughton (McNaughton 1989; McNaughton, Chen et al. 1991). Moreover, the hippocampus is not the only locus of allocentric information. The parietal lobes have also been implicated in the cognitive mapping function by various rat studies (DiMattia and Kesner 1988). In fact, some experiments suggest that there is no single uniform kind of cognitive map, but there are several, serving different functions (Sholl 1987). One possibility is that hippocampal areas are primarily responsible for the relational aspects of

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allocentric representations, whereas parietal areas are responsible for handling metric (distance and angle) information (Poucet 1993). While allocentric representation of space is necessary for objectivity, egocentric representation of space is necessary for allocentric representation. If we use an allocentric frame of reference or a cognitive map, we must somehow place ourselves in it (Lieblich 1982; Campbell 1994). Some of the developmental literature, which suggests that allocentric representations of spatial relations arise only after the infant has progressed through several stages of egocentric representation, also supports the claim that egocentricity is necessary for allocentricity (Pick 1993). Likewise, Bruno Poucet’s hierarchy of animal cognitive maps suggests that allocentric mapping abilities are built on egocentric ones (Poucet 1993). It appears that different and independent brain structures mediate spatial representations from the two different frames of reference. Many studies show that hippocampal and parietal areas are primarily responsible for cognitive maps (allocentric representations). Many rat lesion studies provide evidence that the caudate nucleus is responsible for egocentric abilities. Lesions of medial prefrontal cortex, or dorsal caudate nucleus, result in egocentric spatial deficits, whereas lesions of posterior parietal cortex result in severe deficits of allocentric processing in behavior, learning, and memory (Cook and Kesner 1988; Colombo, Davis et al. 1989; Kesner, Farnsworth et al. 1989; King and Corwin 1992). Studies in monkeys also suggest that egocentric and allocentric spatial orientation

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are dissociable and related to frontal and parietal mechanisms, respectively (Pohl 1973). These data strongly suggest a double dissociation of function between medial prefrontal cortex and parietal cortex in terms of coding of egocentric versus allocentric spatial information. The data are not limited to lesion studies. The functions of allocentric and egocentric representation are so independent that, at least in rats, disruptions in non-lesioned animals can occur in egocentric representations without affecting allocentric representations. For example, experiments have shown that amphetamine-induced disruptions of rotational tendency in rats disrupt learning of an egocentric task (delayed spatial alternation in a water T-maze), but not of an allocentric task (Morris water maze) (Crowne, Tokrud et al. 1992). This is not to say that the data are unequivocal. For example, the experiments suggesting that lesions of the dorsal caudate nucleus result in behavioral deficits restricted to egocentric tasks have come under question (Colombo, Davis et al. 1989). Likewise, the view that egocentric and allocentric spatial orientation abilities are related to frontal and parietal mechanisms respectively has been questioned (Kolb, Sutherland et al. 1983). Christopher Peacocke asserts that we represent nonconceptual contents in terms of spatial relations, and spatial relations in terms of the possible movements of our bodies (Peacocke 1989). Hence, an awareness of body position and the possibility of its movement is necessary for the representation of spatial relations. Alfred Politz traces the argument that the origin and development of space

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perception is to be found in the combination of kinesthesia and the sensation of touch (i.e. that space is perceived originally through bodily awareness and touch) to Berkeley (Politz 1979). John Drummond likewise traces the argument through Husserl back to Berkeley (Drummond 1979). Perhaps unsurprisingly, the phenomenologists have been here too. Merleau-Ponty, writing in the tradition of Husserl, discusses his interpretation of brain-damaged patients as follows: These elucidations enable us clearly to understand motility as basic intentionality. Consciousness is in the first place not a matter of ‘I think that’but of ‘I can’… .Movement is not thought about movement, and bodily space is not space thought of or represented… .In the action of the hand which is raised towards an object is contained a reference to the object, not as an object represented, but as that highly specific thing towards which we project ourselves, near which we are, in anticipation, and which we haunt (Merleau-Ponty 1962, pp. 137-8). In this passage, Merleau-Ponty clearly links bodily awareness, spatial representation, and objectivity. The connection between body and spatiality is even clearer in his subsequent discussion: In so far as I have a body through which I act in the world, space and time are not, for me, a collection of adjacent points nor are they a limitless number of relations synthesized by my consciousness, and into which it draws my body. I am not in space and time, nor do I conceive space and time; I belong to them, my body combines with them and includes them (Merleau-Ponty 1962, p. 140).

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Here, Merleau-Ponty asserts the necessary connection between bodily awareness and spatiality. Two pages later, he in fact uses the word “necessary” in characterizing their relation: Even if subsequently, thought and the perception of space are freed from motility and spatial being, for us to be able to conceive space, it is in the first place necessary that we should have been thrust into it by our body, and that it should have provided us with the first model of those transpositions, equivalents and identifications which make space into an objective system and allow our experience to be one of objects, opening out on an ‘in itself’ (Merleau-Ponty 1962, p. 142). Of course, Merleau-Ponty is not the only phenomenologist to discuss the notion of bodily awareness and its relation to egocentric frames of reference; he is merely the best known. Moss (1989) contains review of phenomenological work on this question. Gareth Evans is perhaps the clearest on this point. The egocentric frame of reference that Evans insists is necessary for having an objective model of the world gets its meaning from the subject’s awareness of his own body: we might specify the spatial information which we imagine [a] perception to embody… in egocentric terms… . These terms specify the position of the sound in relation to the observer’s own body; and they derive their meaning in part from their complicated connections with the subject’s actions (Evans 1982, p. 155). Evans also alludes to Charles Taylor’s arguments about the relation between egocentric representation and bodily awareness (Taylor 1964; Taylor 1970).

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John Campbell has criticized this view of things. For example, in characterizing just exactly what an egocentric frame of reference is, Campbell writes: The obvious proposal is that the subject has to be using direct, nonobservational knowledge of his own body constituted by his possession of a body image… . This proposal relies on a direct relation between the subject’s body image and his ability to act, the possibilities of movement open to him (Campbell 1994, pp. 10-11). This is precisely Evans’proposal. But the problem with this, as Campbell notes, is that we have to wonder how the body image is directly connected with action. And when we ponder that, we may become involved in a regress, “For how are the spatial relations between the parts of the body given in the body image?” (Campbell 1994, p. 12). If they are given egocentrically, then we have made no progress in explaining what egocentricity is. On the other hand, if they are given nonegocentrically, then the body image does not explain egocentricity itself (Campbell 1994, p. 12). Indeed, Campbell believes that a representation of the body is not a necessary feature of experience: while some egocentric reference frame is evidently essential if we are to have spatial action— otherwise the action could not be regarded as spatial at all— it does not seem that a subject needs to have a body image to be capable of egocentric spatial action, action we would want to explain by appealing to his possession of an egocentric frame of reference. Coordination and direction of spatial action may be achieved by purely distal specifications of the locations that are the endpoints of the actions, without the subject’s having a single central body image at all (Campbell 1994, p. 13).

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Campbell himself defines the egocentric frame of reference in terms of a diverse set of axes, including but not limited to the axes of the body (Campbell 1993; Campbell 1994). Basic data on sensorimotor integration (Shepherd 1988; Wolfe 1988; Vanden Abeele, Delreux et al. 1993) and kinesthesia (Goodwin, McCloskey et al. 1972; Roland 1987; Roland and Mortensen 1987; Gandevia, McCloskey et al. 1992) are relevant to this topic, as are the basic neuro-psychology, -physiology and -biology of bodily awareness, in adults (Moss 1989; Tiemersma 1989; Joseph 1990), as well as in children (Novick and Arnold 1988). As with “spatial orientation”, it is important to distinguish among the many meanings of “bodily awareness”. For example, there is a notion of “body image”, also sometimes called “body cathexis” that refers to a person’s impression of his or her own body as it is related to self-esteem or libido. This sense of bodily awareness is clearly only peripherally relevant (at best) to my project. In the psychological literature, the more relevant notion is usually referred to as “body schema”. However, it is important to recognize that psychology distinguishes many subtypes of body schema. To begin with, there is a distinction between postural awareness (knowledge of the spatial arrangement of the parts of the body), awareness of passive movement, awareness of active movement, awareness of resistance to movement, and surface schema (a model of stimuli impinging at the body’s surface) (Clapp 1972; Matthews 1982; Olson and Hanson 1990). Moreover, we should distinguish between body schema, which is

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the unconscious presentation of the body in perception, and body image or body experience, which is a conscious image or representation that encompasses psychological and situational factors (Gallagher 1986). There may also be other components to bodily awareness (Clark 1984). In fact, some have even questioned whether the notion has any theoretically meaningful content given the diversity of its mechanisms and presentations (Poeck and Orgass 1971). There are a number of recognized disorders of the body schema, including autotopagnosia, finger agnosia, right-left disorientation, and asomatognosia (misperception of one’s own body due to neurological disruption) (Benton and Sivan 1993). Finger agnosia (inability to perceive a stimulus applied to the fingers) does not appear to interfere with everyday functioning (Della Sala and Spinnler 1994), suggesting that complete bodily awareness is not necessary for spatial representation. Another form of body schema disturbance that is relevant is anosognosia for hemiplegia (unawareness of or failure to acknowledge partial paralysis) (Green and Hamilton 1976; Bisiach, Vallar et al. 1986; Bisiach and Geminiani 1991; Heilman 1991; Levine, Calvanio et al. 1991; Prigatano and Schacter 1991; Gibson 1992; Gilmore, Heilman et al. 1992). Some basic data on unilateral spatial neglect are presented in Bisiach’s work (Bisiach, Luzzatti et al. 1979; Bisiach and Vallar 1988; Bisiach 1993). Some of the data on neglect suggest that bodily awareness may be necessary for spatial representation. For example, it has been found that contralesional limb

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movements reduce visual neglect in some patients, and this finding has suggested the hypothesis that this may because the limb movements activate a poorly attended body schema which in turn focuses attention on otherwise poorly attended areas of extrapersonal space (Robertson and North 1993). Asomatognosia is also an interesting disorder. Fogel discusses three cases (Fogel 1976), each case involving a patient who does not believe that a certain part of the body belongs to her. It is particularly interesting that many disturbances of body schema can result from damage to the parietal lobes. Anosognosia for hemiplegia appears usually to result from damage to the right parietal lobe (Hier, Mondlock et al. 1983). Finger agnosia can also result from parietal lobe lesions (Erwin and Rosenbaum 1979). And a final manifestation of hemiasomatognosia, Gerstmann’s syndrome (which is characterized by simultaneous finger agnosia, agraphia, confusion of laterality of body, and acalculia) is associated with damage to the posterior portion of the dominant parietal lobe (Wilkins and Brody 1971; Varney 1984; Moore, Saver et al. 1991). As discussed previously, the parietal lobe has been implicated in spatial representation by lesion studies, so its role in body schema disorders suggests that, at least on gross morphological grounds, body schema and spatial representation are interdependent. Likewise, patients with agenesis of the corpus callosum (a congenital malformation of midline structures in the brain that is sometimes regarded as a natural model of the “split brain” phenomenon) demonstrate deficits in both spatial orientation and transfer of kinesthetic

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learning, in particular an inability to identify the locus of a tactile stimulus (Ferris and Dorsen 1975; Reynolds and Jeeves 1977; Field, Ashton et al. 1978; Chiarello 1980; Meerwaldt 1983; Milner 1983; Jeeves 1990; Gordon, Forssberg et al. 1994; Lassonde and Jeeves 1994). These results suggest that spatial representation and bodily awareness are interdependent in some brain areas. Developmental data is also pertinent. For example, it has been hypothesized that the best explanation for the decline and recovery of infants’ reaching for noise-making objects in darkness involves changes in the body schema (Wishart, Bower et al. 1978). If true, this is evidence that spatial behavior is dependent on bodily awareness. Likewise, magnitude of underestimation of arm length decreases with age (Schlater, Baker et al. 1974), which might suggest that the increase in accuracy is at least partially responsible for the corresponding increase in accuracy of spatial behavior. Some psychologists have followed philosophers in explicitly arguing that development of body schema precedes and is essential to the development of spatial orientation (Weinstein 1967), in particular because learning develops unevenly in the absence of kinesthesia and inconsistent, bizarre behavior may result from inadequate kinesthetic perception (Swartz 1978). Some evidence shows that Gerstmann’s syndrome in its “pure” form results from lesions of the left angular and supramarginal gyri, not the parietal lobe (Benton 1977; Mazzoni, Pardossi et al. 1990; Benton 1992). There has been a great deal of discussion in philosophy and psychology about whether vision is necessary for objectivity. In the debate over what is

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usually referred to as Molyneaux’s question, vision has often been privileged over touch and other senses in terms of its necessity for a subject’s having an objective model of the world. Starting with Berkeley (Berkeley 1965), some have even gone so far as to assert that the congenitally blind do not have a notion of space, and so cannot have a notion of objectivity. There is a related question that is also relevant here: whether having the sense of touch is necessary for having a notion of space, and so for having an objective model of the world. In particular, Brian O’Shaughnessy has argued precisely that a sense of touch is necessary for bodily awareness. He writes, for example, “a body-sense-acquired knowledge of the body’s spatial properties sufficient to make possible informed intentional bodily deeds… alone guarantees a sense of touch” (O'Shaughnessy 1989, p. 40). O’Shaughnessy’s argument actually has two parts, each developed from a priori considerations. The first premise is that body-sense is dependent on long-term body image (O'Shaughnessy 1989, p. 55). The second premise is that long-term body image is dependent on tactile sense (O'Shaughnessy 1989, p. 56). So, the argument goes, if body-sense is dependent on body image, and body image is dependent on tactile sense, then body-sense is dependent on tactile sense. Some basic texts and papers on the sense of touch (Loomis and Lederman 1986), and the development of the sense of touch and its relation to bodily awareness (Koblenzer 1987) are relevant. Also, a number of psychophysical studies have explored the relation between haptic perception and spatial

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representation (Wohlwill 1975), or between haptic representation and bodily- or self-awareness (Lee 1993). Errors and illusions in motor-sensory perception would seem to be relevant here (Singh 1990). In particular, it is interesting that people can perceive various things “by touch” even through instruments like scalpels or rods (Solomon and Turvey 1988). Moreover, when a given length is haptically traced, the direction of hand movements, relative to the body, influences the length perceived (Marchetti and Lederman 1983). Loss of cutaneous sensation is a common complaint associated with many nervous system diseases and peripheral nerve injuries (Sekuler, Nash et al. 1973), among them peripheral neuropathy. However, patients who have lost their sense of touch do not appear to have trouble with bodily awareness, spatial representation, or objectivity. This is true even for congenital cases of neuropathy (Rapoport 1969). Patients who have kinesthetic deficiencies due to spina bifida nevertheless apparently develop full body images (Robinson, Lippold et al. 1986). A basic text on peripheral nerve diseases is (Bradley, Daroff et al. 1991). Data in favor of the argument that touch is a necessary part of bodily awareness and spatial representation include the finding that tactile stimulation influences subjects’perceptions of verticality while supported in a tilting apparatus (Nyborg 1971), and findings about errors in localization of concealed body parts that suggest that both central and peripheral variables contribute to the localization of the limb in space (Gross, Webb et al. 1974).

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The necessity of touch raises a further question: in order for a cognitive system to have a sense of touch, is it necessary that it have a body that extends in space beyond the limits of its central processor? A great deal of our current understanding of sensation and perception in general, and touch in particular, can be traced back to Aristotle. In De Anima, Aristotle distinguishes special objects for each of the five senses, objects that can only be perceived by a particular sense. For sight, the special object is color, for hearing sound, and for taste flavor. Aristotle finds that he cannot distinguish a special object for the sense of touch: “what the one thing is which is the subject for touch as sound is for hearing is not clear” (Aristotle 1987, Book II, Chapter 11, p. 183). He considers the possibility that the sense of touch acts “by contact, while the other senses act from a distance” (Aristotle 1987, Book II, Chapter 11, p. 184), as if sensations of touch were somehow unmediated, direct perceptions of objects: “as things are we suppose that we touch the objects themselves and that nothing is through a medium” (Aristotle 1987, Book II, Chapter 11, p. 184). Aristotle rightly rejects this suggestion on the grounds that all of our perceptions, including touch, do occur through a medium. For the sense of touch, the medium is the flesh, which, although it contains the organs of our sense of touch, is not identical with them (Aristotle 1987, Book II, Chapter 11, p. 185). The attempt to associate embodiment with touch did not end with Aristotle. According to Michael Ayers (1991), Descartes offered a reductive explanation of the representative function of perceptual ideas – they must be

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mechanical occurrences systematically caused by perceived objects. There need not be any resemblance between the object and its ‘image’ beyond this systematic correspondence. This has the (intended) effect of expelling intrinsic intentionality from the body and restricting it to the mind. But it also has the (perhapsunintended) effect of making the body necessary for perception. Another relevant text is Armstrong’s Bodily Sensations (1962), but the main text on this subject is again O’Shaughnessy’s. He argues that the sense of touch “is scarcely to be distinguished from the having of a body that can act in physical space” (O'Shaughnessy 1989, p. 38). Much of the developmental data supports this claim. Many developmental psychologists argue that particular motor achievements are integral to developments in the domain of haptic perception (e.g., Bushnell and Boudreau 1993). Another argument from experimental data for the dependence of touch on embodiment is from the fact that various features of the material world influence our sense of touch. For example, it has been demonstrated that cold objects feel much heavier than neutral temperature objects (Stevens 1979), and that pregnancy increases sensitivity to touch (Ruggieri, Milizia et al. 1979). On the other hand, documented cases of amputees with phantom-limb syndrome have demonstrated that patients can feel things in areas to which their bodies do not extend (Katz 1992a; Katz 1992b; Ramachandran, Stewart et al. 1992; Halligan, Marshall et al. 1993a; Halligan, Marshall et al. 1993b; Katz 1993a; Katz 1993b; Katz 1993c). The phenomenon has even been verified in

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patients with congenitally missing limbs (Scatena 1990). These findings may support the contention that embodiment is not necessary for the sense of touch. However, in all of the cases I know of, phantom limb syndrome involves the mistaken localization of touch at one area of the body to an area of the body that does not exist. Thus, it is not clear that phantom limb shows that a body is not necessary for a sense of touch, only that it is not necessary to have a body that extends to the location that seems to be touched. 1.3

Overview of the Dissertation Since Kant, it has been widely accepted that spatial representation plays a

fundamental role in constituting thought. However, exactly what that role is has remained unclear. Recent developments at the intersection of philosophy, psychology, neuroscience and computer science enable us to rigorously specify the role of spatial representation in thought. The thesis of this dissertation is that spatial representation is the fundamental constituent of thought in two ways. First, material objects by their nature (no two physical objects of the same type can be in the same place at the same time) allow human beings to literally “grasp” objects. Grasping a physical object is the fundamental mode of reference. By generalization, we can refer to objects that are distant, both temporally and spatially – the unique location of an object in space-time can be used to identify and re-identify it. Reference to abstract objects is a metaphorical extension of this fundamental mode of reference. Second, the fundamental constituents of concepts are the relative

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positions of representations of the environment in abstract (logical) spaces of arbitrary dimensions determined by the activations of neurons. The first part of the dissertation (Chapter 2 and Chapter 3) situates this research in its philosophical context. Chapter 2 makes the case that a number of important philosophical problems (the mind/body problem, the dispute between materialism and idealism, the problem of knowledge of the external world, and the problem of explaining normativity) could be resolved by an adequate theory of representation. Chapter 3 then considers the history of theories of representation, from the earliest pre-Socratic Greeks through the present day, paying special attention to Kant’s thesis that spatial representation is the fundamental form of representation. The second part of the dissertation (Chapter 4 and Chapter 5) considers in detail Strawson’s arguments, which draw on Kant’s, for the priority of spatial representation. Chapter 4 is concerned primarily with Strawson’s own arguments in Individuals and The Bounds of Sense that spatial representation is fundamental. Chapter 5 considers some of the major critics of Strawson’s work. Together, the two chapters establish that Strawson’s argument is ambiguous. On one interpretation, it establishes the necessity of the representation of material objects in physical space. On the other, it establishes the necessity of an abstract, “mathematical” space in which to locate objects. Chapter 5 concludes with an argument that both interpretations are valid and that Strawson has unwittingly provided us with two sound arguments.

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The final part of the dissertation (Chapter 6) explores representational space in detail. In particular, it addresses the argument from Jerry Fodor and Ernest Lepore that no account of semantics based on activation state spaces can provide a criterion for the identity of content. In addition to presenting a robust and well-defined criterion for the similarity of content between state spaces, Chapter 6 presents the results of empirical investigations with artificial neural networks showing that networks that are architecturally different or have different kinds of sensory receptors can represent the world in similar ways as long as they speak the same “language”. Finally, Chapter 7 contains a summary of the dissertation and some suggestions for further research.

Chapter 2 Philosophical Context 2.1

Abstract In this chapter, I make the case that four important philosophical problems

are really one problem, in the sense that a solution to any one of them entails solutions to the others. The first is the mind/body problem, the question of the relationship between the mind and the body. The second is the dispute between materialism and idealism, the question of whether matter or thought is more fundamental. The third is the problem of knowledge of the external world, the question of how it is possible for us to have knowledge of anything other than our own thoughts. The fourth is the problem of explaining normativity, the question of how notions of right and wrong relate to the physical world. I argue that these four problems are so intimately related that distinctions between them are not merely artificial but actually pernicious. By hiding the essential connections between these problems, the division of philosophy into separate fields has prevented progress on them. I argue that the problem I address in subsequent chapters (giving a general account of the meaning of mental states that is compatible with physicalism) is at the root of all of these problems. I also briefly discuss physicalism, a constraint I will for the most part take for granted in subsequent chapters. Finally, I sketch an outline of the solution that I propose.

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2.2

The Mind/Body Problem and Intentionality Descartes thought that the mind and the body were different kinds of

substances and raised the problem of how two utterly different substances could interact – how was it possible for the mind to control the body? The idea that mind and body are different substances has gone out of fashion, and rightly so. Still, the mind/body problem continues to haunt us. One more modern way of raising the problem is as the problem of “intentionality”, the problem of how our thoughts can be about things. In the following, I explain this problem and show how it raises the mind/body problem in a more compelling way than does Descartes’substance dualism. Most of our thoughts and experiences are about things. Franz Brentano argued that this “aboutness” or “intentionality” was the characteristic mark of the mental. Every mental state, Brentano argued, is characterized by the “inexistence of an object” or “intentional inexistence” (Brentano 1874/1995, Volume I, Book II, Chap. 1). The phrase means two things. Brentano sometimes uses it to mean what we would today call the content of a “propositional attitude”. The term “propositional attitude” is philosophical jargon for a mental attitude (e.g., thinking, believing, doubting, expecting) toward a proposition, or declarative statement (e.g., that the sky is blue or that the sun will rise tomorrow). In the first sense of “intentional inexistence”, the proposition is the “object” of the attitude; we have an attitude toward or about a proposition. In this first sense, the phrase

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“intentional inexistence” refers to the existence of the object (the proposition, i.e., the content) in the thought. However, Brentano also sometimes uses the phrase “intentional inexistence” to talk about the object, or referent, of thought, i.e., the thing the thought is about. This usage can be confusing to non-philosophers, because when “object” is used in this way, the “object” of a thought is usually the subject of the sentence that expresses it. For example Bill Clinton is the object of the thought (note: not the sentence) The current President of the United States is Bill Clinton. Likewise, the present King of France is the object of the thought (again, not the sentence) The present King of France is bald. In this second sense, the phrase “intentional inexistence” refers to the fact that the object of a thought need not exist, as indeed the present King of France does not exist. Brentano argued that intentional inexistence (in both senses) was a “characteristic exclusively of mental phenomena” and that “no physical phenomenon exhibits anything like it” (p. 89). When we talk about physical phenomena, we do not take attitudes toward propositional objects; we merely use declarative sentences. We do not say things like “I think that the sky is blue”. Instead, we say things like “the sky is blue”. Similarly, no true statement about physical phenomena is about something that does not exist. We can assert that water is made of hydrogen and oxygen. We cannot, however, assert that ether is the medium in which light travels without making an error, something which arises from the mind and not from the world.

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Brentano fails to distinguish adequately between the two sense of the phrase. He also has a somewhat bizarre (to my ear, at least) interpretation of “inexistence”, based on the scholastic notion, inherited from Aristotle, that the form of the object of a thought actually inheres in the thinker, whatever that might mean. Nevertheless, Brentano’s view has continued to exert an influence on analytic philosophy of mind through the present day, largely because of Roderick Chisholm’s reinterpretation and defense. By severing Brentano’s view from its scholastic roots, restating it in modern terms, and giving clear criteria for its application, Chisholm made Brentano’s problem relevant to contemporary AngloAmerican analytic philosophers. Chisholm’s explication (or reconstruction) of Brentano’s point in terms of properties of statements about mental states rather than the states themselves makes the phenomenon of “intentional inexistence” more appealing to the modern ear. On Chisholm’s reconstruction of the view, intentional inexistence applies properly, not to psychological states themselves, but rather to the propositional attitudes we use to talk about psychological states. The objects (referents) of these attitudes needn’t exist, even where the attitudes are correctly ascribed (true). For example, it is possible for someone to believe that the present King of France is bald even though there is no present King of France. On the other hand, the objects of physical statements must exist for the statements themselves to be true. For example, the statement “The earth is 93 million miles from the sun” can be true only if the earth exists.

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Chisholm described two tests one could use to distinguish intentional statements from physical statements. The first, substitutivity salva veritate, is: a statement is non-intentional only if substitutions of co-referring singular terms into a true statement always preserve its truth. For example, let us suppose that “John believes that the earth 93 million miles from the sun” is true. Nevertheless, the statement “John believes that the third planet from the sun is 93 million miles from the sun” may be false even though “the earth” and “the third planet from the sun” are co-referential (i.e., even though the earth is the third planet from the sun). This could be the case because John doesn’t know that the earth is the third planet from the sun. On the other hand, if the statements “The earth is 93 million miles from the sun” and “The earth is the third planet from the sun” are true, then so is the statement “The third planet from the sun is 93 million miles from the sun”. Physical statements pass the test of substitutivity salva veritate; intentional statements do not. The second test Chisholm described for distinguishing intentional statements from physical statements is truth-preservation in existential generalization: a statement is non-intentional only if existential generalizations from it always preserve truth-value. For example, the statement “John believes that unicorns have one horn” may be true even though the statement “John believes that unicorns exist” is false, perhaps because John does not believe that unicorns exist but believes that if they existed, then they would have one horn. On the other hand, if it is true that unicorns have one horn, then it must be true that

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unicorns exist. Physical statements pass the test of existential generalization; intentional statements do not. Hence, Chisholm’s reinterpretation of Brentano’s thesis provided a clear criterion for intentionality, in contrast to Brentano’s rather vague characterization in terms of intentional inexistence. Intentional statements are those that fail the tests, non-intentional statements are those that pass. On Chisholm’s reconstruction, intentional states are those that are (properly) described by intentional statements, and non-intentional states are those that are not. Given Chisholm’s reconstruction, Brentano’s thesis becomes: all and only mental states are intentional states, and all and only physical states are non-intentional states. It is well known, however, that the latter statement is false. Modal statements, for example, fail the tests but do not describe mental states. For example, the statement “Necessarily, 9 is greater than 7” is true but the statement “Necessarily, the number of planets is greater than 7” is false, even though the number if planets is 9. (It is possible that there might have been more or less than 9 planets, for example if the conditions that created the solar system had been slightly different.) Conversely, the tests do not even apparently apply to descriptions of some mental states. For example, pain is presumably a mental state, but the test of substitutivity does not even apply to the statement “John is in pain” or even “John feels a pain”, and both statements would seem to pass the test of existential generalization (if “John feels a pain” is true, then there is a pain that John feels).

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Despite these counterexamples, it is clear that Chisholm was on to something. It may not be that all and only mental states are properly described by intentional statements. Nevertheless, most mental states are described by intentional statements, and most intentional statements describe mental states. Moreover, even those intentional statements that do not describe mental states do not thereby describe physical states; modal statements, for example, are sui generis: they neither describe mental states (at least as they are usually conceived) nor physical states (again, at least as they are usually conceived). If we restrict ourselves to the propositional attitudes (i.e., statements of the form “X thinks that… ”, “X wishes that… ”, “X desires that… ”, “X hopes that… ”, “X fears that… ”, etc.), it is clear enough that these statements are statements about mental states and that they are intentional statements. So, even if not all statements about mental states are intentional statements, all propositional-attitude statements are intentional statements. (Hence, propositional-attitude statements have also come to be called “intentional-attitude statements”). We will do best to leave the exceptions to the side for now; the differences between intentional statements and non-intentional statements are sufficient to state the problem. The problem is that there doesn’t seem to be any way to bridge the gap between intentional statements and non-intentional statements. In the interests of parsimony, we would like to think that there is really only one kind of explanation, something akin to physical explanation, and that the explanation of our mental lives should be expressible in the language of that type of explanation.

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(I realize that I am here running the risk of appearing to be a regressive positivist, asserting the unity of science without argument and flying in the face of recent arguments by, e.g., Dupre, that science isn’t, and in fact needn’t be, a unified whole. Properly discussing this view would take a book of its own, so suffice it to say here that unification is a proper desiderata; the incommensurabilities between certain present-day scientific theories are inadequacies with those theories, inadequacies which I believe will be resolved by future developments in the special sciences.) It seems that whenever we try to give an interpretation of an intentional statement in non-intentional terms, we wind up leaving something out. Chisholm attacked behaviorism on precisely these grounds: any behavioristic interpretation of a statement like “Jones hopes to meet his mother at the train station,” he showed, winds up sooner or later falling afoul of our intuitions about the sorts of circumstances that would satisfy Jones. In fact, Ryle, whom Chisholm specifically mentions as a target of his attack, recognizes the problem and uses it to motivate his non-reductive version of behaviorism (the problem with Ryle’s theory, of course, is whether it is ultimately coherent, but this is not the place to go into that issue). Charles Taylor has given similar arguments (Taylor 1964). Donald Davidson uses them to motivate “anomalous monism.” Finally, Dennett takes the dispute up in contemporary terms, arguing that the fundamental concern behind Brentano’s problem is the problem of content — the problem of how mental states relate to their contents (Dennett 1969, Chapter 2, pp. 19-42).

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Hence, one way of describing the problem I address in this dissertation is as the problem of intentionality, or “Brentano’s Problem”. The problem is to explain the intentional properties of the propositional attitudes in a way that is compatible with materialism. 2.3

The Problem of Objectivity Another way of stating the same problem is in terms of objectivity. Foss

usefully distinguishes metaphysical, epistemological and numerical senses of “objectivity” (Foss 1993). Each of the three senses of objectivity may apply both to both things (as in “an objective particular”) and experiences (as in “an objective experience”). The metaphysical sense of objectivity refers to a distinction between that which has experience (a subject of experience) and the things the subject experiences (the objects of experience). “Objectivity” in the metaphysical sense is the ability to distinguish between subject and object. In this metaphysical sense, “objectivity” is the independence of the existence of things in the world, states of the world, and transitions among those states from the existence of our experiences of or thoughts about those things, states, and transitions. Objective things exist independently of the existence of any experience of them, whereas subjective things do not exist independently of the existence of any experience of them (dreams are perhaps an example). Correspondingly, objective experiences are experiences of things that exist independently of experience, whereas subjective experiences are not experiences of independently-existing things.

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By contrast, the epistemological sense of objectivity describes a distinction between that which is true or accurate (the objective) and that which is false or misleading (the subjective). “Objectivity” in the epistemological sense is accuracy. The epistemological component of objectivity is the possibility of our being either correct or incorrect (or more or less correct) about the properties of things, states, and transitions. Epistemologically speaking, objective things may be the subjects of judgements that can be evaluated in terms of correctness, whereas subjective things cannot be the subjects of judgements that can be evaluated in terms of correctness. Correspondingly, objective experiences are judgements, or thoughts, whereas subjective experiences are mere experiences, not judgements. In this sense, “objective” experience allows for the possibility of error. Some of our experiences are veridical, in that they correctly portray the external world, whereas others are not. Our experiences answer to a higher power: the external world. Finally, the numerical sense of objectivity refers to a distinction between that which is publicly accessible (the objective) and that which is only privately accessible (the subjective). Objectivity in the numerical sense is the possibility of access by more than one person. Numerically speaking, objective things may be experienced by more than one person, whereas subjective things can only be experienced by a single person. Correspondingly, objective experiences are public but subjective experiences are private. Strawson writes, for example, that “another name for the objective is the public” (Strawson 1966, p. 151). Despite some

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arguments to the contrary, which I shall address below, the three senses of objectivity correspond. Objective things exist independently of any experience of them, are possible subjects of judgments that may be correct or incorrect, and may be experienced by more than one person. Subjective things, by contrast, do not exist independently of experiences of them, are not possible subjects of judgments, and may only be experienced by a single person. Objective experiences exist independently of the things they are experiences of, are judgements and therefore may be evaluated in terms of correctness, and may be shared by more than one person. Subjective experiences, by contrast, do not exist independently of the things they are experiences of, are not judgements and therefore may not be evaluated in terms of correctness or incorrectness, and cannot be shared by more than one person. This passage from Strawson, for example, uses both the metaphysical and the numerical characteristics of objectivity interchangeably: We think of the world as containing particular things some of which are independent of ourselves; we think of the world’s history as made up of particular episodes in which we may or may not have a part; and we think of these particular things and events as included in the topics of our common discourse, as things about which we can talk to each other… .[O]ur ontology comprises objective particulars (Strawson 1959). The first two clauses use the metaphysical concept of objectivity (objective things and events are independent of experience), while the third clause uses the numerical concept of objectivity (objective things and events may be referred to

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in a public language). However, the sentences refer to the same things. Strawson also equates the metaphysical concept of objectivity with the numerical concept elsewhere, and so do other writers. Foss argues, however, that the numerical distinction is not an instance of the subjective-objective distinction. Foss’s grounds for the claim that the numerical distinction (between the public and the private) is not really a sense of objectivity are the following. (1) That a state available to only one subject is subjective is a necessary but not a sufficient condition of subjectivity in the metaphysical sense. (2) That a state available to many subjects is objective is neither necessary nor sufficient for objectivity in the epistemological sense. A public state may be epistemologically subjective, for example, by being false. And an epistemologically objective state may be available only to god or some unique genius. Foss concludes: “number seems not to be a defining characteristic of the S-O contrast in any sense” (Foss 1993, p. 733). Foss’s arguments, however, beg the question. He shows that the numerical distinction does not correspond to either one of the two subjective-objective distinctions he has identified. Assuming that the epistemological and the metaphysical are the only senses of the subjective-objective distinction, he concludes that the numerical distinction is not a form of the subjective-objective distinction. But it is the claim that the epistemological and the metaphysical are the only senses of the subjective-objective distinction that is in question. I suggest that the fact that the numerical distinction does not correspond to either of Foss’s

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senses of the subjective-objective distinction shows that it is a third sense of that distinction. To return to the main issue: our problem is in a certain sense the problem about the existence of an objective world, specifically, the problem of explaining the relation between our experiences the world that exists independently of them but which simultaneously causes them. Recall our discussion above of the epistemological component of objectivity: in the epistemological sense, the objective-subjective distinction refers to the possibility of our being either correct or incorrect (or more or less correct) about the properties of things, states, and transitions. Objective things may be the subjects of judgements that can be evaluated in terms of correctness, whereas subjective things cannot be the subjects of judgements that can be evaluated in terms of correctness. Correspondingly, objective experiences are judgements, or thoughts, whereas subjective experiences are mere experiences, not judgements. It should be clear that this usage of objectivity marks out a distinction between physical events and certain kinds of mental events. Certain mental events (objective experiences, or, in the language of the previous section, propositional attitudes) allow for the possibility of error. Some of our experiences are veridical, in that they correctly portray the external world, whereas others are not. Again, our experiences answer to a higher power: the external world. By contrast, there is no room for error in the world as understood by the physical sciences. When we imagine a purely physical world, we imagine a world

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in which there is no error: things merely happen. Time passes and states of the world succeed one another. There is no judgement in the physical world, no correct or incorrect, right or wrong, good or bad:

Figure 1

The physical world: a place without error

In the human world, on the other hand, there is room for error. A person may “think” a stick is bent when in fact it is straight. (There are many ways of expressing this: the person may “see” or “represent” the stick as bent, or “take it” to be bent; the stick may “seem” or “look” bent to the person.) Some parts of our world (us, for sure, and perhaps animals and computers) bear special relations to others: representational relations. Crucially, these representational relations have properties nothing in the purely physical world has: properties of being right and wrong (correct and incorrect, error-free or error-full):

Figure 2

The representational world: a place where error is possible

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A person is, among other things, a nexus of causal activities, between those arriving at the sensory transducers and those causing movements and other behaviors by contracting and expanding muscle tissue. Hence, one way of viewing a person is as a strictly physical mechanism: To Motor Transducers

From Sensory Transducers Figure 3

The person as object

However, our social practices (including language) do not make sense except under the supposition that people represent aspects of the external world. Hence, one way of expressing the difference between experience, thought, or representation (on the one hand) and physical events (on the other) is that the former sorts of things allow for the possibility of error, whereas the latter sorts do not. McDowell states the point quite clearly in the Introduction to his book Mind and World:

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To make sense of the idea of a mental state’s or episode’s being directed towards the world, in the way in which, say, a belief or judgement is, we need to put the state or episode in a normative context. A belief or judgement to the effect that things are thus and so— a belief or judgement whose content (as we say) is that things are thus and so— must be a posture or stance that is correctly or incorrectly adopted according to whether or not things are indeed thus and so… .This relation between mind and world is normative, then, in this sense: thinking that aims at judgement, or at the fixation of belief, is answerable to the world— to how things are— for whether or not it is correctly executed (McDowell 1994, pp. xi-xii). Hence, any account of experience must allow for the normativity characteristic of representation. When we ask how thought or experience is possible, we are at the same time asking how error, judgement, or normativity is possible. While force, mass, causation and the rest are all acceptable primitives of the natural sciences, judgement is not. McDowell, paraphrasing Sellars (Sellars 1956/1963), summarizes the dichotomy between nature and reason: “whatever the relations are that constitute the logical space of nature, they are different in kind from the normative relations that constitute the logical space of reasons” (McDowell 1994, p. xv). This position is also taken by Davidson (Davidson 1970/1980). In order to maintain an essentially naturalistic worldview, we must explain how experience, judgement and thought can coexist with, or be incorporated into, the natural order. Sellars, Davidson, and McDowell all attempt to do so in different ways, and in ways that are different from the way I attempt in later chapters. My point here is only that any adequate account of mind must account for the possibility of error.

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It is the very possibility of error, or falsity, that distinguishes experience (thought) from mere physical transition. In fact, the purpose of invoking the language of thought (the intensional idioms of folk psychology: thinking that, believing that, etc.) in describing human behavior is to explain the cases when behavior deviates from what would be expected of an organism perfectly in tune with the world. If there were no distance between thought and world, then there would be no use for thought at all. Austen Clark, following Sellars makes a corresponding point about “qualia”: qualia are introduced in order to describe the looks or appearances of things— those cases where x ‘looks’P even though x is not P1… one describes this by proposing that both situations present one with the same quale (Clark 1985b, p. 380). the concepts of ‘qualia’or ‘qualitative content’are introduced precisely to account for the similarity presented by an x which looks P, (even though it is not), and a y which really is P. What purportedly is common to those two situations is the presentation of the same qualitative content to the observer: the same ‘looking as if it is P’content, which is satisfied in the case of y, but not in the case of x (Clark 1985b, p. 390). Exactly the same may be said of thoughts and, indeed, of the states described by all representational idioms. The purpose of ascribing propositional attitudes to individuals is to describe cases where someone behaves as though Q even though not Q. One describes this situation by proposing that the person “believes that” Q.

1

Here Clark cites Sellars (1956/1963, p. 133).

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If such situations did not exist— if there were no essential distance between thought and world— the idioms of representation would be unnecessary. But it is precisely because a gap can arise between appropriate behavior given the state of the world and actual behavior that introducing the representational idiom is necessary. Hence, the errorfulness of representation is not a mere side effect of some antecedently-existing apparatus: it is the very reason for the apparatus itself. As a consequence, any plausible account of thinking or experience must make sense of the possibility of being wrong. The possibility of error is not incidental to thought; rather, the possibility of error is the essence of thought. In an important sense, explaining the possibility of error — explaining the relation between the physical world and the representational world — is the fundamental problem of philosophy. It is the central concern in every subdiscipline of philosophy. In the philosophy of mind, it is the mind-body problem. In the philosophy of language, it is the problem of reference. In metaphysics, it is the problem of skepticism. And it has dominated the history of philosophy. (I make some attempt to substantiate this claim in Chapter 3.) 2.4

The Problem of Naturalizing Epistemology A third way of describing the problem I address here comes from Quine’s

description of the task of a naturalized epistemology: Given only the evidence of our senses, how do we arrive at our theory of the world?… .Science itself teaches that there is no clairvoyance; that the only information that can reach our sensory surfaces from external objects must be limited to two-

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dimensional optical projections and various impacts of air waves on the eardrums and some gaseous reactions in the nasal passages and a few kindred odds and ends. How, the challenge proceeds, could one hope to find out about that external world from such meager traces? In short, if our science were true, how could we know it? (Quine 1974, p. 2) This question, as Quine is well aware, is not the question the great modern philosophers thought they were interested in when they considered our knowledge of the external world: “they saw their problem as one of challenging or substantiating our knowledge of the external world. Appeal to physical sense organs in the statement of the problem would have seemed circular. The building blocks had to be irreducibly mental, and present to consciousness” (Quine 1974, p. 2). Quine’s new problem is different. Rather than a challenge from outside of physical science, it is a challenge from within. Rather than attempt to derive the truth of science from first principles, we will assume the truth of science and show that it is knowable (“if our science were true, how could we know it?”). In so doing, we have available a whole new set of tools: Clearly, in confronting this challenge, the epistemologist may make free use of all scientific theory. His problem is that of finding ways, in keeping with natural science, whereby the human animal can have projected this same science from the sensory information that could reach him according to this science (Quine 1974, p. 2). He can, in short, use all the tools of science.

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I have said that Quine’s problem is different from the problems the modern philosophers thought themselves to be addressing. Quine agrees with that much, but he believes that his problem is continuous with the problems the moderns were really addressing, whether they were aware of it or not. His epistemology, he writes: is no gratuitous change of subject matter, but an enlightened persistence rather in the original epistemological problem. It is enlightened in recognizing that the skeptical challenge springs from science itself, and that in coping with it we are free to use scientific knowledge (Quine 1974, p. 3). Quine writes this despite his own acknowledgement that the great modern philosophers were interested in justifying our knowledge of the external world, whereas he sees his own problem as explaining the genesis of our knowledge of the external world. What is the connection between these problems? Quine believes the moderns were actually working on his problem (the problem of explaining the genesis of our knowledge of the external world). However, they viewed the problem incorrectly because they were laboring under the misapprehension that it was possible to start from introspective knowledge of sense data alone: The old epistemologists may have thought that their atomistic attitude toward sense data was grounded in introspection, but it was not. It was grounded in their knowledge of the physical world. Berkeley was bent on deriving depth from two-dimensional data for no other reason than the physical fact that the surface of the eye is two-dimensional (Quine 1974, p. 2).

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The project I am engaged in, then, is continuous with, though not identical with, the project of modern philosophy (It is also continuous with the project of philosophy in general, as I shall argue in Chapter 3). It is continuous with the project of the moderns in that it is an attempt not only to explain the genesis of our knowledge of the external world but also to explain the nature of and to justify that knowledge. I do not claim to have solved all of the problems of epistemology. My project is a contribution to epistemology because the project of justifying our knowledge makes sense only in a context in which we can think about (and so have knowledge of) the external world and in which we can be wrong as well as right. Hence, solving the problem of intentionality and the problem of normativity are essential precursors to addressing the central problems of epistemology. As the last sentence should make clear, I do not take myself to be engaged in the same project as Quine sometimes writes as though he is. I do not intend to eliminate normativity; rather, my goal is to explain normativity and intentionality in naturalistic terms. 2.5

Physicalism For most of the rest of the dissertation, I will be taking physicalism for

granted. Hence, I must say something here about what I take physicalism to be, and to entail. Despite Chalmers’recent attempt to resurrect dualism and Dupre’s attempts to argue for a kind of pluralism, I think there are good reasons to believe in monism, not only in the philosophy of mind but in metaphysics in general, and

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to hold out hope for the unity of science. (Adequately justifying these claims is another project, but I have alluded to my arguments for the unity of science above, and I will give the arguments for monism in Chapter 3, in the context of discussing the history of this problem.) If we grant that there is only one fundamental substance (if we deny dualism and pluralism), then the next obvious question is: what is that substance? What is this thing that underlies all other things? I don’t know; nor does anyone else. However, I think it is obvious that the best method for finding out is the method of the sciences: continually and rigorously to test hypotheses about what that stuff is. I can say that I think that stuff is physical stuff — in a sufficiently broad sense of the word “physical”. To a first approximation, physicalism is the view that “in some sense there are no facts over and above the purely physical facts” or that “physical facts determine everything else” (Harman 1973, p. 36). In can also be stated as the view that “everything is a manifestation of the physical aspects of existence” or that “all aspects of reality… are related to physics in certain specifiable ways” (Poland 1994, pp. 1 & 10). To make this view concrete, it is necessary to spell out what are the specifically “physical” facts or aspects of existence and to specify in what ways other sorts of things must be related to the physical. One frequently asserted view is that the “physical” aspects of existence are those studied by the discipline of physics. For example, Jeffrey Poland writes: “I shall be conceiving of the physicalist programme as a unification programme

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which aims at building a system of knowledge that is grounded in physics” (Poland 1994, p. 12). Gilbert Harman, himself an advocate of this view, points out that “is more trivial than it might at first appear” because if “scientists discover a new phenomenon that has physical effects but is not reducible to phenomena currently accepted as physical, they classify the new phenomenon as a new physical phenomenon” (Harman 1973, p. 36). As an example, Harman cites the subsumption of the newly discovered electromagnetic phenomena into physics. If any newly discovered phenomenon can be subsumed by physics, the claim that physics has some kind of logical priority over the other sciences is vacuous. This sort of thing might lead one to suppose that the notion of “physical facts” is entirely devoid of meaning. If the “physical facts” is the set of facts of all realms that have any interaction with the physical realm, then it might as easily be expanded to accomodate dualistic interactionism as electromagnetism. Harman raises this criticism for himself: “should we then suppose, e.g., that the mind is something like a mental field, different from and not reducible to other physical phenomena but interacting with them?” (Harman 1973, p. 36). One way to resolve this problem would be to define physical phenomena as the phenomena currently (say, circa 2000 AD) studied by physics. But that is clearly too provincial a view. We would not have wanted to have identified physical phenomena with physical phenomena as we knew them in 1000 AD, and we have no reason to think that we are in a qualitatively different position today.

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To the objection (that identifying “the physical” with “whatever is studied by physics” is too weak) Harman himself responds by knocking down a straw man: Although the suggestion might be defended by appeal to alleged instances of mental telepathy, ESP, and psychokinesis, along with speculation that free choice operates in the area of quantum indeterminacy, that would really be to indulge in a kind of crackpot science (Harman 1973, pp. 36-7). Harman is right that ESP and the grounding of free choice in quantum indeterminacy are crackpot science. But that does not address the issue, which is that “what is studied by physics” just might have to be expanded in unexpected ways to explain some aspects of the mental. The most likely candidates are the qualitative properties of consciousness. I do not want to suggest that Searle is right that consciousness is some fundamental property of living nervous tissue, nor that Penrose is right that it is generated by quantum processes in microtubules. Rather, my point is that we must be careful in how we go about refuting these claims. We cannot merely assert that they are incorrect because they do not conform to our present conception of physics — as Harman himself correctly points out, our conception of physics is subject to change. We must at least demonstrate why the physics Searle and Penrose propose is bad physics. An adequate view of the mental that is reducible to physics as we know it would be much more palatable. While the latter should clearly be our goal, it seems to be some way off, at least judging by the breadth and depth of disagreement within the physicalist

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camp over just what form our explanation of the mental, and hence the reduction, should take. Meanwhile, we can make some progress by addressing the former issue. With Searle’s proposal, matters are rather easy, because it is too vague to be taken seriously as a scientific hypothesis. With regard to Penrose, matters are slightly more difficult. One route we should clearly not take is that of asserting that his principles operate “at the wrong level,” because his claim is (or should be) precisely that we have got the levels wrong. Another, more promising, route is the criticism of his claims on the same grounds that we would criticize any other claim as “bad science” — e.g., that his theory is not disconfirmable, or has been disconfirmed. There is a broader lesson in this conclusion. Although we cannot identify “the physical” simply as “the subject matter of physics, whatever that may be,” we may be able to identify it as the subject matter of “physics, properly done”. Perhaps this should go without saying, but it has to my knowledge gone without saying up to now. One further caveat is needed: if we are to take this route, in determining what is “physics, properly done,” we must be careful not to exclude new theories merely because they deal with material at the level of the special sciences. We need some substance for the “properly done” bit of things. How widely held physicalism is is debateable, given reports such as that appearing in a recent issue of Time magazine, that a majority of Americans believe in angels. It would be more accurate to say that a majority of scientists believe in physicalism:

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Scientists believe that the totality of physical facts completely determines all other facts and that, in particular, all mental processes are completely determined by whatever physical processes there are (Harman 1973, p. 36). Some scientists do believe that; so do many non-scientists, especially philosophers, including myself. However, there must be other reasons for believing it besides the fact that some (or many) scientists believe it. The reason that I take to be decisive is that, despite its many faults, science is the best method we have for acquiring knowledge. Perhaps it will be useful to briefly canvas some of the alternatives. Harman gives a typical argument for dualism: We are tempted to take conscious experience to be paradigmatically mental. Moreover, a headache, an itch, a sudden thought, a feeling of joy, a pang of longing, or the awareness of a beautiful blue may seem very different from any physical process such as the excitation of nerve ends in the brain. We have a direct acquaintance with experience and mental processes in general that, it seems, we can never have with physical processes (Harman 1973, p. 35). This statement of the evidence is, I think, neutral. We can all agree that we have relations with experience that it seems we could never have had with physical events. About the argument that is supposed to lead from this observation to dualism, Harman is equally circumspect: Some such line of thought may persuade us to accept a form of dualism— the idea that mental and physical processes are basically and irreducibly different. We may even decide that there must be two basic kinds of substances, minds and bodies… . Such dualism tends naturally to a form of dualistic

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interactionism— the theory that there is a causal interaction between the mental and the physical (Harman 1973, p. 35). Subsequently, Harman, resorts to physicalism to refute the dualist. This is, of course, unacceptable. The proper response is the argument that, if dualism (or pluralism) were true, we would have a bizarre, divided understanding of the world around us. We would be forced to hold that two different and incommensurable sciences are necessary to explain the facts. This would be intolerable, for it is precisely one of our most fundamental intuitions that the world is a unified whole. This is admittedly a very sketchy argument, but I go into it in more depth in Chapter 3, where I consider the origins of dualism in the pre-Socratic philosophers. There is also a common feeling that our having free will is incompatible with physicalism. Physicalism requires supervenience of the mental on the physical. That is, it requires that all mental facts be determined by the physical facts. The physical facts are of two kinds: deterministic and nondeterministic. In deterministic physics (such as Newtonian mechanics), earlier states of the system determine later states of the system. In nondeterministic physics (such as quantum mechanics), earlier states of the system do not determine later states of the system. The argument that free will is incompatible with physicalism depends on turning this dichotomy into a dilemma. The reasoning goes like this: Assume supervenience is true. Then all mental facts are determined physical facts. All physical facts are either deterministic or nondeterministic. Therefore, all mental

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facts are either deterministic or nondeterministic. If mental facts are deterministic, then we do not have free will (because free will depends on the outcomes of our decisions not being determined by our earlier states). On the other hand, if mental facts are nondeterministic, then we do not have free will either (because free will depends on the outcomes of our decisions being justifiable). Therefore, if supervenience is true, then we do not have free will. But we do have free will. Therefore, supervenience is false. Therefore, physicalism is false. The argument, of course, begs the question. It is not clear that we do have free will, especially in the sense of a kind of transcendent supra-physical control over “our bodies” which is neither determined nor random. It may be simply that the impression we have of freedom is an illusion, an epiphenomenon of the physical brain processes that do, in fact, control our bodies. Or it may be that all we really mean by free will is freedom from coercion. I do not assert here that either of these possibilities is the best account of freedom of the will, only that each is an open possibility. We cannot assume that freedom of the will entails nonphysicalism, or that the possibility of free will requires the refutation of physicalism. 2.6

Sketch of the Solution My solution to these problems began with the observation that there is

something very interesting and important about spatial representation: the way that animals (and thinking subjects in general) represent the space in which they live and through which they move. Spatial representation appears to be a

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fundamental organizing property of our conceptual schemes. Consequently, spatial representation has a privileged role in many domains of cognitive experience. For example, many linguists have argued that space has a privileged position in language and thought. Spatial location is expressed by forms that have “the fundamental role of acting as an organizing structure for further conceptual material” (Talmy 1983, p. 4). Moreover, many parts of our conceptual scheme are understood in terms of spatial metaphors (Lakoff 1987). This sort of evidence indicates “that space has a privileged position as a foundational ontological category in language, a position which most other domains do not share” (Regier 1995, p. 1). However, in order to show just how important space is, we shall have to back up quite a bit, and survey the history of these problems. In doing so (in Chapter 3), we will also see more clearly the connections I alluded to above between mind, metaphysics, and epistemology. Then, in Chapter 4 and Chapter 5, we will look in detail at Strawson’s reconstruction of Kant’s arguments for the priority of spatial (and temporal) representation. Our consideration of Strawson will lead us to the conclusion that spatial representation is far more fundamental than even the psychologists and linguists I mentioned above have realized. We will see that the proper conclusion of Strawson’s arguments is that the fundamental form of representation itself is spatial (in an abstract, mathematical sense), not linguistic (as is commonly assumed in the literature). In particular, we will see how representation of objects as located in space gives us the capacity to

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refer to objects. Finally, in Chapter 6, we will see how vector coding in connectionist networks represents properties of these objects by proximities in an abstract, high-dimensional activation space. The explication of the differences between these two interpretations of “spatial representation” and their different roles in constituting thought provide answers to the problems I have raised here in the following way. The representation of material objects in physical space allows us to refer to them, and the representation of those objects in activation space allows us to conceptualize them. Together, the two senses of “spatial representation” explain how it is possible for thought to exist in a purely physical world (the metaphysical problem of justifying materialism). The fact that thought is explained in material terms explains how it is possible for “the mind” to control “the body” (the mind/body problem). The fact that we can refer to material objects in physical space explains how it is possible for us to have knowledge of the external world (the epistemological problem). Finally, the fact that we can refer to things independently of our conceptions of them explains how we can be wrong about the properties of those things (the problem of normativity).

Chapter 3 Historical Background 3.1

Abstract In this chapter, I give a brief sketch of the philosophy of mind, from the

earliest pre-Socratic philosophers through the present day. Such a short synopsis obviously leaves a great deal to be desired. Nevertheless, I use it as a way of situating the problems I address in subsequent chapters with respect to the history of philosophy. I also explain my own view about when, how, and why the philosophy of mind took the wrong turns that left us with the problems of explaining the relation between the mind and the body, the possibility of materialism and knowledge of the external world, and the nature of normativity. 3.2

The Ancients As I mentioned in Chapter 2, the problem of explaining the relation

between the representational world and the physical world is the problem with which philosophy began. The dispute between monism, dualism, and pluralism didn’t merely arise at the beginning of philosophy; it was, in fact, the reason for the development of philosophy. In a study of Anaximander, for example, Charles Kahn argues that the earliest philosophers actually created the separation between the representational and the physical realms, or, as Kahn refers to them, between “Nature” and “Society” (Kahn 1960, pp. 192-3). Whether philosophy actually created this distinction, or only attempted to cope with a distinction that had

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already developed in the larger culture, is an issue I will not attempt to address in this work. Nevertheless, it soon became the task of philosophy to reintegrate the two realms – to somehow repair what had been torn asunder, whether by philosophy itself or by developments prior to philosophy – and that task continues to engage philosophers to this day. Kahn claims that society (the representational world) was all people were aware of before the advent of science. With the advent of science (an awareness of the physical world), philosophy was called on to elucidate the distinction between the representational world and the physical world. Since that time, we have needed a reconciliation of the two world-views. It is well known that some of the earliest Greeks were physicalists, in the sense that they believed everything had its origin in the physical world. Thales, for example, thought that everything was a form of water, one of the traditional elements. As Aristotle writes: Of the first philosophers, most thought the principles which were of the nature of matter were the only principles of all things; that of which all things that are consist, and from which they first come to be, and into which they are finally resolved (the substance remaining, but changing in its modifications), this they say is the element and the principle of things, and therefore they think nothing is either generated or destroyed, since this sort of entity is always conserved… .So they say nothing else comes to be or ceases to be; for there must be some entity— either one or more than one— from which all other things come to be, it being conserved.… Thales, the founder of this school of philosophy, says the principle is water (Metaphysics Book I, 983 b 6-20, in Barnes 1984, pp. 1555-6).

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Subsequently, Anaximander argued that the primary substance could not itself be one of the elements. This argument, that the fundamental substance cannot be one of the common elements, recurs many times in early Greek philosophy. Anaximander hypothesized a single substance, which he called “the indefinite”, that was the foundation of all of the traditional elements (cf. Simplicius , 24.1321). Aristotle paraphrases Anaximander’s argument in the Physics, Book III, Chap 5: The elements were thought to be complementary – cold air and hot fire annihilate each other, and moist water and dry earth annihilate each other – so none of them could be the substantial ground of the others, because it would annihilate its opposite. Instead, the elements must be in perfect balance, never more or less air than fire, never more or less water than earth (see Physics Book III §5, 204b 2228, in Aristotle 1930). Although the terms have changed, the form of this argument for monism persists through the present day. In the case of Aristotle’s criticism of Anaximander, the argument is that the fundamental substance cannot be one of the elements, because the elements annihilate each other; therefore whatever underlies all of them must be some other thing, or it would have annihilated everything else. The talk of “annihilation” is peculiar to Greek philosophy, but the essential argument for monism is the same today: for any two substances in the world, there must be some third, more fundamental, substance that underlies them. For, if there were not, the two could not interact. If there were a substance that could not interact with other substances, we could have no knowledge of it, and the question never

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would have arisen whether there was some more fundamental substance that underlies it. Here is another way of putting the argument: Suppose there is more than one fundamental substance. Then, either the fundamental substances interact, or they do not. If they interact, then there must be something more fundamental that grounds their interaction; then that is the (only) fundamental substance. If they do not interact, then they can have no effects on each other. Therefore, only one of them can have effects on us; and that is the only fundamental substance worth caring about. There are of course some lacunae in this argument. The most obvious but least important is that it does not establish the conclusion that there is only one fundamental substance, only the conclusion that there is only one fundamental substance worth caring about. More important is the justification of the premise that, if two substances interact, there must be something more fundamental grounding their interaction. Perhaps it is possible that there could be many fundamental substances which interact, but whose interaction is not grounded in anything more fundamental. Ultimately, this step expresses a faith in the order of things: that everything is explicable in a single, unified framework. This might not be so, but I believe that it is, and so, I think, do many others. (Not that this agreement constitutes an argument for the claim that there is a unified explanation for everything, only that agreement makes it plausible enough for me to take it for granted for the purposes of this work.)

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Like Anaximander, Anaximenes had monistic conception of the universe. However, Anaximenes regresses from Anaximander’s arguments that the fundamental substance cannot be one of the elements, and argues instead that the fundamental substance is air (Theophrastus, quoted by Simplicius , 24-26-25.1). Democritus too is a monist, because he “distinguishes between the qualities that we can experience, and what there is ‘in truth,’namely atoms and void” (Annas 1992, p. 5). Democritean atomism, like today’s physics, hypothesizes tiny particles that underly everything else. In fact, all of the major theories in Hellenistic philosophy of mind were physicalist theories. They postulated that everything (including the mind) can be explained using only the concepts of physics. During this period, dualism was not taken seriously (see Annas 1992, pp. 2-4 for an elaboration of this point). However, a number of Greeks have been interpreted as dualists on the grounds that they believed in the transmigration of souls. Pythagoras, for example, famously objected to the beating of a puppy on the grounds that it was the soul of a friend: Once [Pythagoras] passed by as a puppy was being beaten, the story goes, and in pity said these words: “Stop, don’t beat him, since it is the soul of a man, a friend of mine, which I recognized when I heard it crying” (Laertius ).

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While this view is novel, it is not dualist. Pythagoras is an idealist, not a dualist. He did not think that the material bodies of animals were animated by immaterial souls, but rather that the animals were themselves souls: First he declares that the soul is immortal; then that it changes into other kinds of animals; in addition that things that happen recur at certain intervals, and nothing is absolutely new; and that all things that come to be alive must be thought akin. Pythagoras seems to have been the first to introduce these opinions into Greece (Porphyry ). Hence, on Pythagoras’view, there is still a single substance that underlies everything; however, for Pythagoras, in contrast with his materialist predecessors, the substance is immaterial. Empedocles had a similar view, expressed in passages such as the following: Fools, for their meditations are not far-reaching thoughts, men who suppose that what formerly did not exist comes into existence, or that something dies and is completely destroyed (Empedocles 1981, 104(11)). A man who is wise in such matters would not surmise in his mind that men are, and good and ill befall them, for as long as they live, for a lifetime as they call it, and that before they were formed, and after they have disintegrated, they do not exist at all (Empedocles 1981, 106(15)). whenever one in error, from fear (defiles) his own limbs, having by his error made false the oath he swore… he wanders from the blessed ones for three times countless years, being born throughout the time as all kinds of mortal forms, exchanging one hard way of life for another (Empedocles 1981, 107(115)).

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For before now I have been at some time boy and girl, bush, bird, and a mute fish in the sea (Empedocles 1981, 108(117)). In these passages, Empedocles expresses his belief that experience transcends physical form. However, he does not assert that there are separate substances underlying the two. This is a common argument, and I believe that it underlies a great deal of the dualism that we later see in Plato and, subsequently, Descartes. Ultimately, dualism is a view motivated by the belief that existence must somehow transcend the short existence of a physical body. It is motivated by a kind of religious optimism, a faith that there must be something more to existence than the frail and short-lived body. As we have seen, the earliest Greek philosophers were monists, and most of them were physicalists as well. However, problems with monism and physicalism soon became evident. Any monist, whether physicalist or idealist, has trouble accounting for the fundamental characteristic of the representational world: the possibility of error. As I pointed out in Chapter 2, in the purely physical world, events are driven by causes, and there is no room for judgement or error. Conversely, the idealist cannot explain why our ideas should ever be wrong, because he refuses to postulate an external world that might contradict them. The physicalist also has problems accounting for other features of our experience: its qualitative aspects, and the sense of free will. Hence the development of dualism.

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Anaxagoras was the first clear dualist, in the sense that he gives an argument why there must be more than one kind of substance, rather than merely an assertion that the existence of the soul transcends the existence of the body: The other things share in a portion of everything, but mind is unlimited and self-controlling and has not been mixed with anything, but exists alone itself by itself; for if it were not by itself but had been mixed with something else, it would share in all things, if it had been mixed with any (for in everything there is a portion of everything, as I have said earlier); and the things mixed together with it would be preventing it so that it would not control anything in the same way as it actually does being alone by itself. For it is finest of all things and purest; and moreover it harbours every discerning judgement about everything, and [so] harbours greatest strength; and moreover all the things that have soul, both the greater and the smaller, all of them mind controls (Schofield 1980, Fragment 12, pp. 3-4). Anaxagoras separates the world into the physical and mental realms, separate substances, much as Descartes does later. Anaxagoras’arguments for dualism are based on two of the problems I identified with physicalism: (1) the possibility of error, and (2) the sense of free will. Anaxagoras first refers to the faculty of the mind for judgement. Judgement is representation. One judges the apple to be red (i.e., represents the apple as red), judges the stick to be bent (represents it as bent), and so on. Anaxagoras recognized the difficulty of accounting for error on a purely physicalist basis. He also acknowledged the problem of free will: mind, as he puts it, controls bodies.

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Plato’s dualism is a refinement of Anaxagoras’. In several of the dialogs, and especially in the Phaedo, Plato claims that souls are not only separate from bodies but are different kinds of things. He himself emphasizes the problems this raises about the relationship between the body and the soul (see Annas 1992, p. 4). Nevertheless, he makes a point of arguing in the Timaeus that Reason and Life are prior to Body and to blind physical causation (see Kahn 1960, p. 207). Thus, by the time of Plato, the essential tension in philosophy has been explicitly recognized. Although people initially recognized only a representational, or social, world, the advent of science forced us to acknowledge a physical world. Philosophy was called upon to explicate the relation between the newly acknowledged physical world and the traditional, representational world. The initial impulse was to reduce everything, including the representational, to the physical order (Thales, Anaximander, Anaximenes). In response, others argued for the primacy of the representational (Pythagoras, Empedocles). Finally, Anaxagoras and then Plato argued that neither the physical nor the representational could be reduced to the other; there must be both kinds of substance, existing separately and yet somehow interacting. These positions define the field to this day. Platonic dualism, for example, was resuscitated in the Middle Platonist schools, fully rejuvenated by the Neoplatonists (Annas 1992, p. 4), forgotten for some time, and eventually reincarnated in Descartes. The tension between monism and dualism is manifest in Aristotle as well. Beginning with Aristotle, knowledge was the ability of the person to be part of

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relations with reality as it is in itself; representational states were direct relations between the person and the external world (Aristotle , DeAnima 424a15ff; 425b20ff; 429a10-432a10). The later scholastic epistemology, like Aristotelian epistemology, hypothesized an identity between the knower and the object of knowledge. Knowledge consisted in a person’s becoming identical with the object of knowledge (cf. Aquinas 1964 I, Q78, A3, ans.; IQ84, A2, ans.).2 On both Aristotelian and Scholastic theories, therefore, knowledge is a direct relation between a knower and an object. The directness of knowledge in the Scholastic tradition contrasts markedly with the Platonistic conception of knowledge, wherein knowledge is mediated by the Forms, with which direct contact is impossible. Nevertheless, Aristotle was primarily a monist. He believed that the soul could be explained using only the concepts of physics (see Annas 1992). For Aristotle, the senses receive the forms of material objects: “with regard to all sense-perception, we must take it that the sense is that which can receive perceptible forms without their matter, as wax receives the imprint of the ring

2

Rorty writes of the Thomists that they had a “hylomorphic conception of knowledge— a conception according to which knowledge is not the possession of accurate representations of an object but rather the subject’s becoming identical with the object” (Rorty 1979, p. 45). Likewise, Richard Aquila writes: “What characterizes the Scholastic account is the notion of some kind of ‘identity’uniting the knower and what it knows” (Aquila 1983, p. 4). We have seen how this notion of “identity” between subject and object itself becomes an expression of the problem of physicalism in Brentano’s discussions of it as “intentional inexistence”.

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without the iron or gold” (DeAnima 424a15ff, Aristotle 1987, 424a, 18-19). The form of a thing is the kind of thing it is, the properties that distinguish it qualitatively from other things in the universe. The matter of a thing, on the other hand, is what permits distinguishing quantitatively different individuals of the same form. Hence, several different things can be qualitatively identical, but nevertheless quantitatively different, by being composed of different matter. (There are, moreover, two sorts of form: sensible and intelligible form. The sensible form of a thing is that which determines its presentation to the senses, for example, its color or shape. The intelligible form of a thing, on the other hand, is the kind of thing that it is, for example, a tree or a building.) The eyes, for example, receive the colors of objects: “even that which sees is in a way colored; for each sense-organ is receptive of the object of perception without its matter” (Aristotle 1987, 425b, 23-24). These passages clearly demonstrate that, despite Aristotle’s impulse toward monism, he believes that there is something (form) that is distinct from matter. Consequently, the fundamental tension between the physical and the representational rearises in Aristotle’s notion of the mind. Annas notes that the “difficult doctrine of separable nous may provide a limited exception to” Aristotle’s physicalism (p. 3, n. 5).3

3

For more on Aristotle’s notion of the soul, see Nussbaum (1991).

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3.3

The Moderns Descartes reacted against the Scholastic view that the mind could become

identical with material things; rather, the Cartesian mind was completely nonspatial. Hence, while activity in the brain might in some way resemble the matter that it represents, the mind does not come to resemble that which it represents in any way. For Descartes, knowledge was the ability of the person to be part of relations with mental representations of the external world; mental states were relations between the person and her mental representations. Hence, the representational view of mind traces its heritage through Descartes to Plato. The first step toward a representational view of mind is the rigid separation of mind from the external world, as in Plato’s Forms or Descartes mental substance. Such a separation forces one to view thought, not as a relation between people and objects, but rather as a relation between peculiarly mental entities (ideas or forms) and objects. The problem of justifying belief in the external world arises for Descartes because he, like many seventeenth-century scientists (and many since then as well), divided the process of perception into three parts: the physical, the physiological, and the psychological. Each part had its own medium and location. Part: Medium: Location: Name:

Physical Light Outside Body Reflection

Physiological Retina, Nerves Inside Body Sensorium

Psychological Perceptions Mind Sensory Given

On such theories, light reflected from objects outside the body (a physical process), strikes the retina, creating a retinal image. The retinal image travels via

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the optic nerve to the sensorium (a physiological process). At the sensorium, the retinal image is perceived as the sensory given, which may be operated on by the mind (a psychological process). The sensations caused in the mind by physiological events at the sensorium are the immediate objects of consciousness; thus, the mind stands in a perceptual relation to them. This tripartite division was a common feature of seventeenth-century accounts of spatial perception. During the seventeenth century, scientists became increasingly concerned with the properties of space. Philosophers interested in justifying the claims of modern science therefore found that they had to justify knowledge of spatial properties. Philosophical treatments of spatial perception tended to address the question whether knowledge of the spatial properties of matter is based only on sensory experience, whereas psychological treatments considered primarily the mechanisms by which distance is perceived. However, the two questions were not always kept separate. These sorts of theories of vision gave rise to the veil of perception problem. The sensation is a third thing between the mind (perception) and the external world (physics, physiology); it stands in a relation to the mind analogous to that in which external objects stand to the senses. The postulation of such a third thing suggests that our acquaintance with the external world is only indirect, since it is mediated by a causal chain. If that is the case, we can imagine the chain going awry, so awry in fact that there needn’t even be an external world to cause our perceptions. Hence, the veil of perception makes our belief in objectivity

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problematic. If we are only acquainted with our own sensations, how can we ever know that they are caused by an external world?4 Because, during the early modern period, the objects of direct awareness were considered to be mental states, the main problem of epistemology was to determine how mental states inform us about an independently existing world. Philosophers became known, in part, for their different positions on this issue. Descartes and Locke believed that our mental states do inform us about a material world, and were thus realists about the external world. Berkeley, famously, denied that there was such a world, and so became known as an idealist. Hume denied the possibility of knowledge of a transcendent reality, arguing that the question of the relationship between our ideas and a world of things in themselves cannot be answered. We may call Hume an “agnostic” (cf. Hatfield 1990, p. 51), since he refused to take a stand on what the relationship is. On Descartes’and Locke’s views, ideas do give us knowledge of an external world of mind-independent objects. In even his earliest works, Descartes rigidly separated subject and object. In Descartes’first work, the Regulae, when

4

The idea of sensation as a third thing standing between the external world and the mind is not unique to Descartes or Locke, or even to the modern period. In the early 20th century, it was defended by C. D. Broad (1923), Bertrand Russell (1914), G. E. Moore (1922), and Price (1932, Chapter 5). On the other hand, it has also regularly been criticized, from Reid (1785,Essay 2, Chapter 14, 1:298-306) to Bennett (1971, pp. 31-2, 124-5), Kenny (1968, pp. 116, 1225), and Rorty (1979, pp. 45-51). For historical background on the veil of perception problem, see Hatfield (1990), a work to which my own account owes a great deal.

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he turns to the question “What is human knowledge and what is its scope?” in Rule 8, he immediately divides his inquiry into two parts. He writes, “the question ought to relate either to us, who have the capacity for knowledge, or to the actual things it is possible to know” (Descartes 1628/1988, p. 9). Some pages later in Rule 12, he reiterates the point: “Where knowledge of things is concerned, only two factors need to be considered: ourselves, the knowing subjects, and the things which are the objects of knowledge” (Descartes 1628/1988, p. 12). Likewise, in the Discourse, Descartes emphasizes the gap between the subject and the external world. Through his method of doubt, Descartes claims to discover that he “could pretend that I had no body and that there was no world and no place for me to be in” (Descartes 1637/1988a, p. 36). He concludes that he is “a substance whose whole essence or nature is solely to think, and which does not require any place, or depend on any material thing, in order to exist” (Descartes 1637/1988a, p. 36). The mind, Descartes concludes, “is entirely distinct from the body, and indeed is easier to know than the body, and would not fail to be whatever it is, even if the body did not exist” (Descartes 1637/1988a, p. 36). In other words, “the intellectual nature is distinct from the corporeal” (Descartes 1637/1988a, p. 38). Although the work is less well known, in the Optics, published the same year as the Discourse, Descartes gives an equally clear picture of the separation between the mind and the external, physical, world. He opens the fourth Discourse of the Optics with the assertion that “We know for certain that it is the

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soul which has sensory awareness, and not the body” (Descartes 1637/1988b, p. 61). Again, Descartes emphasizes the difference between the mind as the locus of sensation and the body as merely another part of the material world. In the Meditations, Descartes makes even clearer his belief that the mind is independent of any external, spatial world. After a day’s meditation, he claims to have convinced himself that “Body, shape, extension, movement and place are chimeras” (Descartes 1641/1988, II(24)) and yet still believe that he exists. He claims that the method of doubt he has applied to his piece of wax “may be applied to everything else located outside me” (Descartes 1641/1988, II(33)) and thus that “the objects of my sensory experience and imagination may have no existence outside me” (Descartes 1641/1988, III(35)). Descartes’theory of sense perception has allowed him to doubt the existence of the external world. Descartes next takes up the problem concerning “the ideas which I take to be derived from things existing outside me: what is my reason for thinking that they resemble these things?” (Descartes 1641/1988, III(38)). Descartes considers the possibility that it is only natural for him to think that his ideas resemble their objects, but rejects it on the grounds that other natural impulses have led to error in the past. Second, he considers the possibility that it is because his ideas are not subject to his will. However, he argues that “it does not follow that they must come from things located outside me” (Descartes 1641/1988, III(39)) because they might be generated by an unknown part of himself.

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In apparent failure, Descartes turns to “another way of investigating whether some of the things of which I possess ideas exist outside me” (Descartes 1641/1988, III(40)). He considers the priority relationships among his various ideas, and discovers that all of his ideas except for his idea of God could have come from his idea of himself. Hence, he concludes, God necessarily exists. And from his knowledge of God, Descartes derives his knowledge of other external things, including spatiotemporal bodies. Obviously, we can no longer take seriously arguments premised on the existence of God. But Descartes also marshals a number of additional arguments for the existence of God. One particularly interesting one begins with the nature of time: “it is quite clear to anyone who attentively considers the nature of time that the same power and action are needed to preserve anything at each individual moment of its duration as would be required to create that thing anew if it were not yet in existence” (Descartes 1641/1988, III(49)). Since Descartes cannot find within himself a power that would allow him to cause himself to continue to exist, he concludes that he depends on something distinct from himself (God). And that is how he justifies his belief in the external world. Although Descartes is sometimes accused of having a “picture” or “resemblance” theory of mental representation (hence Dennett’s denigrating term for the locus of representations in such views, the “Cartesian theater”), Descartes makes it quite clear in the Optics that he does not think that representation is resemblance:

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We must take care not to assume… that in order to have sensory awareness the soul must contemplate certain images transmitted by objects to the brain; or at any rate we must conceive the nature of these images in an entirely different manner from that of the philosophers. For since their conception of the images is confined to the requirement that they should resemble the objects they represent, the philosophers cannot possibly show us how the images can be formed by the objects, or how they can be received by the external sense organs and transmitted by the nerves to the brain. Their sole reason for positing such images was that they saw how easily a picture can stimulate our mind to conceive the objects depicted in it, and so it seemed to them that the mind must be stimulated to conceive the objects that affect our senses in the same way — that is, by little pictures formed in our head. We should, however, recall that our mind can be stimulated by many things other than images — by signs and words, for example, which in no way resemble the things they signify. And if, in order to depart as little as possible from accepted views, we prefer to maintain that the objects which we perceive by our senses really send images of themselves to the inside of our brain, we must at least observe that in no case does an image have to resemble the object it represents in all respects, for otherwise there would be no distinction between the object and its image. It is enough that the image resembles its object in a few respects (Descartes 1637/1988b, p. 62). Descartes concludes: “in order to have sensory awareness the soul does not need to contemplate any images resembling the things which it perceives” (Descartes 1637/1988b). Clearly, Descartes does not accept the picture theory of meaning he is often accused of originating. At this point in the Optics, Descartes gives a lengthy account of the physical and physiological processes leading to vision, up to the retinal image and

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its passage along the optic nerve to the brain. When the retinal image “passes to the inside of our head, it still bears some resemblance to the objects from which it proceeds” (Descartes 1637/1988b). However, the resemblance is not essential: we must not think that it is by means of this resemblance that the picture causes our sensory awareness of these objects — as if there were yet other eyes within our brain with which we could perceive it. Instead we must hold that it is the movements composing the picture which, acting directly upon our soul in so far as it is united to our body, are ordained by nature to make it have such sensations (Descartes 1637/1988b, p. 64). In fact, Descartes has a particular story for each sensory modality: we must suppose our soul to be of such a nature that what makes it have the sensation of light is the force of the movements taking place in the regions of the brain where the optic nerve-fibers originate, and what makes it have the sensation of color is the manner of these movements. Likewise, the movements in the nerves leading to the ears make the soul hear sounds; those in the nerves of the tongue make it taste flavors; and, in general, movements in the nerves anywhere in the body make the soul have a tickling sensation if they are moderate, and a pain where they are too violent. But in all this there need be no resemblance between the ideas which the soul conceives and the movements which cause these ideas (Descartes 1637/1988b, pp. 64-5). Again and again, Descartes denies the resemblance theory of representation: “As regards position,… [o]ur knowledge of it does not depend on any image” (Descartes 1637/1988b, p. 66). “The seeing of distance depends no more than does the seeing of position upon any images emitted from objects” (Descartes 1637/1988b, p. 67). “It is obvious too that we judge shape by the knowledge or

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opinion that we have of the position of the various parts of an object, and not by the resemblance of the pictures in our eyes” (Descartes 1637/1988b, p. 68). At times in the Meditations, it appears that Descartes has reconsidered his position of the Optics that ideas need not resemble the objects they represent. For example, he writes that “it is clear to me, by the natural light, that the ideas in me are like images” (Descartes 1641/1988, III(42)). However, it is important that in this passage Descartes only likens ideas to images, but does not identify ideas with images. Moreover, his purpose in likening ideas to images is only to demonstrate, by analogy, how ideas can be incorrect. Ideas can, like images, “easily fall short of the perfection of the things from which they are taken” (Descartes 1641/1988, III (42)). Descartes’language (“easily fall short of the perfection”) is an instance of the argument from error. Ideas are, for Descartes, like pictures in the sense that they are representational, i.e., allow for the possibility of error; Cartesian ideas, however, need not be pictorial or imagistic. Locke, on the other hand, develops a clearly pictorial view of representation. Once Descartes had developed a rigid separation between mind and body, it became possible for Locke to write that “the Ideas of primary Qualities of Bodies, are Resemblances of them, and their Patterns do really exist in the Bodies themselves” (Locke 1689, II.viii.15) and that “the Understanding is not much unlike a Closet wholly shut from light, with only some little openings

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left, to let in external visible Resemblances, or Ideas of things without” (Locke 1689, II.xi.17). Some Locke commentators have suggested reading of the Essay in such a way that the representational relation between ideas and objects is cast in language that does not invoke the notion of resemblance. The suggestion is that Locke’s phrase “perceiving ideas” means having a certain perception, rather than standing in a perceptual relation to an idea considered as a thing (Hatfield 1990, p. 53). However, I think that this goes too much against the grain of the text: Locke himself uses the word “resemblance” in an apparently literal way, as the passages I have cited show. There is, however, a familiar skeptical objection to the “resemblance” or “pictorial” version of representational realism. To judge whether our ideas accurately portray the external world, we must be able to compare our ideas with the world; but a direct comparison between ideas and the world is impossible, because our experience is limited to our own ideas (Hatfield 1990, pp. 51-2). This is again the problem of accounting for the possibility of error. It is clear that we must reject the resemblance account of representational realism. It may be possible to defend a version of representational realism that does not depend on resemblance. Goodman, for one, has called into question the notion of “resemblance” as applied to the relation between image and object (Goodman 1968). However, this raises the problem of content. If ideas are third things between minds and the external world, then they can have the properties of

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(that is, resemble) their contents. On the other hand, the parts of minds do not generally have properties that resemble the contents of their ideas. So how can states of mind represent, for example, colored and shaped objects in such a way that color and shape are phenomenally available to consciousness, even though the states of mind themselves are not colored or shaped? (Hatfield 1990, p. 53). On this view, the content of an idea is its intentional object. These “intentional objects” are third things equivalent neither to external objects nor to states of mind; they do not, however, exist independently of states of mind. On Locke’s view, knowledge of the existence of an external, spatiotemporal, world can be obtained only by sensation: “The Knowledge of the Existence of any other thing we can have only by Sensation.… ’Tis therefore the actual receiving of Ideas from without, that gives us notice of the Existence of other Things, and makes us know, that something doth exist at that time without us, which causes that Idea in us” (Locke 1689, IV.xi.1-2). Although the argument is not deductively certain, Locke asserts that we do have compelling knowledge of the existence of an external world: “The notice we have by our Senses, of the existing of Things without us, though it be not altogether so certain, as our intuitive Knowledge, or the Deductions of our Reason, employ’d about the clear abstract Ideas of our own Minds; yet it is an assurance that deserves the name of knowledge” (Locke 1689, IV.xi.3). Locke gives four reasons why we can be reasonably sure that there is an external world. The first is that persons lacking sense organs for a particular

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modality do not have sensations in that modality; therefore, Locke concludes, sensations must come from the external world via the sense organs. Locke’s second reason is that ideas of the existence of an external world are not subject to the will. (But here we must remember Descartes’point in the Meditations: the fact that our ideas are not subject to our will does not show that they come from a world external to us, because they may come from a part of us that is not subject to our will.) The third reason is that sensations are sometimes painful in a way that even memories of them are not, the difference presumably being caused by the effects of external objects on the sense organs. Locke’s fourth reason for confidence in the existence of an external world is the fact that different sense modalities corroborate each other. Despite all his arguments, however, Locke backs down in response to the determined Cartesian skeptic: That the certainty of Things existing in rerum Naturâ, when we have the testimony of our Senses for it, is not only as great as our frame can attain to, but as our Condition needs. For our Faculties being suited not to the full extent of Being, nor to a perfect, clear, comprehensive Knowledge of things free from all doubt and scruple; but to the preservation of us, in whom they are; and accommodated to the use of Life: they serve to our purpose well enough, if they will but give us certain notice of those Things, which are convenient or inconvenient to us.… So that this Evidence is as great, as we can desire, being as certain to us, as our Pleasure or Pain; i.e. Happiness or Misery; beyond which we have no concernment, either of Knowing or Being. Such an assurance of the Existence of Things without us, is sufficient to direct us in the attaining the Good and avoiding the Evil, which is

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caused by them, which is the important concernment we have of being made acquainted with them (Locke 1689, IV.xi.8). Locke’s answer, like Descartes’, amounts to a kind of pragmatism: while it may be possible in principle to doubt the existence of an external world, we are certain of it in practice. Hume took an agnostic attitude about the metaphysics of mindindependent material substance, on the grounds that the mind cannot grasp anything without the aid of the senses (Hatfield 1990, p. 59). Whereas Descartes’ theory of knowledge provides a criterion for truth and a methodology for attaining it, Hume denies that there is a criterion for objective truth, and argues that our best methodology can only aim at cultivating habits that are useful in the course of experience (Hatfield 1990, p. 63). For Hume, the normative aspect of epistemology is limited “to offering recommendations for cultivating useful habits” (Hatfield 1990, p. 64). Hume, however, appealed to the failure of direct intellectual intuition in particular cases to reject its use to establish the possibility of objective knowledge. Nevertheless, Hume must acknowledge some room for error, even if it is only enough to warrant drawing a distinction between those habits that are useful in the course of experience and those that are not. Berkeley, by contrast, used the theory of ideas and his own theory of spatial perception in order to deny the existence of material substance, by denying that we are unable to form any coherent conception of matter itself (Hatfield 1990, p. 58). His first argument is against the abstract idea of substance in

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general: “when I consider the two parts or branches which make the signification of the words material substance, I am convinced there is no distinct meaning annexed to them” (Berkeley 1710, I.17). His second argument is against the abstract ideas of extension and motion: when we attempt to abstract extension and motion from all other qualities, and consider them by themselves, we presently lose sight of them, and run into great extravagancies, All which depend on a twofold abstraction: first, it is supposed that extension, for example, may be abstracted from all other sensible qualities; and secondly, that the entity of extension may be abstracted from its being perceived. But whoever shall reflect, and take care to understand what he says, will, if I mistake not, acknowledge that all sensible qualities are alike sensations, and alike real; that where the extension is, there is the color too, to wit, in his mind, and that their archetypes can exist only in some other mind: and that the objects of sense are nothing but those sensations combined, blended, or (if one may so speak) concreted together: none of all which can be supposed to exist unperceived (Berkeley 1710, I.99). Besides Berkeley’s arguments against the abstract notions of material substance, extension and motion, he also uses his theory of distance perception to deny that the objects of touch and sight exist in a common, external space. In paraphrasing his theory of distance perception from the Essay towards a New Theory of Vision, Berkeley asserts that distance… is neither immediately of itself perceived by sight, nor yet apprehended or judged of by lines and angles, or anything that has a necessary connection with it: but that it is only suggested to our thoughts, by certain visible ideas and sensations attending vision, which in their own nature have no

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manner of similitude or relation, either with distance, or things placed at a distance (Berkeley 1710, I.43). This is so because the ideas of sight and touch make two species, entirely distinct and heterogeneous. The former are marks and prognostics of the latter.… in strict truth the ideas of sight, when we apprehend by them distance and things placed at a distance, do not suggest or mark out to us things actually existing at a distance, but only admonish us what ideas of touch will be imprinted in our minds at such and such distances of time, and, in consequence of such or such actions.… visible ideas are the language whereby the governing spirit, on whom we depend, informs us what tangible ideas he is about to imprint upon us, in case we excite this or that motion in our own bodies (Berkeley 1710, I. 44). As we have seen, in the early modern period, philosophers distinguished themselves by staking out what often seem to be all of the logically possible positions with respect to the relationship between the physical and the mental realms. Nevertheless, none of them was able to make a good enough case for his position to convince the others. 3.4

Kant With Kant, things took a different turn. Even if Kant was not ultimately

successful in effecting a “Copernican revolution” in philosophy, we must nevertheless admit that his influence has been dramatic. Moreover, as I shall argue, his view that spatial representation is the fundamental form of representation, although held for the wrong reasons and subsequently largely lost

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to analytic philosophy, is an important insight into the nature of representation, one to which it is time to return. Although Hobbes may have been the first to remark that the concept of a thing without the mind requires a concept of space, Kant was the first to argue in detail that the concept of space is prior to the concept of an independently existing world. This view was not fully developed until the Critique of Pure Reason but its origins lie in Kant’s inaugural dissertation of 1770, On the Form and Principles of the Sensible and the Intelligible Worlds. In that work, Kant first argued that space is a pure intuition, a form of representation that underlies our ability to experience objects: “the possibility of outer perceptions, as such, presupposes… the concept of space” (Kant 1770/1928, §15 A). Kant believes that space is “pure”–i.e., not derived from sensation, or nonempirical – because of the “‘necessity’with which the nature of space forces itself upon our attention as precisely what it is and not otherwise” (Kant 1770/1928, §15 A) or “because of [the] identity of its so-called particulars with its so-called general term” (Kant 1770/1928, §15 B). Space is neither an object nor a quality of an object. Any “particular” space (e.g., “this space” or “that space”) has all the characteristics of “space” in general, whereas other particulars (e.g., “the person Aarre”) have more than the characteristics of their general terms (“person”). Space is “intuitive”— i.e., not derived by inference, or reflection— because of the “immediacy with which this necessary character displays itself” (Kant 1770/1928, §15 B, C). The argument, in short, is that knowledge of space is immediate, whereas knowledge of other universals is

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derived. There is no distinction between a spatial particular and space in general, whereas there is an important distinction between particulars such as “the tree on my lawn” and trees in general. Our knowledge of space is not obtained by abstracting qualities from particular spaces – to know any one space is to know space in general. This is in contrast with other sorts of things; our knowledge of trees, for example, is abstracted from our familiarity with particular trees. In the case of every other sort of thing, there is a distinction between the particular and the universal; but in the case of space (and time), there is no such distinction. Our knowledge of space and time is a priori (cf. Garnett 1939, pp. 127-9). The conclusion of the 1770 work is that “space is given originally through the nature of the mind” (Kant 1770/1928, §15 A). However, in the work of 1770, there was nothing to suggest what was to become the most characteristic feature of Kant’s theory of spatial representation: that the concept of space is necessarily prior to experience. As Garnett puts it, in the early work, there is nothing “to suggest that that space is prior to experience either temporally or logically. Space does not lie in the mind, nor is it prior to sensation. It is merely not given in sensation, and, unlike the objects of sensation, it has a necessary nature” (Garnett 1939). Garnett also points out a difficulty with the general form of argument that Kant uses in the inaugural dissertation: Kant’s argument ran roughly as follows: since space is nonempirical and different from general conceptions, therefore it is a pure intuition… .A silent assumption underlies this entire body of argument: a nonempirical representation is a necessary representation, and a necessary

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representation is nonempirical. Unlike the intuitive nature of space, which depends upon a different argument, its ‘pure,’necessary nature is assumed to be the outcome of its nonempirical character. The doctrine that space is nonempirical in its source is, however, quite different from the view that it has a necessary nature (Garnett 1939, p. 165). Garnett goes on to point out Alexander’s argument that one may hold that space is nonempirical without holding that it has a necessary nature by taking a sufficiently broad view of experience (Alexander 1934). However, Garnett argues, Kant was justified in using this hidden premise because he held the view “that experience refers only to the contents of sense perceptions… .Now all such contents are relative and contingent whereas space has a necessary nature. Hence to establish its necessary nature meant to establish its nonempirical nature, and vice versa” (Garnett 1939, p. 165). In the Critique, as we shall see, Kant avoided this difficulty by separating his theory of the nonempirical nature of space from his theory of the necessity of space. In the 1770 work, Kant also gives a second argument, based on “incongruent counterparts,” that space is a pure intuition. Incongruent counterparts are things like left and right hands, which are, as we would say today, topologically identical but rotated through a fourth dimension in Euclidean space. In order to comprehend the difference between the two hands, we must actively reflect on the nature of space. When we attempt to grasp the difference between the left hand and the right hand, we must construct in our minds the spatial relations that parts of each hand bear to other parts of the same hand.

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When we reflect on this construction, we see that the spatial relations between the parts of the hand are identical for the left hand and the right hand. Yet, there is no way to move the left hand so that it corresponds to the right hand. In reflecting on this difficulty, we come up against the nature of space itself. We grasp the essence of space as the relations that objects bear to each other. Of course, the example of incongruent counterparts is deceptive because it forces us to actively construct a notion of space, whereas it is precisely Kant’s point that no such activity or construction is necessary. For Kant, the representation of objects in space is not formed by a process of abstraction, nor is it a matter of judgement (the sort of thing about which we could be right or wrong). In contrast with the categories, the forms of intuition (space and time) do not require any sort of activity on the part of the subject. They are necessary, automatic, and inescapable. The point of the second, constructive argument based on incongruent counterparts is only to emphasize that the origin of our concept of space is different from the origins of general concepts like that of tree. Kant’s critical turn, generally dated from the publication of the Critique of Pure Reason in 1781, marks Kant’s departure from Descartes’ method of establishing the possibility of objective knowledge by appealing to direct intellectual intuition. Kant argued that it is impossible in principle to justify an explanation of the possibility of direct intellectual intuition. The only grounds for such an explanation would appeal to a harmony preestablished by a benevolent deity between the intellect and a mind-independent reality. But knowledge of that

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deity and its benevolence could only be established by direct intellectual intuition, thus presupposing the very capacity it was supposed to legitimate (Kant 1781/1787, B167-8; Kant 1977, §36 (319, n. 34); Hatfield 1990, pp. 78-9). Because Kant rejected Descartes’ method of establishing the possibility of objective knowledge, and because he saw no other alternative, Kant pursued the task of explaining the possibility of objective knowledge by transcendental characterization of the subject’s contribution to knowledge. Transcendental argument starts from a given cognitive achievement; if it can be shown that the cognitive achievement is possible in only one way, then, given that the achievement is actual, the only possible means for its possibility must be actual, too (Hatfield 1990, p. 79). Therefore, transcendental knowledge (knowledge arising from transcendental arguments) is not trivially analytic in the sense of being knowledge arising merely from the analysis of given concepts (Kant 1781/1787, A64-6/B89-91, A783/B811, A787-8/B815-6; Hatfield 1990, p. 305, n. 50). Among the starting points for Kant’s transcendental arguments is the fact that we have objective (i.e., intersubjective) experience. In the Critique of Pure Reason, especially in the Transcendental Aesthetic, Kant gives a number of arguments that space is a pure a priori intuition. Some of them are expanded and redeployed versions of the arguments from the inaugural dissertation; others are entirely new. Kant’s view of space as a pure intuition led him to the view that space is prior to experience. Because the representation of

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space is necessary, it is not given in experience, and therefore must be given prior to experience. In the Aesthetic, Kant argues that objects must be immediately given to us for mental representation to be possible: “In whatever manner and by whatever means a mode of knowledge may relate to objects, intuition is that through which it is in immediate relation to them, and to which all thought as a means is directed” (Kant 1781/1787, A19/B33). Experience relates immediately to objects through the intuition. Intuition is here a simple conduit for objects to enter the mind. However: intuition takes place only in so far as the object is given to us. This again is only possible, to man at least, in so far as the mind is affected in a certain way. The capacity (receptivity) for receiving representations through the mode in which we are affected by objects, is entitled sensibility. Objects are given to us by means of sensibility, and it alone yields us intuitions; they are thought through the understanding, and from the understanding arise concepts. But all thought must, directly or indirectly, by way of certain characters, relate ultimately to intuitions, and therefore, with us, to sensibility, because in no other way can an object be given to us (Kant 1781/1787, A19/B33). For objects to be given to us, they must affect the mind in certain ways, through our faculties of sensation. We sense appearances: “The effect of an object upon the faculty of representation, so far as we are affected by it, is sensation. That intuition which is in relation to the object through sensation, is entitled empirical. The undetermined object of an empirical intuition is entitled appearance” (Kant 1781/1787, A20/B34).

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While appearances are what we sense, sensations (appearances) can stand in certain ordering relations (the tree can be to the left of the car, the firework may be seen before it is heard, etc.). Kant calls that which determines these ordering relations the forms of appearance. Sensations cannot order themselves in a certain form, because sensations are only appearances, not forms. Forms, therefore, must be a priori: That in the appearance which corresponds to sensation, I term its matter, but that which so determines the manifold of appearance that it allows of being ordered in certain relations, I term the form of appearance. That in which alone the sensations can be posited and ordered in a certain form, cannot itself be a sensation, and therefore, while the matter of all appearance is given to us a posteriori only, its form must lie ready for the sensations a priori in the mind, and so must allow of being considered apart from all sensation (Kant 1781/1787). Because forms are a priori, we must be able to consider them in the absence of and apart from any sensation – as pure representations. Pure representations exist in the mind a priori, even without any actual objects of sensation. By abstracting away from cognition and even sensation, we discover that space is a pure representation: if I take away from the representation of a body that which the understanding thinks in regard to it, substance, force, divisibility, etc., and likewise that which belongs to sensation, impenetrability, hardness, colour, etc., something still remains over from this empirical intuition, namely, extension and figure (Kant 1781/1787, A20-1/B34-5).

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Aquila considers this an argument of the following form. (1) The forms of intuition are those features in virtue of which an intuition is an awareness of an object. (2) It is possible, in imagination, to experience an intuitional state in which the object is simply a spatial expanse. (3) Therefore, the representation of spatial form is a sufficient condition for the occurrence of intuition (Aquila 1983, p. 67). Or, as Aquila later puts the conclusion, the representation of shape is a necessary and a sufficient condition for the kind of object-directedness that an internal state requires considered independently of its sensory causes. Aquila calls this argument the phenomenological reflection: “it is simply phenomenologically evident that ‘stripping away’mere sensory clothing from our representation of bodies in space, we arrive at a kind of pure imagination of spatial regions” (Aquila 1983, pp. 80-1). Or as he later puts it, Kant regards “the imagining of spatial forms as a mode of presentation with particulars of a spatial sort, namely imagined regions of space” (Aquila 1983, p. 99). As a result, on Kant’s account: pure intuition always involves a genuine activation of the referential capacities of our cognitive nature. For whatever conceptual or predicative elements might be present in some instance of pure intuition, they could only be functioning as part of our attempt to conceptualize some imagined object presented in that intuition. So there is an objectdirected element in every sensory awareness that is already ingredient in the internal ‘form’of that awareness, quite apart from external considerations concerning mind-independent reality (e.g., apart from reference to other possible perceptions) and over and above whatever intentional elements are

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introduced by the particular concepts in question (Aquila 1983, p. 99). Another way of putting the point is that “concepts applied to instances of imaginative representation are always applied in order to conceptualize some imagined region of space. This imagined region of space must therefore possess a content whose presence is not wholly a function of those concepts themselves” (Aquila 1983, p. 99). Or yet another way: “intuitive representations always contain intrinsic yet nonconceptual features helping to determine their objectdirected character. If they didn’t, then we could never account for the phenomenological fact that attachment of concepts to an intuition serves precisely to conceptualize some (at least possible) object presented in that intuition” (Aquila 1983, p. 99). Hence, the concept of space must be a priori because we could not have acquired our ability to represent space through experience. Our identification of material bodies (objects) is dependent on our representation of space: “By means of outer sense, a property of our mind, we represent to ourselves objects as outside us, and all without exception in space” (Kant 1781/1787, A22/B37). As it stands, this is merely a claim about the fact of spatial representation: in fact, we represent objects in space by means of our minds. But Kant further claims that it is impossible for us to do otherwise: “For I may not conceive of something as placed outside me unless by representing it as in a place which is different from the place in which I myself am, nor may I conceive of things outside one another unless by locating them at different places in space” (Kant 1770/1928, §15A,

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2:402). The concept of space is not an empirical concept; it could not have been learned by sensation. In order to sense something outside of me, I must already be able to represent it as outside me. Therefore, I cannot learn to represent space by considering the relations between objects outside of me; on the contrary, I can only sense the relations of objects outside of me if I can already represent objects as outside of me. Kant writes: Space is not an empirical concept which has been derived from outer experiences. For in order that certain sensations be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must be presupposed. The representation of space cannot, therefore, be empirically obtained from the relations of outer appearance. On the contrary, this outer experience is itself possible at all only through that representation (Kant 1781/1787, A23/B38). In other words, our experience of objects outside of ourselves (in the language of Chapter 2, objective experience) requires that we have a prior concept of space. Kant is arguing that the ability to represent space is innate. We cannot acquire the ability to represent space, because any experience from which it could be acquired would be an experience of the “outside” relation and therefore itself an experience of space. (As we have seen, a similar argument also appears in Section 15A of the inaugural dissertation (Kant 1770/1928).) Having argued for the a priority of spatial representation, Kant goes on to argue that it is a necessary feature of experience. The argument above is followed

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in the Critique by a second argument that takes the a priori nature of space for granted and emphasizes its necessity in experience: Space is a necessary a priori representation, which underlies all outer intuitions. We can never represent to ourselves the absence of space, though we can quite well think it as empty of objects. It must therefore be regarded as the condition of the possibility of appearances, and not as a determination dependent upon them. It is an a priori representation, which necessarily underlies outer appearances (Kant 1781/1787, A24/B38-9). In this passage, Kant’s emphasis is not so much on the a priority of spatial representation as its necessity in experience. The representation of space is not only a priori, but also necessary, because we cannot have experience without it (cf. Allison 1983, pp. 86-9). Kant also uses a version of the argument developed in the inaugural dissertation to buttress his claim that the concept of space is a priori. To begin with, he argues that there can be only one concept of space, whereas there can be many particulars of almost every other kind of thing: “we can represent to ourselves only one space; and if we speak of diverse spaces, we mean thereby only parts of one and the same unique space” (Kant 1781/1787, A25/B39). Hence, we cannot have learned our concept of space the way that we learn our concepts of other universals, by abstracting properties from a set of particulars. In the case of the concept of space, unlike in the case of the concepts of tree or animal, there are no particulars from which to abstract. Other concepts, like tree or animal, determine an arbitrarily large number of particular instantiations (i.e., particular

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things with the necessary properties), but they do not contain their particulars. The concept of space, on the other hand, does not determine its particulars. Rather, it contains them. One might think that the separate parts of physical space (my bedroom, say, versus my office at the University) are actually particular instances of the general type space. In that case, perhaps the concept of space in general could somehow be extracted from experiences of these particulars in the way that the concept of tree is extracted from experiences of particular trees, or that the concept of animal is extracted from experiences of particular animals. Kant denies that this is possible: “these parts cannot precede the one all-embracing space, as being, as it were, constituents out of which it can be composed; on the contrary, they can be thought only as in it. Space is essentially one” (Kant 1781/1787, A25/B39). Our concept of space, unlike any of our other concepts (except perhaps that of time) is singular. All space is the same space. Supposedly “different” spaces, like my bedroom and my office, are contained of the whole, but they are not parts of it in the sense that an engine is a part of a car, nor are they separate particulars from which the general concept is abstracted. Our concept of separate spaces relies on introducing limitations into the general concept of space as a whole; thus, my office and my bedroom are two separately delimited regions of space in general. However, space in general is not a concept abstracted away or composed of individual spaces; the whole comes first, and then the parts are identified. In this respect, the concept of space is unlike any other kind of concept:

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it cannot have been learned by generalizing from particular spaces, because the concept of space in general is logically prior to the concept of a particular space. Therefore, the concept of space must be a priori. As Kant puts it, “it follows that an a priori, and not an empirical, intuition underlies all concepts of space (Kant 1781/1787, A25/B39). We cannot have learned the concept of space through experience, because experience itself requires that we already have the concept of space. This is, as I have mentioned, another version of the argument Kant first developed in the inaugural dissertation. All empirical concepts allow for a difference between particular and general. The general concept tree subsumes many particular trees, the general concept animal subsumes many particular animals, and so on. However, the concept of space admits no such distinction. There is no notion of a general space that subsumes particular spaces, because space is essentially a single unity. “Different” spaces are really just parts of space, whereas different trees are not parts of the universal tree. In the “Transcendental Exposition of the Concept of Space”, Kant gives a different kind of argument that the concept of space is a priori, based on the possibility of geometrical knowledge. Some have taken these arguments to be Kant’s fundamental arguments for the a priori nature of the concept of space. For example, Hatfield writes that Kant “was committed to the apriority of space as a form of representation because he needed a foundation for the necessity he found in Euclidean geometry” (Hatfield 1990, p. 121). However, Henry Allison has

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argued, convincingly to my mind, that Kant’s main argument for objectivity was not the argument from the assumed validity of Euclid’s geometry, but rather the arguments from the Metaphysical Exposition that we considered above (Allison 1983, Chapter 5). Kant begins the argument from geometrical knowledge by asserting the by now familiar claim that “our representation of space… must be found in us prior to any perception of an object” (Kant 1781/1787, B40-1). In this case, however, he justifies that claim on the grounds that his explanation of spatial representation as a priori is “the only explanation that makes intelligible the possibility of geometry, as a body of a priori synthetic knowledge” (Kant 1781/1787, B41). Geometry is synthetic knowledge in that its theorems give us truths about the world (the world of appearances, at least) that go beyond its axioms. In order that such knowledge may be possible, our representation of space must be representational in origin. From a concept, no propositions can be obtained which go beyond the concept; all merely conceptual knowledge is analytic. Geometry, however, gives us knowledge about the world of appearances, knowledge that goes beyond the axioms of geometry. Kant believes that the only way that we can explain our knowledge of geometry is by taking our concept of space to be a priori. Taking space as an a priori representation is the only explanation that makes sense of the possibility of geometry as a body of a priori synthetic knowledge. The consequence is that “Space does not represent any property of things in themselves” (Kant 1781/1787, A26/B42), nor does it represent them in

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their relation to one another. Space is not determined by objects themselves (it does not remain when we have abstracted from all the subjective conditions of representation), because nothing can be determined before the existence of the things that determine it. Space is, rather, “nothing but the form of all appearances of outer sense… .the subjective condition of sensibility, under which alone outer intuition is possible for us” (Kant 1781/1787, A26/B42). Space is not a property of objects; rather, it is the form in which our experience of objects is presented to us. Space does not represent any property of things in themselves; it is nothing but the form of all representations. Space is the subjective condition of all sensation; without it, outer perception is impossible for us. Therefore, because a subject’s capacity to be affected by objects must necessarily precede all representations of these objects, the form of all representations must be given before any actual perceptions (and so exist in the mind a priori). Moreover, the form of all representations, as a pure representation, by which all objects must be determined, must contain, before any experience, principles that determine the relations of these objects. Therefore, we can only speak of space from the human point of view. If we abandon the subjective condition of being liable to be affected by objects, then the representation of space stands for absolutely nothing. The predicate spatial can be ascribed to things only as they appear to us, that is, only to objects of sensation. We can perceive objects as outside of us only if we can represent space; and if we abstract from these objects, it is a pure representation. The

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conditions of sensation are not conditions on the possibility of things themselves, but conditions on the possibility of the appearances of things. Therefore, we can say that space encompasses all things that appear to us as external, but not all things in themselves. We cannot know whether the representations of other thinking beings are bound by the same conditions that limit our representations. All things are side by side in space, under the limitation that these things are viewed as objects of our representations. That is, all things, as outer appearances, are side by side in space. Therefore, space is real (objectively valid) with respect to whatever can be presented to us outwardly as object. At the same time, space is ideal with respect to things in themselves, that is, without regard to the makeup of our sensory systems. Space is empirically real, with regard to all possible outer experience; at the same time, space is transcendentally ideal, meaning that it is nothing at all if we do not limit it to possible experience and look on it as something that underlies things in themselves. Space is the only subjective representation of something outer that is both objective and a priori. There is no other subjective representation from which we can derive a priori synthetic representations. Therefore, other subjective representations are not ideal, even though they are like the representation of space in belonging only to the subjective constitution of our sensory systems. For example, the sensations of color, sound and heat are merely sensations and not representations, and therefore do not by themselves yield knowledge of any object, let alone any a priori knowledge.

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Colors, tastes, etc. are not properties of things, but only changes in the subject, changes that may be different for different people. Nothing perceived in space is a thing in itself. Space is not a property of things in themselves. Objects in themselves are completely unknown to us. What we call “outer objects” are only representations in our sensory systems, the form of which is space. The true correlate of sensation, the thing in itself, cannot be known by these representations. In experience, no question is ever asked about the thing in itself. Kant concludes from these arguments that space is subjective; it is a property of our experiences, but not of things-in-themselves. An outer perception which precedes objects themselves, and in which the concepts of these objects can be determined a priori, can exist in the mind only insofar as the perception has its seat in the subject only. It is only from the human standpoint, with respect to things as they appear to us that we can speak of spatial relations, extension, etc. (Kant 1781/1787, A26-7/B42-3). Everything that appears to us as an external object appears in space, but it makes no sense to say of the things-in-themselves that they exist in space, that they stand in spatial relations to one another, that they are extended, etc. Space is objectively valid only for us as experiencers: it is empirically real but transcendentally ideal (Kant 1781/1787, A28/B44). Or, in other words, “nothing intuited in space is a thing in itself,… space is not a form inhering in things in themselves as their intrinsic property,… objects in themselves are quite unknown to us, and… what we call outer objects are nothing but mere

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representations of our sensibility, the form of which is space” (Kant 1781/1787, A30/B45). The representation of space is necessarily a priori. Although we can think of space as absent of objects, we can never represent to ourselves the absence of space. The representation of space must therefore be regarded as a condition of the possibility of experience. The representation of space cannot be learned from experience. Kant gives parallel “Metaphysical” and “Transcendental” expositions of the concept of time. Although these are equally important, practical considerations of space and time prevent me from presenting them here. A consideration of the fundamental role of time in representation is material for another project. Many psychologists have taken passages in Kant about the connection between spatial representation and objectivity as evidence that Kant was a nativist about space perception (Boring 1942, pp. 28 and 233; Wertheimer 1979, pp. 37-8, 41; Leary 1982; Lowry 1982, pp. 18-21, 65-6, and 80). Hatfield, however, argues that while Kant clearly thought that the ability to represent spatial relations in general could not be acquired though experience, he was not a nativist about visual space perception (Hatfield 1990, pp. 102-7). Hatfield believes that “On the one hand, Kant believed that our cognitive faculties are so constituted that all sensory intuitions are conditioned by the rule that they must be disposed in space as described by Euclid’s geometry. On the other hand, he accepted the typical

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eighteenth-century doctrine that we must learn to see a world of threedimensional objects” (Hatfield 1990, p. 106). This is true because “Kant’s doctrine of the aprioricity of space merely maintains that our sensibility must be such that our perceptions must occur within the framework of three-dimensional space. This transcendental fact does not guarantee that the sense of vision is innately disposed to generate spatially elaborated perceptions of a threedimensional world at the onset of optical stimulation (or after a brief period of maturation)” (Hatfield 1990, p. 106). In other words, “the faculty of sensibility must develop in such a way that… sensations come to be ordered within a threedimensional framework. Yet this a priori condition on the form that any representation of outer sense may take does not guarantee that our original visual representations will be representations of the three-dimensional world of adult experience” (Hatfield 1990, p. 107). This is an extremely important point for our purposes. It shows that Kant’s contribution to the problem at hand is not that the representation of space as a three dimensional manifold available to the visual system is a priori and necessary for experience. Rather, Kant’s contribution is that the representation of space in general is a priori and necessary for experience. We shall have to put off for later a discussion of precisely what the representation of space in general means. Precisely what this means will become clear in Chapter 4 and Chapter 5.

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3.5

The Twentieth Century Kant’s insights about the centrality of spatial representation for

representation in general have largely been lost on twentieth-century analytic philosophy (with the exception of Strawson, to whom most of the next two chapters are devoted). In part, this was because of the influence of positivism and its rejection of essentially all metaphysics, especially Hegel’s speculative metaphysics. Kant was condemned by his association with Hegel. In part, it was because of the influence of Frege and Russell and the “linguistic turn” that they initiated, the primary consequence of which was that the fundamental form of representation came to be seen as linguistic representation, not spatial representation. And in part, it was because of the influence of the rise of the digital computer as the dominant metaphor for the mind. In fact, the second two factors are related, given the intimate relation between the linguistic model of representation (the “language of thought”) and the computer model of mind, which Fodor has so forcefully articulated in virtually all of his philosophical work. Indeed, one could say without exaggeration that all three factors are in a certain sense the same, for it was largely through the writings of the positivists and their contemporaries that the intimate relations between logic, language, and computation came to be widely appreciated in the philosophical and mathematical communities. As we have seen in Chapter 2, in the late 19th century Brentano presented a formidable challenge to any reduction of the mental to the physical. The first

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attempts to surmount it were various versions of behaviorism, including Carnap’s reductive behaviorism and Ryle’s non-reductive version. As Chisholm, Taylor, Davidson, and others have forcefully pointed out, both kinds of behaviorism seem to be dead ends. The ascription of mental states is ultimately far too holistic and subject to rational, interpretive constraints for any simple behavioristic reduction to be remotely plausible, and no coherent version of non-reductive behaviorism has ever been given, to my knowledge. Reactions to these developments were extreme. Sellars pointed out that one could view propositional-attitude psychology as a kind of theory very much like a developing scientific theory, unobservable entities and all. It then became possible for Feyerabend, Rorty, and Churchland to assert that propositionalattitude psychology was simply false and useless and so would be eliminated in the fullness of time, and for Dennett to assert that it was false but also happened to be useful. These reactions, as the saying goes, threw the baby out with the bathwater. Propositional-attitude psyhology is useful, indeed, one might say, indispensible. And the most likely explanation for its utility is, it seems to me, that it is at least partially true. Until the 1980’s, the only plausible theories that might explain the successes of propositional-attitude psychology in physicalistic terms were all varieties of computational functionalism. Computational functionalism (sometimes referred to as the Classical view, or as Good Old Fashioned Artificial Intelligence – GOFAI) asserts that the mind is a computer in the sense that

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thoughts (and other propositional attitudes) are simply the tokenings of symbols (syntactic tokens) in appropriately causally-connected ways. On this view, the representational vehicles of mental content are syntactic tokens devoid of semantic properties. This has made the problem we are concerned with (the problem of explaining the intentionality of the propositional attitudes, or the objectivity of experience, or the normativity of thought – take your pick) has come to be a central problem in the contemporary philosophy of mind. It is known as the “problem of mental content”. Views about mental content are as numerous as philosophers of mind, and perhaps more so. There are essentially two kinds of theories. The first kind are theories that take the content of a token to be determined by its causes. These are variously called “covariance semantics” or “informational semantics”. The view known as “teleological semantics” is also a view of this kind, although a somewhat more sophisticated one. The second kind of theories are those that take the content of a token to be determined by the kind of role it plays in the system Versions of this kind of theory include “causal role semantics”, “functional role semantics”, “computational role semantics”, and “conceptual role semantics”. The basic idea behind covariance semantics (Fodor 1987) or informational semantics (Dretske 1981) is that mental state tokens represent the things or properties that reliably cause them. The fundamental problem with this kind of view is obvious: it becomes very difficult to deal with cases of misrepresentation. If a token means “horse” in virtue of being caused by horses, how could a person

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ever mistake a cow for a horse? That is, how could a state with the content That’s a horse ever be caused by something not a horse, if what it is for a state to mean That’s a horse is for it to be caused by horses? On covariance views, it is the very fact that the state is caused by horses that gives it the content horse. A covariance theory asserts that “S” means S just in case all and only S's (withing perceptual range) cause “S”-tokens. There are problems with both directions of the biconditional: read in either direction, it seems to make misrepresentation impossible. On the one hand, if “S” means S just in case only S's cause “S”tokens, then how could a T ever cause an “S”-token. For example, how would it be possible for us to mistake a cow-on-a-dark-night for a horse? On the other hand, if “S” means S just in case all S's cause “S”-tokens, then how could an S ever cause a “T”-token? Again, how would it be possible for use to mistake a cow-on-a-dark-night for a horse? One evident way of explaining misrepresentation on a covariance-type view is to idealize: a state has the content S just in case it is reliably caused by S's under ideal conditions. This is the solution that Dretske (1981) uses. The difficulty with this view is obvious: how should “ideal conditions” be spelled out, exactly? Dretske’s solution has been subject to a series of counterexamples and revisions that reminds one uncomfortably of the Gettier-problem literature of 1960’s epistemology. Fodor's solution to the problem of misrepresentation for his covariance theory is a bit different, although no less problematic. He appeals to the notion of

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asymmetrical dependence. Roughly, the idea is that the fact that “horse” means horse even though it is sometimes caused by cows depends on the fact that cows couldn't cause “horse”-tokens unless horses caused “horse”-tokens, but horses would cause “horse”-tokens regardless of whether or not cows did. The problem with this sort of view, simply put, is that the explanation depends on a metaphysical device (“possible world semantics”) that is even more suspect than what it is supposed to explain (mental content). According to functional role theories of representation, a representational state has the content it has in virtue of its functional role. Its functional role is just the part it plays in the behavior of the system of which it is a part. There are at least two varieties of functional role theories: causal role theories and computational role theories. They differ on what sort of role determines the content of a given state – whether the causal role or computational role. A causal role is a position in a network of possible causes – the meeting point of the set of things that may cause the state and the set of things the state may cause. A computational role is a position in a network of possible computational states – the meeting point of the set of states that may lead to a given state and the set of states that may result from it. Because many different causal systems can instantiate the same computational architecture, a state with a given computational role may be instantiated by states with many causal roles. That is, computational roles individuate contents more coarsely than do causal roles.

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According to conceptual role theories of representation, a representational state has the content it does in virtue of the role it plays in the cognitive process of inference. The conceptual role of a representational state S is a position in a network of possible inferences. In particular, it is the meeting point of the states from which S may be inferred and the states that may be inferred from S. For example, the state with the content This is a fruit might be caused by states with such contents as This is an apple, This is a banana, and This is a pear, as well as cause states with such contents as This is good to eat. According to conceptual role semantics, the content of This is a fruit is constituted by its position with respect to the others. The problem with all of the “role” theories of semantics – conceptual role semantics, causal role semantics, computational role semantics, and functional role semantics – is that they all apparently lead to an intolerable kind of holism. If I like fruit and you don't, it seems that we have different attitudes toward the same thing. However, all of the role theories would have to insist that we are really thinking about different things, since the two concepts play different roles in our respective conceptual, causal, computational, or functional networks. At first glance, one might think that this is not such a big deal. After all, so what if we mean slightly different things by “fruit”? There are a number of reasons, however, why it is much worse than it appears at first glance. One is learning. It is at least plausible that, in learning a language, we learn it bit by bit. That is, we come to understand some small portion of the language, then

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incrementally add to this portion until we understand the whole thing. If, however, the meanings of our words are determinate only relative to the entirety of our language, then it seems that I cannot learn only part of a language. Any part of such a language is, in effect, a different language. I have been emphasizing mental representation rather than linguistic representation, so it may not be evident how the point about language learning is relevant. But there is an exact parallel with understanding. It is intuitively plausible that at least some forms of communication (e.g., persuasion) are successful only insofar as the hearer comes to believe the same thing as the speaker. However, if holism is true, hearer and speaker can only share any belief as long as they share all of their beliefs. That seems ridiculous on the face of it: surely I can share some beliefs with you (e.g., that grass is green), without sharing all your beliefs. Moreover, if two people did share all of their beliefs, then it is unclear why communication would be necessary in the first place. For our purposes, though, the most important reason that holism would be unacceptable that it would preclude psychological explanation. Psychological explanations quantify over individuals in virtue of the contents of their mental states. Thus, for example, if we ask questions like “Why did Mary wave her hand?”, we get answers like “Mary believed that her friend Joe was standing across the street. Mary wanted to say ‘hi’to Joe. All other things being equal, people who want to greet others in contexts where speaking is impractical wave their hands. Therefore, Mary waved her hand.” Notice in this case that the

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explanation appeals to a law (“All other things being equal, people who want to greet others in contexts where speaking is impractical wave their hands”) that adverts to the contents of people's mental representations (wanting to greet others and believing that speaking is impractical). However, if holism is true and different individuals do not share the same belief contents, this sort of explanation is impossible. 3.6

Conclusion In the course of this (admittedly perfunctory) survey of the history of the

philosophy of mind, we have seen that the problems I identified in Chapter 2 have been central problems throughout the history of philosophy. Since its beginning, philosophy has struggled to explain the relation between mind and matter, the intentionality of the propositional attitudes, the objectivity of experience and the normativity of judgement in physical terms. All of the attempted solutions have been unsatisfactory for one reason or another. Recently, most attempts to solve these problems have taken the fundamental form of representation to be linguistic and the fundamental mechanism of cognition to be computation. We have seen hints, however, of a neglected alternative in Kant’s argument that spatial representation is the fundamental form of representation. In the next two chapters, I turn to Strawson’s interpretation of Kant’s views on spatial representation, and show that the conclusion we should draw from these arguments is that the fundamental form of representation is representation in space, not representation in language.

Chapter 4 Strawson 4.1

Abstract I have suggested in the previous chapters that Kant’s view that spatial

representation is the fundamental form of representation may provide an alternative to the popular belief that the fundamental form of representation is linguistic representation. In so doing, Kant’s view might provide a solution to the problems of explaining the intentional, objective and normative features of the representational in naturalistic terms. The time has come to make good on that suggestion. I do so in this chapter by considering Strawson’s Kantian arguments in Individuals and The Bounds of Sense. I use Strawson not because I think he is the best interpreter of Kant (he is not, but I am not trying to defend Kant here), but because Strawson’s arguments are closer to those that I wish to make than Kant’s are. Hence, Strawson provides a kind of “middle ground” between Kant and myself. My views emerge naturally in the context of my interpretation of Strawson (again, not as an interpreter of Kant, but on his own terms). In what follows, I shall be moving back and forth between Individuals and The Bounds of Sense. The arguments in the two books are somewhat different but they are also very similar and for my purposes the similarities are more important than the differences. I also distinguish two arguments. The first, which I call the “here-now” argument, first appears in Chapter 2 of Individuals (the “Sounds” chapter), and can also be found in The Bounds of Sense. The second, which I call

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the “persons” argument, first appears in Chapter 3 of Individuals (the “Persons” chapter), and can likewise be found in The Bounds of Sense. 4.2

The Importance of Mathematical Space The question Strawson presents for himself in the famous “Sounds”

chapter of Individuals is whether there could be “a scheme, providing for a system of objective particulars, which was wholly non-spatial” (Strawson 1959, p. 62). By considering this question, Strawson attempts to establish that objectivity (objective experience) requires the representation of space. In introducing this question, Strawson echoes his definition of objective particulars, referring to the “distinction made by the user of a conceptual scheme between himself and his own states on the one hand, and other particulars of which he has knowledge or experience on the other” (Strawson 1959, p. 64). In order to answer the question whether there could be a non-spatial scheme that provided for objective particulars, Strawson considers an imaginary sound world, in which auditory particulars are the only particulars. Restricting his consideration to a purely auditory universe gives Strawson a reason to give a more detailed argument for his switch from the numerical concept of objectivity to the metaphysical one. If a sound is to be public it must be possible “that different people may hear one and the same particular sound” (Strawson 1959, p. 67). To make sense of this, “we must give meaning, in auditory terms alone, to the idea of other people and to the idea of their being in identical particular surroundings” (Strawson 1959, p. 68). But this presents a

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challenge, because “the sounds in terms of which we were to give sense to this idea would themselves have to be public sounds; otherwise, they could not provide particular-identity of surroundings for the different enjoyers of auditory experiences. But it is precisely the possibility of public sounds, in a purely auditory world, that is in question” (Strawson 1959, p. 68). We may generalize this argument from the auditory world to the real world, in all of its complexity. We want to consider whether it is possible for a system of particulars to be objective without being spatial. If “objective” means “public”, then we are asking whether it is possible for a system of particulars to be public without being spatial. Then we are asking whether it is possible, in a nonspatial world, for different subjects to experience the same particulars. This is precisely the question that the version of the “here-now” argument in The Bounds of Sense has in common with that in Individuals. Indeed, the following passage, from The Bounds of Sense, expresses the gist of the argument more clearly than any passage of comparable length in Individuals: for self-consciousness to be possible… it must at least be possible to distinguish between the order and arrangement of our experiences on the one hand and the order and arrangement which objects of those experiences independently enjoy. For this, in turn, to be possible, objects of experience must be conceived of as existing within an abiding framework within which they can enjoy their own relations of co-existence and succession and within which we can encounter them at different times, these encounters yielding the merely subjective order of our experiences of them. The abiding framework, of course is spatial, is physical space (Strawson 1966, p. 27).

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As Strawson himself admits, this may not be Kant’s argument. However, as he also points out, it is a very Kantian argument. One condition on our distinguishing qualitative from numerical identity of particulars is that we must specify identity of surroundings. That is, we are asking whether it is possible, in a non-spatial world, for different subjects to experience the same particulars in the same surroundings. Because our world is wholly nonspatial, we now need to make sense of identity of surroundings in terms of identity of non-spatial particulars. But it was just the possibility of making sense of the identity of non-spatial particulars that was at question. So we are caught in a circle. Strawson escapes from this circle by resorting to the metaphysical definition of objectivity. The possibility of experiencing objective particulars is the possibility of making a “distinction between oneself and one’s states on the one hand, and anything on the other hand which is not either oneself or a state of oneself, but of which one has, or might have, experience” (Strawson 1959, p. 69). The question of whether a subject whose experience is non-spatial can experience objective particulars is the question whether a subject whose experience is nonspatial can “make use of the distinction between himself and his states on the one hand, and something not himself, or a state of himself, of which he had experience on the other?” (Strawson 1959, p. 69). A subject who can make that distinction has a “non-solipsistic consciousness” (Strawson 1959, p. 69). The first premise of Strawson’s argument is that a subject can have objective experience if

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and only if that subject can distinguish his own experiences from particulars that are not parts of his own experiences. To have objective experience, a subject must be capable of distinguishing his own experiences from other things – for the objective experiencer, not everything is one of his experiences. But what does this require? The question is what the necessary conditions are of experience of particulars that are not experiences of the subject himself. In philosophy, there is a long history of asserting that material bodies (spatio-temporal objects) are the basic particulars. According to this argument, all other particulars are ultimately constructed of or caused by material bodies. But this tradition, which goes back at least as far as Greek atomism, is metaphysical: it is an assertion about what the basic constituents of the world really are. In considering our ability to identify particulars, we are concerned with a different, epistemological, question: whether there is a kind of particular whose identification is basic in the sense that identification of all other kinds of particulars depends on identification of that kind. The question is actually somewhat meatier. Because we want a notion of identification that is adequate for full objectivity, we must face the possibility that not any form of identification will do. One task in the following will be to elucidate the precise kind of identification that is necessary to support full objectivity.

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Strawson argues that objectivity requires first of all that the existence (or temporal ordering) of particulars that are not experiences of a subject be logically independent of the existence (or temporal ordering) of the subject’s experiences. In Individuals, Strawson writes that “to have a conceptual scheme in which a distinction is made between oneself or one’s states and auditory items which are not states of oneself, is to have a conceptual scheme in which the existence of auditory items is logically independent of the existence of one’s states or of oneself” (Strawson 1959, p. 72). Despite its specificity to the sound world, this is really a quite general claim. A subject who can distinguish between his own experiences and particulars that are not his experiences must take it that the existence of particulars that are not his experiences is logically independent of his experiences. The problem is to make sense of this claim. What is the justification for the assertion that a subject can distinguish his own experiential states from particulars that are not his own experiential states if and only if the existence of particulars that are not his experiential states is logically independent of the existence of his experiential states? We might suppose that this is an instantiation of a more general claim: a subject can distinguish X’s from Y’s if and only if the existence of X’s is logically independent of the existence of Y’s. With a bit of a gloss on “logically independent,” we can paraphrase the whole thing as: a subject can distinguish X’s from Y’s if and only if the existence of X’s is consistent with the non-existence of Y’s and the existence of Y’s is consistent with the non-

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existence of X’s. Slightly more intuitively: a subject can distinguish X’s from Y’s if and only if X’s could exist without Y’s and vice-versa. It is not immediately clear why that should be true. After all, I can distinguish things on the left from things on the right, but things on the left could not exist without things on the right. (It is a familiar point that without left there would be no right, without up there would be no down, and so on). But maybe that is a trick example. I could not identify things as on the right if I could not identify things as on the left. But the relevant question is not about identification but about existence. Could things on the left exist without things on the right? Less intuitively but more precisely, is the existence of things on the left consistent with the non-existence of things on the right? I suppose it is, since I can distinguish things on the left in virtue of there being a place on the right, even though that place may contain no objects. Still, there is a need here for some sort of general argument. Why is it that distinguishability is tied to existence? In The Bounds of Sense, Strawson makes a more limited version of this claim. Rather than saying that objectivity requires logical independence of existence, he asserts that objectivity requires logical independence of temporal relations: “Experience of the objective demands the possibility of determining objective time-relations. To say that objective time-determination is possible is to say that we can assign to objects and happenings temporal relations of coexistence and succession and that we can, where necessary, distinguish these relations from the temporal relations of our perceptions” (Strawson 1966, p. 132).

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Likewise, in his consideration of Kant’s second and third Analogies, Strawson writes that “the general problem of the Analogies is… the determination of the conditions of the possibility of objective time determination” (Strawson 1966, p. 140). In order to make intelligible the notion of experience of an objective reality, we must be able “to distinguish between the subjective timeorder of perceptions and the time-relations of objects which the perceptions are perceptions of” (Strawson 1966, pp. 140-1). That is, the possibility of objectivity requires the logical independence of the temporal ordering of experiences and other particulars. We might ask why a subject of objective experience must be able to distinguish the ordering of his experiences from the objective ordering, rather than merely distinguishing his experiences in themselves from particulars that are not his experiences. Why must the subject be aware of the temporal order of his experiences and not just of the experiences themselves? More generally, why must we distinguish an experiential ordering from an objective ordering, as opposed to merely distinguishing an experience from its non-experiential object? In other words, why is it not sufficient merely to distinguish an experience from an object? Perhaps the answer is that the problem of distinguishing order seems to be easier than the problem of distinguishing existence. The next step in Strawson’s argument is the claim that the logical independence of a subject’s experiences from particulars that are not his experiences requires that it be logically possible that the particulars that are not

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his experiences should exist whether or not he is experiencing them. Strawson also makes this claim in the “Sounds” chapter of Individuals, writing that “to have a conceptual scheme in which the existence of auditory items is logically independent of the existence of one’s states or of oneself… . is to have a conceptual scheme in which it is logically possible that such items should exist whether or not they were being observed” (Strawson 1959, p. 72). It is easier to see Strawson’s justification for this claim. Suppose it is not logically possible for a subject that particulars that are not his own experiential states should exist whether or not they are being experienced. Then there cannot be particulars that are not states of the subject and that exist whether or not they are being experienced. For every particular that is not a state of the subject, either that particular exists only when it is being experienced by the subject or it exists only when it is not being experienced by the subject. In each case, the existence of the particular is dependent on the state of the subject, which violates the requirement that their existences should be logically independent. Strawson also makes this claim in The Bounds of Sense. In his discussion of Kant’s Second and Third Analogies, Strawson had claimed that in order to make intelligible the notion of experience of an objective reality we must be able “to distinguish between the subjective time-order of perceptions and the timerelations of objects which the perceptions are perceptions of” (Strawson 1966, pp. 140-1). The possibility of objectivity requires the logical independence of the temporal ordering of experiences from other particulars. In order to be capable of

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making that distinction, we must be able comprehend “currently unperceived objects which are nevertheless objects of possible perception, co-existing with, or existing at the same time as, objects of actual perception” (Strawson 1966, p. 141). The logical independence of subjective particulars (experiences) and objective particulars (objects) requires that objects that are not being perceived must be capable of existing at the same time as objects that are being perceived. Strawson finds Kant’s presentation of his arguments in the Refutation of Idealism and the first Analogy, if not the arguments themselves, lacking. Strawson gives the argument as he would have liked to have seen it presented: It is impossible to draw the necessary distinctions between (1) the time-relations of the members of a subjective series of perceptions and (2) the timerelations of at least some objects which the perceptions are perceptions of, unless the objects in question are seen as belonging to an enduring framework of relations in which the objects themselves enjoy their temporal relations… with each other independently of the order of our perceptions of them. This enduring framework of relations is spatial. Space is the necessary permanent framework for objective time-relations” (Strawson 1966, pp. 125). The next step in Strawson’s argument is the claim that, for it to be logically possible for particulars that are not experiences of a subject to exist whether or not they are being experienced by the subject, it must be logically possible for particulars that are not experiences of the subject to continue to exist through an interval during which they are not being experienced by the subject. In Individuals, Strawson writes:

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to have a conceptual scheme in which a distinction is made between oneself or one’s states and auditory items which are not states of oneself, is to have a conceptual scheme in which the existence of auditory items is logically independent of the existence of one’s states or of oneself. Thus it is to have a conceptual scheme in which it is logically possible that such items should exist whether or not they were being observed, and hence should continue to exist through an interval during which they were not being observed (Strawson 1959, p. 72). From the last sentence, we see that Strawson thinks that it follows from the first fact (that it is logically possible for a subject that particulars that are not experiences of that subject should exist whether or not they are being experienced) that it must be logically possible for that subject that particulars that are not experiences of that subject should continue to exist through an interval during which they are not being experienced. Negating the consequent of this claim helps make it clearer why we should believe it. Suppose that it is not logically possible for a subject that particulars that are not states of the subject should continue to exist through an interval during which they were not being experienced. Then particulars that are not states of the subject could not continue to exist through an interval during which they were not being experienced. I take it this means that they could not continue to exist over a period in which they were first objects of the subject’s experience, then not objects of the subject’s experience, and then again objects of the subject’s experience. But this is inconsistent with their existing whether or not

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they are being experienced. Once a particular had been experienced for the first time, it would have to cease to exist before being experienced a second time. In The Bounds of Sense, Strawson asserts, “there is only one way in which perceived things or processes can supply a system of temporal relations independent of the order of the subject’s perceptions of them— viz. by lasting and being re-encounterable in temporally different perceptual experiences” (Strawson 1966, p. 127). That is, the subject’s experiences must be experiences of lasting, re-encounterable particulars. The next step of the argument is that, for it to be logically possible for a subject for particulars that are not his experiences to continue to exist through an interval during which they are not being experienced, it is necessary that the subject be able to re-identify them. That is, the main criterion for objectivity is “re-identifiability” – that the subject be capable of re-identifying the same particular at different times. In Individuals, Strawson writes that “to have a conceptual scheme in which it is logically possible that [auditory items which are not states of oneself] should… continue to exist through an interval during which they were not being observed.… it seems that it must be the case that there could be reidentifiable particulars in a purely auditory world” (Strawson 1959, p. 72). This claim is a key step in the argument, but it seems false at face value. Particulars that are not states of a subject could continue to exist through an interval during which they were not being experienced without the subject being able to re-identify them. It might be that the subject believes that he consistently

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mis-identifies particulars. That is, every one of his experiences seems to be a new one, but he nonetheless believes that it is possible, even likely, that many of the objects of his current experience have been objects of his experience in the past, without him knowing it. In The Bounds of Sense, in the section on the Second and Third analogies, Strawson argued that in order to distinguish the temporal ordering of experiences and other particulars we must be able to comprehend “currently unperceived objects which are nevertheless objects of possible perception, co-existing with, or existing at the same time as, objects of actual perception” (Strawson 1966, p. 141). The logical independence of subjective particulars (experiences) and objective particulars (objects) requires that objects that are not being perceived must be capable of existing at the same time as objects that are being perceived. Now Strawson argues that “there is something right about Kant’s answer” to the question of how this, in turn, is possible: that it is the character of our perceptions themselves that enables us to count perceptions which succeed each other as perceptions of objects which do not. This character of the perceptions themselves can be expressed by saying that we perceive (some of) the things we do perceive as things of certain general kinds, as things falling under general concepts of relatively persistent and re-identifiable objects. We cannot, that is to say, characterize those perceptions themselves except with the help of concepts of persistent things which we perceive the objects of those perceptions as instances of (Strawson 1966, p. 142).

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In other words, in order for objects that are not being perceived to be capable of existing at the same time as objects that are being perceived, we must perceive some objects as persistent and thus re-identifiable. Whether this step in the argument is attributable to Kant is, I think, dubious. Regardless, it is clear that Strawson believes it. As he puts it in Bounds of Sense: “the fundamental condition of the possibility of empirical self-consciousness is that experience should contain at least the seeds of the idea of one experiential or subjective route through an objective world” (Strawson 1966, pp. 127-8). Surely, stating the thesis in terms of a “route” biases the case. I think it would be fairer to say that experience must allow for the possibility of distinguishing experiential order from objective order. Strawson claims that the “idea of a mere temporal succession of representations, of the form ‘Now A, now B, now C’, etc.” does not allow for the possibility of this distinction (Strawson 1966, p. 128). I want to grant that step, but first I would like to generalize it slightly. Why should we suppose that a mere succession of representations is temporal? Why import more than ordering into our premises? If we thus generalize the claim, it becomes the claim that the idea of a mere ordering of representations (of the form A, then B, then C) does not allow for the possibility of the distinction between experiential order and objective order. So generalized, the truth of the claim is obvious. We want a distinction between one ordering (the perceptual) and another (the objective), but we have only one ordering.

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Strawson claims that we can allow for the possibility of this distinction “[i]f and only if we enlarge the form to ‘Here now A’, etc.” (Strawson 1966, p. 128). But we can generalize this claim as usefully as we did the previous one: we can allow for the possibility of distinguishing between an experiential ordering and an objective ordering only if we have the idea of at least two independent orderings. The form of our experience must be not merely (A, then B, then C) but, (in this ordering: A, then B, then C). I do not see that we have to allow for the possibility of a space in which to locate these orderings. All we need are the orderings themselves. Strawson, it would seem, disagrees. He claims that “the addition of ‘here’ to ‘now’ is completely otiose unless it carries with it the possibility of such contrasts as ‘somewhere else now’and ‘here again later on’” (Strawson 1966, p. 128). This is false. It is true that the addition would be useless if it did not carry with it something suitably generalized from ‘somewhere else now’, e.g., ‘at the same position in another ordering’. But the mere possibility of distinguishing between ‘here now’and ‘somewhere else now’(or, again suitably generalized, between ‘at a certain position in this ordering’and ‘at the same position in another ordering’) is sufficient to allow for the distinction between an experiential order and an objective order. Distinguishing between an experiential order and an objective order is what Strawson had said we needed to make sense of the objectivity thesis. Therefore, I claim, the mere possibility of distinguishing

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between ‘at a certain position in this ordering’and ‘at the same position in another ordering’ is sufficient to make sense of the objectivity thesis. To allow in addition for the possibility of a contrast such as ‘here again later on’ is something more. There are two ways of interpreting what Strawson means to capture by the contrast, but neither of them is necessary for distinguishing an experiential order from an objective order. The differences between the two interpretations may be seen by how we would have to generalize ‘here again later on’ in order to fit it into my more abstract framework. The first way it might be generalized would be as ‘in this ordering later on’, that is ‘at a later point in this ordering’; the second would be as ‘in the same position in the objective world at a later point in this ordering’. Let us begin with the first possibility. Is it necessary for our imagined experiencer to be able to distinguish between ‘in this ordering now’and ‘in this ordering later on’ in order to allow for the possibility of distinguishing an experiential ordering from an objective ordering? More generally, is it necessary for our imagined experiencer to be able to distinguish between ‘at this point in this ordering’and ‘at another point in this ordering’, in order to allow for the possibility of distinguishing an experiential ordering from an objective ordering? The reasoning behind an affirmative answer to this question would, I think, be that we cannot allow for the possibility of distinguishing orderings if all we can compare are elements of orderings. Two different orderings may contain identical elements. Therefore, the argument would go, our imagined experiencer

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cannot distinguish between an experiential ordering and an objective ordering unless he can distinguish between ‘at this point in this ordering’and ‘at another point in this ordering’. Unless he can make that distinction, he cannot distinguish between ‘at this point in this ordering’and ‘at this point in another ordering’. However, this is false. To see why, we will need to look at a few pictures. Let ‘E’be the experiential ordering and ‘O’ be the objective ordering. Orderings are indicated in the mathematical notation of ordered n-tuples. A ‘*’ indicates ‘now’ in the ordering in which it is present. If the situation is the following: E:

then our experiencer can distinguish his experienced ordering from the objective ordering, for now in his experience he experiences ‘1’while now in the objective ordering ‘3’ is present. However, we might suppose that the situation is as follows: E: O: in which case our experiencer could not distinguish his experiential ordering from the objective ordering, because he experiences ‘3’now, while in the objective ordering ‘3’ is also present now. Furthermore, our experiencer could never distinguish his experiential ordering from the objective ordering if, as the case might be, successive states were as follows:

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E: T1< O: -----------------------------------------E: T2< O:

In that case, the experienced world would always be identical with the objective world, and thus our hypothetical experiencer would not be able to distinguish between his experiential order and the objective order. However, the objectivity thesis did not require that an experiencer should be able to distinguish in every case between his experiential order and the objective order. Rather, it required that it should be possible for the experiencer to make that distinction. And the first case I diagrammed showed that it was possible for the experiencer to make that distinction. In the first case, the experiencer could distinguish his experienced state ‘1’from the objective state ‘3’. It is the possibility of making this distinction that is necessary, not that it should be practicable in every case. What I have said already is enough to show that my proposal meets the necessary criteria for objectivity. However, I said that there was a second possibility for generalizing Strawson’s claim that objectivity requires a contrast between ‘here now’and ‘here again later on’, and it will be instructive to dwell on this possibility. The second form of the generalization was as a contrast between ‘at a given position in the objective world now’and ‘at the same position in the objective world at a later point in this ordering’. The introduction of the concepts

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of ‘position’and ‘world’does seem to introduce genuine spatiality, and at the same time it throws my whole conceptualization of the problem into question. Implicit in my statement of the argument and diagrammatic examples above was the supposition that there was no important or relevant objective ‘world’. There were only orders of experience, one of them singled out as ‘objective’. It seems more in keeping with our common notion of objectivity, however, to consider it apart from any possible order of experience. The objective is not just one of many possible orderings of experience. Rather, it is that which gives rise to all possible orderings of experience. This reconceptualization of the problem does not detract from the force of my conclusion above, but it does require one adjustment. Rather than conceiving of the objective as an ordering of experience, we must conceive of it as the set of all possible orderings of experience. Given the conventions I have been using then, an objective world might be: O: [,,,] That is, it is possible in this world to experience ‘1’ and then ‘1’, or ‘1’and then ‘2’, and so on. (In this world, every experiencer has only two experiences — a short life indeed.) Now, in order to fulfill the objectivity condition, I submit, it is only necessary that our experiencer should be able to conceive of there being more than one ordering of experience. He cannot compare his ordering of experience with the objective ordering of experience, for there is no such thing. He can, however, compare his ordering of experience with the ordering of

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experience of another possible or actual experiencer. The possibility of the ordering of experience differing between experiencers is implicit in the fact that the world consists of more than one possible ordering of experiences. With that emendation of my argument about the first possibility in mind, let us return to our consideration of the second possibility. The second possibility is that a contrast between ‘at a given position in the objective world now’and ‘at the same position in the objective world at a later point in this ordering’ is necessary for objectivity. There are again two possible interpretations of this generalization, depending on what we take ‘position in the objective world’to mean. One possibility is a purely phenomenal understanding of ‘position’ whereby identity of position is equivalent to identity of experience. The other possibility is a more full-blooded understanding of ‘position’, whereby it means something independent of experience. Is it necessary for objectivity that our experiencer be able to make the distinction between ‘having this experience now’and ‘having this experience at another point in this ordering’? Not if my arguments above have been correct. The experiencer does not depend on making this distinction in order to have the possibility of distinguishing between his order of experiences and another ordering. That much is clear. There is, however, the question of whether distinguishing between one’s own order of experiences and another ordering is all that objectivity requires. I will postpone considering that question until I have considered the other possibility for interpreting ‘position’.

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The other possibility was to take ‘position’as meaning something that is independent of experience. We might suppose that the objective world consists in something above and beyond the set of all possible orderings of experience: a set of positions. Positions may in fact be correlated in systematic ways with experiences, but if position and experience are to be truly independent, there may be no necessary connections between positions and experiences. One must be able to be at the same position at different times and have different experiences. This possibility seems, at least on the face of it, as though it might require a more fullblooded notion of spatiality than the mere orderings I have been arguing are sufficient. However, the question is whether the objectivity thesis requires that an experiencer be able to make the distinction between ‘having experience A at position X’and ‘having experience A at position Y’. This, like the question with which I concluded the last paragraph, is a question about precisely what the objectivity thesis entails. It is to that issue that we must now return. I started by glossing Strawson’s Kantian claim that experience must allow for the possibility of conceiving of an experiential route through an objective world as the claim that experience must allow for the possibility of distinguishing experiential order from objective order. When it became obvious that this was inadequate (because there is no objective order of experience), I retreated to the gloss that experience must allow for the possibility of distinguishing one experiential order from another. My claim has been that (full-blooded, material) spatial concepts are not necessary to distinguish experiential orderings. The

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question now is whether the gloss was correct. Is the Kantian thesis only that experience must allow for the possibility of distinguishing one experiential order from another, or is it something more than that? Because the gloss was a gloss on the objectivity thesis, and that the notion of objectivity in question is that of objects existing independently of experience, the Kantian thesis must be more than merely that experience must allow for the possibility of distinguishing one experiential order from another. We started, even in considering the very first possibility, with a comparison between orderings of experiences. One of the orderings was supposed to be merely experiential, the other objective. What we need, however, is not a distinction between merely experiential experiences and objective experiences, but a distinction between experiences and objects. Likewise, a distinction between the ordering of subjective experiences and the ordering of objective experiences will not do. We need a distinction between the ordering of objects and the ordering of experiences. If we again resort to pictures to get a grasp on this, we may represent an objective world as, for example: ABC where ‘A’, ‘B’, and ‘C’represent objects and the arrows represent constraints on the ordering of experiences. Then, if ‘[A]’stands for an experience of the object named ‘A’, some of the possible orderings of experiences of this world would include: [A]-->[B]-->[C] [A]-->[B]-->[A]

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and so on. With that notation in mind, let us return to the original question: does the possibility of a subject’s making a distinction between the order of his experiences and the order of the world depend on his having some spatial framework? Strawson had said that we must allow for the possibility of making contrasts such as ‘somewhere else now’and ‘here again later on’. I agreed that the contrast between ‘here now’and ‘somewhere else now’(suitably generalized to a contrast between ‘now in this ordering’and ‘now in another ordering’) was necessary if our subject was to make sense of the distinction between the order of his experiences and the order of the objective world. In fact, I argued that the ability to make that distinction was sufficient and that, therefore, it was not in addition necessary for our subject to be able to make a distinction between ‘here now’and ‘here again later on’. However, the distinction between experiential order and objective order calls this conclusion into question. Now it is no longer clear that we can make a distinction between ‘here now’and ‘somewhere else now’along the lines of the distinction between ‘in this ordering now’and ‘in another ordering now’. The latter distinction made sense as a comparison between a pair of experiential orderings, relative to both of which it was (relatively) easy to see what ‘now’ meant. But what can ‘now’ mean in the objective ordering? We imagined that we had an ordering relation between three objects: ABC

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However, there is no notion of the passage of time in this objective world. It is timeless and unchanging. We can incorporate the notion of time by allowing the ordering of the objects to change. Thus we might have: T0: ABC T1: BAC and so on. In doing so, we must conceptualize ‘positions’as the ‘slots’ in an ordering, which may be occupied by different objects: ( )( )( ) We can identify these positions independently of the objects that occupy them, say by numbers: (1)(2)(3) And then we can make sense of a subject being ‘here’ by placing the subject in one of the positions: T0: (A)(S)(B) What it would be for the subject to be ‘somewhere else’would be for the subject to be in another position: T0: (A)(B)(S) Now the question is whether and how the subject can make sense of his being in different positions. But let’s step back a moment. Perhaps we have gone too fast. The way we interpreted the subject’s making sense of the possibility of his being in different positions was as his awareness of the possibility of different experiential orders. Why won’t that still work?

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On that interpretation, what it was for the subject to be in a different place was for him to have a different ordering of experience. Can’t we still make sense of this? We must now distinguish between position in the world, the objects that occupy each position, the location of the subject, and the experiences that a subject has: Experience: Subject: Object: Position:

[B] S A B C ( )( )( )

I’m not at all clear that this doesn’t capture what’s important in our notion of objectivity. However, it clearly doesn’t capture at least two aspects of our overall view of the world: (1) that the subject cannot be in the same place as an object, and (2) that the subject’s experience is dependent on not only position but orientation. To try to capture these aspects of our common-sense view of the world in our model, let us introduce some ‘empty’positions into the framework such that the subject may occupy them. From any given empty position, the subject’s experience may be of any one of the objects reachable from that position. That is, we must distinguish between these two situations: Experience: [A] Subject: S Object: A C Position: ( )( )( ) ------------------------------------Experience: [C] Subject: S Object: A C Position: ( )( )( )

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However, we are still missing one important aspect of our ordinary experience. Our experience of an object changes depending on the location from which we see it. That is, we also must distinguish these two situations: Experience: [C] Subject: S Object: A C Position: ( )( )( )( ) ----------------------------------------Experience: [C] Subject: S Object: A C Position: ( )( )( )( ) Let us do so as in the following diagrams where ‘[C-2]’, for example, means ‘an experience of object C as observed from position 2’: (1)

Experience: [C-2] Subject: S Object: A C Position: (1)(2)(3)(4) ---------------------------------------------------(2) Experience: [C-4] Subject: S Object: A C Position: (1)(2)(3)(4) On this interpretation, what is the distinction between ‘here now’and ‘somewhere else now’? Well, in the following diagram, S and S’are in different locations at the same time: (2)

Experience: Subject: Object: Position:

[C-2] S

[C-4] S’

A C (1)(2)(3)(4)

Initially, I suggested that S could tell the difference between ‘here now’and ‘somewhere else now’by grasping the concept of separate orderings of

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experience. This came into question when I suggested that this did not allow for our subject to make a distinction between an experiential ordering and an objective ordering. Instead, there were only experiential orderings. But now we have introduced an objective ordering into the world, separate from and independent of the subject. Eventually we will need to decide whether the subject can grasp the notion of this separate and independent ordering. But first, let us consider how the subject could make sense of a difference between ‘here now’ and ‘somewhere else now’. I still think that, as I suggested before, the subject could make sense of that distinction by being able to make sense of a distinction between experiential orderings. But now the experiential orderings would contain as elements ordered pairs of objects and places. So the experiential orderings that would distinguish between subjects S and S’would be the following: (..., , ...) (..., , ...) But how, one wants to ask, is the subject supposed to make sense of the notion of ‘place’or ‘position’not only independently of but antecedently to his experience? It is a commonplace that concepts of ‘thing’and ‘place’are inextricably intertwined. Let us suppose it a fact that our subject does not have an antecedent understanding of position or place. Can we then still make sense of a distinction between an objective ordering and an experiential ordering along the lines I have been suggesting? Yes we can. In fact, the assumption that the notion of ‘place’or ‘position’ cannot be an element of a subject’s experience until after the subject has acquired

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the distinction between the objective ordering and his own experiential ordering is a simplifying assumption. Let us instead suppose that, in our fantasy twodimensional world, a subject’s experience is presented as an experience as of being between two particulars. In that case, the previous diagram might be represented as: Experience: Subject: Object: Position:

[A-C] S

[C--] S’

A C (1)(2)(3)(4)

Here again, we may contrast our subject’s experience (‘here now’) with another possible subject’s experience (‘somewhere else now’) as a difference in an ordering: (..., , ...) (..., , ...) And because the subject surely could, as I suggested before, understand the possibility of making such a distinction between his own experiential ordering and another experiential ordering, he could make sense of an objective ordering. The objective ordering is something different in kind from an experiential ordering. One way of thinking of it would be as the set of all possible experiential orderings; another would be as the ordering of particulars that allows for the set of all possible experiential orderings. Now, as long as we assume, as I have been assuming, that particulars other than subjects do not ‘move’(that is, that the objective ordering is constant), then we have a case where a subject can distinguish between an objective ordering and

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an experiential ordering without being able to distinguish between ‘here now’and ‘here again later on’. The assumption that the objective ordering is constant is ridiculous with regard to our actual world, but it was the conceptual possibility of distinguishing between objective and experiential that Strawson (and we) were discussing. Now it is time to complicate matters again. But before we do so, let us simplify a little first. Since I have shown that it is not theoretically important for our purposes, let us return to a world in which subjects and other particulars may occupy the same positions and in which a subject’s experience is of whatever other particular is in the position the subject is in. Thus, a picture of the state of the world at a given time might be: Experience: Subject: Object: Position:

[B] S A B C (1)(2)(3)

And some of the possible orderings of experience for this world might include: So far, nothing about this world is significantly different from the kind of world about which I drew my last conclusions. But now suppose that the ordering of non-subject particulars in the world can change. Thus, the world at some other time might be pictured as follows: Experience: Subject: Object: Position:

[C] S A C B (1)(2)(3)

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As a result of this change, our subject would have had the following ordering of experience: However, it seems that another subject, or even our own subject, could have had that ordering of experience without the objective ordering changing, simply by changing his place in the ordering (that is, by moving from position (2) to position (3) in the unchanging first world). And, if that is the case, doesn’t it challenge my claim that the subject has the resources to distinguish between the objective ordering and an experiential ordering, because my thesis depended on the possibility of the subject distinguishing his own experiential ordering from another experiential ordering? There are a number of things to say about this. The first is that it is possible even in a changing world for a subject to distinguish his own experiential ordering from another experiential ordering. All that is necessary is that the subject should be able to distinguish between how things seem to him now and how things might seem to someone else now. That is, it is necessary that the subject should be able to imagine the possibility of having a different experience. The possibility of having a different experience is what is captured by the talk of ‘here now’and ‘somewhere else now’or ‘in this ordering of experience’and ‘in another ordering of experience’. It would still be possible, even in a changing world, for the ordering of one subject’s experience to differ from the ordering of another subject’s experience. But even if that were impossible, it might still be

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possible for the subject to conceive of having a different experience. Who is to say what a subject can or cannot possibly experience? It is the nature of the subject, and not just the nature of the world, that determines what the subject can and cannot conceive. Let us agree then (keeping in mind that it is a stipulation about the nature of our subjects) that our subjects can at any given moment conceive of experiencing things other than those which they do experience. If that is the case, I claim, they have the resources not only for distinguishing between their own experiential ordering (what they experience) and another experiential ordering, but also for distinguishing between their own experiential ordering and an objective ordering. (Where an objective ordering is conceived of as either the set of all possible (conceivable) experiential orderings or as the grounds or cause for the extent and limitations of that set.) Thus even subjects in a changing world, so long as they can distinguish experiences (or orderings of experiences) other than their own, can distinguish between their own experiential ordering and an objective ordering. It is another matter entirely whether they can determine the objective ordering on the basis of their experiential ordering. Surely, that is more difficult in a world in which the objective ordering can change. However, as we shall see later, it is in fact the case that subjects in non-material but nevertheless spatial worlds can determine the objective orderings of particulars on the basis of their experiential orderings.

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I want to draw three conclusions from this discussion. The first is that for subjects to be able make this distinction between experiential ordering and objective ordering, they must be able to make the distinction between their actual experiences and other possible experiences or, in other words, between their place in their own experiential ordering and another experiential ordering. It is this distinction (between my actual experience now and another possible experience now) that corresponds to Strawson’s ‘here now’and ‘somewhere else now’. The second conclusion is that for subjects to be able to make the distinction between experiential ordering and objective ordering, they need not make any distinction corresponding to Strawson’s ‘here now’and ‘here again later on’. In other words, a grasp of time is not necessary for distinguishing experiential orderings from objective orderings. To put the point more generally, re-identification in one dimension is sufficient for distinguishing experiential orderings from objective orderings. The next step is the crucial one. Strawson thinks that a subject can reidentify particulars that are not his experiences only if the subject can represent those particulars as located in space. Strawson thinks that the way that we do, in fact, reidentify particulars over discontinuities of experience is by representing them as located in regions of space that are far from us. In Individuals, he asks, “with what feature or complex of features of our familiar world is the idea of reidentifiable particulars, existing continuously while unobserved, most intimately, naturally and generally connected?” (Strawson 1959, p. 73). The

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“simple and obvious” answer is that “the crucial idea for us is that of a spatial system of objects, through which oneself, another object, moves, but which extends beyond the limits of one’s observation at any moment, or, more generally, is never fully revealed to observation at any moment. This idea obviously supplies the necessary non-temporal dimension for, so to speak, the housing of the objects which are held to exist continuously though unobserved” (Strawson 1959, pp. 734). Even if we think of a world full of non-spatial particulars, such as sounds, “the most familiar and easily understood sense in which there exist sounds that I do not hear is this: that there are places at which those sounds are audible, but these are places at which I am not now stationed” (Strawson 1959, p. 74). The fact that the representation of space is the means by which we allow room for the possibility of reidentifying particulars in our actual conceptual scheme, however, does not entail that the representation of space is the only means by which we allow room for that possibility. Strawson does allow that there are “other senses which can be given to the idea of unheard sounds” (Strawson 1959, p. 74). However, he appears to think that these fall exclusively into two categories, neither of which is adequate to provide for the possibility of reidentifying particulars without representing space. The first category contains those that “turn on correlations between auditory phenomena and phenomena of other kinds (e.g., non-auditory phenomena causally associated with auditory phenomena)” (Strawson 1959, p. 74). Such correlations cannot be of any use in a wholly auditory world. The other possibility is no more helpful: “Alternatively,

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they turn on such an idea as that of failing sensory powers. But why do we think of our powers failing rather than the world fading? This choice cannot be used to explain a conception it presupposes” (Strawson 1959, p. 74). Strawson does acknowledge that the idea of space “cannot be given a meaning in purely auditory terms” (Strawson 1959, p. 74). However, he thinks that “we must have a dimension other than the temporal in which to house the at present unheard sensory particulars, if we are to give a satisfactory sense to the idea of their existing now unperceived, and hence to the idea of reidentification of particulars in a purely auditory world” (Strawson 1959, p. 74). By this “dimension” he means “some sort of variable feature in auditory items which will provide what we might call an analogy of Space… a sufficiently close analogy for our purposes” (Strawson 1959, pp. 74-5). So the argument here is that reidentifiability requires some sort of dimension of variability other than the temporal. Supposing it to be true that reidentifiability requires an additional dimension of variability, why should we say that this dimension is “an analogy of space”? One reason Strawson might adduce is that the additional dimension is an analogy of space because it allows for that “non-temporal dimension for, so to speak, the housing of the objects which are held to exist continuously, though unobserved” (Strawson 1959, p. 74). That is, the additional dimension is “analogous to space” because it plays the same role that space plays in allowing for the possibility of reidentification. This strategy, however, would beg the

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question, which is whether any scheme that allows for the possibility of reidentification must be spatial. The only other reason I can imagine Strawson giving for calling his additional dimension an “analogy of space” is that it is a “dimension”. However, mathematicians use the word “dimension” in reference to many things that are not literally (“physically”) spatial. On the other hand, Strawson might argue, these are all analogous to space. I would take it then that what he means is that the additional dimension is an analogy of space in that it provides room for variability. This is to my mind a very weak analogy. However, I think it would be an unreasonable terminological quibble to insist on pushing the issue. Strawson and I can agree that what is necessary is some non-temporal dimension of variability. Strawson does say a few things about what is supposed to be analogous between his dimension and space. He asserts that the dimension must “provide something like the idea of absence and presence” (Strawson 1959, p. 75). I take it that the concepts of “absence” and “presence” are supposed to correspond to those of “observed” and “unobserved”. That is, what is “present” is “observed”, while what is “absent” is “unobserved”. If that is the case, then we should not even need a full, continuous dimension of variability, but only a duality. It must be possible for objective particulars to be present/observed or absent/unobserved. Such a duality seems very unlike the concept of continuous space that we actually have, and thus not very analogous to it.

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Strawson asserts, however, that the analogy must be stronger. We need the idea “not just of absence and presence in the most utterly general sense these words could bear, but absence or presence in a sense which would allow us to speak of something being to a greater or lesser degree removed from, or separated from, the point at which we are” (Strawson 1959, p. 75). I take it that the idea of absence and presence “in the most utterly general sense these words could bear” is the idea I advanced in the previous paragraph of a duality, such that every particular is either absent or present. Strawson is thus asserting that the dimension we need must be variable in some continuous sense, such that there is not just a duality between absent and present, but a continuous, or at least, multi-valued, variation. Thus, a particular can be more or less absent, and by the same token, less or more present. But I don’t see why we need such a notion of multi-valued variability. Strawson actually gives as his reason that “only… under this condition would we have anything like the idea of a dimension other than the temporal in which unperceived particulars could be thought of as simultaneously existing in some kind of systematic relation to each other, and to perceived particulars” (Strawson 1959, p. 75). But Strawson has given no reason why we need to think of unperceived particulars existing in a systematic relation to each other. Remember that we are trying to make sense of the possibility of reidentification, of identifying objects as the same across discontinuous stretches of observation. That is, we are trying to make sense of the possibility of a particular’s being present

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(observed, identified), then of being absent (unobserved), and then of being present again (re-observed, re-identified). Strawson has given no reason why, in order to make sense of that possibility, we need the absent/unobserved particulars to be in a systematic relation to each other. It is a fact about our actual, spatial system that unobserved particulars are all in a systematic relation to each other and to observed particulars. But we have always to keep in mind that we are trying to see if it makes sense to have a system of objective particulars that is nonspatial. It seems that all we really need to accomplish that is a bivalence between present/observed/identified and absent/unobserved. Our actual spatial system allows for additional possibilities, but these are not, or at least Strawson has not argued that they are, necessary for a system of objective particulars. But suppose we allow for the sake of argument the assertion that the necessary dimension must not be merely bivalent but multivalent. Strawson writes “In other words, we want an analogy of distance— of nearer to and farther away from” (Strawson 1959, p. 75). Distance is a spatial concept, and therefore, establishing that the needed dimension is analogous to distance establishes in some sense that it is analogous to space. But, how strong is the analogy? What Strawson now calls “nearer to” and “farther away from”, he had previously referred to as “to a greater or lesser degree removed from, or separated from”. That is, the concept we need is just the concept of “magnitude of difference”. But the concept “magnitude of difference” is not inherently spatial. There are, for example, magnitudes of difference between temperatures and lifespans.

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Strawson is still correct that the concept we need (“magnitude of difference”) is “an analogy of distance”. The analogy can be expressed by the phrase “is a kind of”. That is, “distance” is to “magnitude of difference” as “apple” is to “fruit”. But for Strawson to say “we want an analogy of distance” is misleading. It is like a chef who is making a fruit salad saying to his purchasers “we want an analogy of apples”. The chef is strictly correct, in that what he wants is something that is to apples as animals are to dogs. But he is also ambiguous, since his purchasers might interpret him as meaning that he wants things that are to apples as green things are to plants (he wants red things), or many other things as well, when what he really wants is fruit. What Strawson really wants is magnitude of difference, and I for one don’t see how it helps us at all for him to say that what he wants is “an analogy of distance”. Strawson himself admits that “though the analogy… may be fairly persuasive, fairly attractive, it is not compelling” (Strawson 1959, p.77). Because he goes on to talk about the necessity of ruling out skepticism about identifying particular as opposed to universal sounds, it is not clear that he is actually criticizing his own analogy, as opposed to the claim that it provides for a scheme of reidentifiable particulars. Thus there are two ways to criticize Strawson’s argument. To begin with, it is not clear that it provides for a certain scheme of reidentifiable particulars. However, even if it does, the purported “analogy” with space on which it depends is weak and misleading. Thus, Strawson has not shown by this argument that spatial representation is necessary for objectivity. He has

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not even shown that spatially-analogous representation is necessary for objectivity. In The Bounds of Sense, Strawson, in chastising Kant for not arguing for the spatiality thesis independent of the objectivity thesis, writes: From the truth that objects of our experience conceived of as existing independently of experience of them are in fact spatial objects, it does not seem to follow immediately that the spatial is the only mode in which we could conceive of such objects. That the spatial is the only conceivable mode of existence of such objects might nevertheless perhaps be allowed if we stripped the concept of spatiality of its usual sensory associations and gave it a mainly formal meaning; and even if we allow the concept to carry its normal visual and tactile associations, it can still be maintained that the spatial mode is at least that on an analogy with which any alternative mode of existence of independent objects of our experience would have to be conceived by us (Strawson 1966, p. 25). In so doing, he echoes in a more reasonable way the theme of Chapter 2 of Individuals: that objectivity requires representation of particulars as existing in some analogy with space. However, by the time of The Bounds of Sense, Strawson has tempered his claim somewhat. He now admits explicitly that the notion required is analogous to a concept of spatiality “stripped” of “its usual sensory associations” and given “a mainly formal meaning”. The formal meaning that is required is, as I have argued, at most the meaning of “magnitude of difference”.

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Strawson is, however, not uniformly recalcitrant. Just after the part in the section on the Second and Third analogies where Strawson argues that, in order for objects that are not being perceived to be capable of existing at the same time as objects that are being perceived, we must perceive some objects as persistent and thus re-identifiable, he juxtaposes this thesis with another: “that we must conceive of such objects as ordered in some system or framework of relations such as along can give sense to the notion of particular identity of such objects” (Strawson 1966, p. 142). This is unabashedly a reference to the spatial frame of reference, as we shall see, although here Strawson admirably if not confidently puts it in a very general form. Strawson has not considered this second thesis at length, but its force is obvious. If it is required that we be able to identify and reidentify persistent objects, then there must be some system by which such identifications may be accomplished. And it is precisely Strawson’s point here to show the relation between the two theses. He explains that they are not independent because “the notion of having general concepts of the kind required and perceiving objects as falling under them without, however, having any idea of how questions of particular identity regarding such objects might be settled is a senseless one” (Strawson 1966, p. 142). Now this argument again gets us to some general formal relationship between objects. But it has not quite got us to spatial representation. And Strawson lets us down here again. His only remark on the connection of this argument with the thesis that we must represent space is that it “has been

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sufficiently remarked already that the most natural way, and perhaps the only way, for us to conceive of a possible framework or system of relations of the kind required is to conceive of it as spatial” (Strawson 1966, p. 142). As usual, Strawson relies on the argument that a spatial framework is the only game in town. We have already considered this argument and set out its flaws. Strawson gives another indication that this is his considered view in his criticism in The Bounds of Sense of Kant’s quick move from the objectivity thesis to the spatiality thesis. Strawson writes: There remains something not wholly explicit about [Kant’s] process of argument. It would have been clearer, and perhaps more characteristic of the philosopher, to argue that the general conditions of the possibility of experience require the existence of some mode of sensible ordering, different from the temporal and at least analogous to the spatial, of particular items encountered in experience; and then to proceed to the declaration that, as things are, we cannot conceive of any alternative to the spatial mode itself. If this last assertion were challenged, as it might be, it would then be possible to retreat to the lesser claim; viz. that any system of relations between particular items such as previous arguments have shown to be necessary to the possibility of experience must be conceived, at least by us, on analogy with space (Strawson 1966, p. 51). However, in the succeeding paragraph, Strawson does give a somewhat new version of that argument, one which is possibly immune to the charge I leveled against the No-Space World Argument (that it depends on an induction). The argument is that the distinction that subjects do need (between a subject’s actual experience now and another possible experience now) is not an inherently spatial

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concept, in the sense in which Strawson uses “spatial”. When Strawson uses the word “spatial”, he refers to the common three-dimensional space of material objects. What we have found, however, is that what is really necessary to support objectivity is ordering along different dimensions – i.e., an abstract, mathematical “space”, not necessarily containing any material objects, and of an arbitrary number of dimensions. Now, whether this concept is only just an “analogue of space which we can make intelligible to ourselves only as an analogue of space” (Strawson 1966, p. 128) is a question I cannot hope to answer. I will leave the matter at this: I do not think it is. In the course of the sounds chapter, Strawson argues that, although a subject in a non-spatial world could potentially reidentify non-spatial particulars, we could not make sense of a subject in a non-spatial world making a distinction between himself and his states and particulars that are not himself or states of himself. He writes that in the non-spatial world “it did seem possible to find a place for the idea of a reidentifiable particular, by exploiting certain auditory analogues of the idea of spatial distance” (Strawson 1959, p. 87). He was unable, however, to make a compelling case that it was possible to have “a scheme in which a distinction was made between oneself and what is not oneself” (Strawson 1959, p. 88) in such a world. The subject of the auditory world, although he “might recognize sound-universals and reidentify sound-particulars and in general form for himself an idea of his auditory world” would nevertheless “have no place for the idea of himself as a subject of this experience, would make no distinction

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between a special item in this world, namely himself, and the other items in it” (Strawson 1959, p. 88). That is, Strawson was unable to show how it was possible to have experience of objective particulars in a non-spatial world. In the third chapter of Individuals, Strawson directly confronts the question whether in fact it is possible to have experience of objective particulars in a non-spatial world. I am not sure that Strawson actually argues for this proposition. I take it that Strawson believes that it follows directly from the definition of identification. Statements of this premise may be found at various places in Chapter 3 of Individuals. For example, Strawson writes that “it is a necessary condition of one’s ascribing states of consciousness, experiences, to oneself, in the way that one does, that one should also ascribe them, or be prepared to ascribe them, to others who are not oneself” (Strawson 1959, p. 99). On the next page, he rephrases “One can ascribe states of consciousness to oneself only if one can ascribe them to others” (Strawson 1959, p. 100). Later, he writes, “There would be no question of ascribing one’s own states of consciousness, or experiences, to anything, unless one also ascribed, or were ready and able to ascribe, states of consciousness, or experiences, to other individual entities of the same logical type as that thing to which one ascribes one’s own states of consciousness. The condition of reckoning oneself as a subject of such predicates is that one should also reckon others as subjects of such predicates” (Strawson 1959, p. 104). Then again, he writes, “There is no sense in the idea of ascribing states of

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consciousness to oneself, or at all, unless the ascriber already knows how to ascribe at least some states of consciousness to others” (Strawson 1959, p. 106). The argument for this proposition comes at the end of a long footnote in response to a possible objection, where Strawson writes, “The main point here is a purely logical one: the idea of a predicate is correlative with that of a range of distinguishable individuals of which the predicate can be significantly, though not necessarily truly, affirmed” (Strawson 1959, p. 99). This is a form of the “generality constraint” (Evans 1982), and although I believe that it is challengeable, to challenge it at this point would take us too far afield. In order to properly evaluate Strawson’s claim, we would need to make a serious inquiry into the nature and truth of the generality constraint. Just what is the generality constraint? Does it apply to thoughts or to sentences? Is it a purely logical question, as Strawson says, or rather an empirical one, as, for example, Fodor and McLaughlin imply? And finally, is it true? These are questions for another work. So let us allow Strawson this principle. On page 100, Strawson had written that “One can ascribe states of consciousness to oneself only if one can ascribe them to others.” He follows in the next sentence, “One can ascribe them to others only if one can identify other subjects of experience” (Strawson 1959, p. 100). Likewise, he had written on page 104 that the “condition of reckoning oneself as a subject of such [consciousnessascribing] predicates is that one should also reckon others as subjects of such predicates” (Strawson 1959, p. 104). He continues in the next sentence “The

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condition, in turn, of this being possible, is that one should be able to distinguish from one another, to pick out or identify, different subjects of such predicates, i.e. different individuals of the type concerned” (Strawson 1959, p. 104). That is, we can ascribe states of consciousness to others only if we can identify the others to whom we ascribe them. Strawson makes similar remarks in The Bounds of Sense. For example, he writes, “It is a quite general truth that the ascription of different states of or determinations to an identical subject turns on the existence of some means of distinguishing or identifying the subject of such ascriptions as one object among others” (Strawson 1966, p. 102). That is to say that, in order to be capable of ascribing experiences to a subject, we must be able to identify the subject to which the experiences are to be ascribed. The clause “as one object among others” anticipates the argument somewhat. Strawson’s argument is by reductio ad absurdum. He supposes that we could ascribe experiences to things to which we could not ascribe material characteristics, and derives a contradiction. In each of the several versions of this argument, however, the contradiction is not particularly apparent. Here is the first version: “if we try to think of that to which one’s states of consciousness are ascribed as something utterly different from that to which certain corporeal characteristics are ascribed, then it becomes difficult to see why states of consciousness should be ascribed to, thought of as belonging to, anything at all” (Strawson 1959, p. 98). I suppose that the contradiction here is between “states of

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consciousness belong to something” and “states of consciousness do not belong to anything”. However, the argument is lacking. In order to get to “states of consciousness do not belong to anything” we need the additional premise “if states of consciousness do not belong to any material thing, then they do not belong to anything”. But that proposition has not been justified. We may suppose that states of consciousness belong to immaterial souls, or to the mind of god, or some other such immaterial thing. Then they belong to something, although it is not a material thing. We might suppose that this proposition could be justified on the grounds of some general statement of materialism such as “immaterial things do not exist”, but that would contradict the hypothesis that states of consciousness exist. A slightly refined version of this argument might start from the proposition that “immaterial things cannot have properties”. This would rule out the possibility of an immaterial thing having the property of having any experiences. However, experiences themselves surely have properties, for example, of being intense, or long-lasting. So the refined version does not work either. If we refine the statement any further (“immaterial things cannot have the property of having experiences”) then we have begged the question, which was precisely whether it was possible for something immaterial to have states of consciousness. Perhaps looking at another, more detailed statement of the argument will help: how is it that one can ascribe [states of consciousness] to others? Now one thing here is

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certain: that if the things one ascribes states of consciousness to, in ascribing them to others, are thought of as a set of Cartesian egos to which only private experiences can, in correct logical grammar, be ascribed, then this question is unanswerable and this problem insoluble. If, in identifying the things to which states of consciousness are to be ascribed, private experiences are to be all one has to go on, then, just for the very same reason as that for which there is, from one’s own point of view, no question of telling that a private experience is one’s own, there is also no question of telling that a private experience is another’s. All private experiences, all states of consciousness, will be mine, i.e., no one’s (Strawson 1959, p. 100). Here again we can see that the form of the argument is a reductio. The hypothesis is that only experiences and not corporeal properties can be ascribed to subjects of experience. And the conclusion is that it is impossible to ascribe experiences at all. But does the conclusion follow? There is something compelling about this argument. Think of all the experiences you can identify directly. They all, in my case and I assume in yours, seem to be unique in the sense that I cannot imagine anyone else having them, and pervasive in the sense that, although I can imagine others having experiences, I cannot have such experiences as another, but always only as myself. If I imagine that there are no other subjects of experience, then it is perhaps best to say only that “there are experiences,” not that “I am the subject of experience”. What right do I have to identify myself as the subject of the experience that is, by hypothesis, pervasive? How can I separate myself, as subject, from that experience?

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So we go back to the generality constraint: my ascriptions of states of consciousness to myself are interdependent with my ascriptions of states of consciousness to others. How do I identify others as the subjects of experience? I cannot, for the reasons I have just rehearsed, identify them merely as the subjects of experience. Strawson argues that I must identify them primarily as persons, that is, as entities possessing both corporeal properties and experience-properties. But why could I not identify them primarily as bodies, that is, by their corporeal properties alone? Strawson has a reply to this objection as well. His objector proposes: “Another subject of experience is distinguished and identified as the subject of those experiences which stand in the same unique causal relationship to body N as my experiences stand in to body M” (Strawson 1959, p. 101). The problem with this proposal, as Strawson notes, is that it presupposes the prior identification of “my” experiences, but this begs the question. My experiences are only identifiable as my own after I have identified myself, as well as others, as persons, that is, as both body and consciousness. It begins to seem that we have understood Strawson’s argument. But Strawson gives a third formulation of the argument as well, and it will be worthwhile to check our interpretation against it. it becomes impossible to see how we could come by the idea of different, distinguishable, identifiable subjects of experiences— different consciousness— if this idea is thought of as logically primitive, as a logical ingredient in the compound-idea of a person, the latter being composed of two subjects. For there could never be any question of assigning an experience, as such, to any subject other than

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oneself; and therefore never any question of assigning it to oneself either, never any question of ascribing it to a subject at all (Strawson 1959, p. 102). The argument is, as we have come to expect, in the form of a reductio. We begin by supposing what is to be contradicted, in this case, that the idea of a subject of experience (a consciousness) is logically primitive. The claim is then that there would be no question of ascribing experiences to any subject other than oneself. From this it follows (by the generality constraint) that there would be no question of ascribing experiences to oneself. And, since one could neither ascribe experiences to oneself nor to another, there would be no question of ascribing them to any subject at all. But here is the contradiction: we do ascribe experiences both to ourselves and to others. Hence, the hypothesis must be false. The last two steps are (provided we accept the generality constraint) simple enough. But what of the move from the supposition that the idea of a subject of experience (a consciousness) is logically primitive to the conclusion that there would be no question of ascribing experiences to any subject other than oneself? This step is the key to the argument, but is it valid? Strawson, as we have seen, does not add anything to justify it in any of its presentations. Can we reconstruct a justification? Let us begin by imagining the situation as it is presented in the initial supposition: that the idea of a subject of experience is logically primitive. We may imagine ourselves confronted by a world composed of subjects-of-experience. The presentation of an experience, then, is constitutive of the subject to which it

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“belongs”. If subjects of experience are primitive, there are no subjects independent of their experience. To have a particular experience just is to be the subject that has that experience. Put that way, the argument makes more sense, at least to me. Now, “this possibility requires that there be empirically applicable criteria of identity for subjects of experience” (Strawson 1966, p. 102). Which is just to say that, in order to be able to identify a potential subject of experience, we must have some criteria by which to identify him. In The Bounds of Sense, Strawson does not immediately argue, as he did in Individuals, that the criteria of identity of subjects must be the identity of the subjects’corporeal bodies. It is only that “In actual practice this condition is satisfied by the fact that each of us is a corporeal object among corporeal objects, is indeed a man among men” (Strawson 1966, p. 102). It being the case that, in fact, the criteria by which we identify subjects of experience are corporeal, does not entail that the criteria by which we identify them must be corporeal. Strawson acknowledges as much: “Our personal pronouns, the pronoun ‘I’ included, have an empirical reference; and in some way such a reference must be secured if the general notion of ascribing experiences to a subject of them is to make sense” (Strawson 1966, p. 102). The phrase “in some way” shows us that Strawson has not here overstepped the bounds of reason. He concludes that we must have some empirical criterion of identification of subjects of experience, and that in fact this criterion is corporeal. He does not, however,

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assert in this passage that our criterion of identification of subjects of experience must be corporeal. He does, however, in the succeeding pages, appear to identify an “empirical” criterion with a “corporeal” one, even to the extent of giving in to the objection that, unless Kant provides us with such a criterion he has not shown us the sufficient conditions for the ascription of experiences. Kant, Strawson seems to say, has given us one necessary condition on the ascription of experiences. It may also be (and in fact appears to be) an additional necessary condition that we should have an empirical (i.e., corporeal) criterion of identification for potential subjects of experience. Strawson writes: “it has in effect been conceded… that the fulfillment of the objectivity-condition is not sufficient to make self-ascription of experiences possible… .An adequate explanation would involve referring to the full conditions of the possibility of self-ascription of experiences (including the existence of the subject as an intuitable object in the world” (Strawson 1966, p. 106). 4.3

Conclusions We have been through a lengthy and detailed exegesis and reconstruction

of Strawson’s arguments that objectivity requires the representation of space. We have seen that one form of the argument reaches only the weak conclusion that objectivity requires the representation of space in a weak, mathematical sense, as independent dimensions of variability. I shall argue in Chapter 5 that this sense of spatial representation is required for predication – we conceptualize objects as

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having certain properties by locating them relative to other objects in an abstract, high-dimensional activation space that codes similarity by proximity. Finally, we have seen that a second form of the argument reaches the stronger conclusion that objectivity requires the representation of space in the much stronger, material sense of three-dimensional Euclidean space wherein only one object can occupy a given position at a given time. I shall argue in the next chapter that this sense of spatial representation is required for reference. It is only by locating physical objects, including our own bodies, in physical space that we are able to identify and re-identify (and so refer to) them. Hence, a careful analysis of Strawson’s arguments for “spatial representation” shows us that there are really two senses of spatial representation at issue. The first sense, representation of properties in an abstract, high-dimensional space, is necessary for conceptualization. The second sense, representation of objects in the familiar three-dimensional Euclidean space of folk physics, is necessary for reference. Together, but not in isolation, the two senses of spatial representation give us a grasp on how it is possible for us to think about things.

Chapter 5 Strawson’s Critics 5.1

Abstract In this chapter, I consider in detail some of the secondary literature on

Strawson’s arguments about spatial representation and objectivity. I demonstrate that Strawson’s critics, albeit in a sometimes confused and confusing way, recognize Strawson’s equivocation between the two forms of “spatial representation”. For the most part, Strawson’s critics focus on the second sense of “space” I identified in the previous chapter, the sense of space as a threedimensional, physical container of material objects. Nevertheless, keeping in mind the two senses of space allows us to see where and why Strawson’s critics become confused about what he means by “spatial representation”. Furthermore, it allows me to clarify the two senses of spatial representation that Strawson confuses and their respective contributions to my own argument. 5.2

Bennett In his book Kant’s Analytic, Jonathan Bennett gives an interpretation of

Strawson’s arguments for spatial representation. Bennett ignores the argument in Chapter 3 of Individuals (“Persons”), and instead considers only the argument in Chapter 2 (“Sounds”). Bennett also ignores Strawson’s conditioning of his conclusion and interprets the argument of Chapter 2 as an argument to the conclusion “that outer experience must pertain to things in space” (Bennett 1966,

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p. 33). This is, I believe, a mistake. The considerations Strawson adduces in Chapter 2, as Strawson himself acknowledges, are not strong enough to show that spatial representation is necessary for outer experience. Although the No-Space world does allow for re-identifiable particulars, it does not, by Strawson’s own admission, meet the requirement “for a scheme in which a distinction [is] made between oneself and what is not oneself” (Strawson 1959, p. 88). That is, it does not allow for the possibility of outer experience (a distinction between outer experience and inner experience). Moreover, the Sound world of Strawson’s Chapter 2 is, by design, not a spatial world. Strawson even refers to it as the “No-Space world” (e.g., Strawson 1959, p. 87). Admittedly, it was necessary, in order to provide for the conditions of re-identifiable particulars, for Strawson to admit into this world “certain auditory analogues of the idea of spatial distance” (Strawson 1959, p. 87), that is, the changing pitch of the master sound, by reference to which individual sound particulars may be re-identified. The master sound provides a dimension along which variation can be tracked. Does it thereby provide for “space”? That depends on how broad our definition of space is. It would be less misleading, in any case, to phrase that conclusion of Strawson’s Chapter 2 as: the reidentifiability of individual particulars requires at least two dimensions of independent variability. This is to emphasize that Chapter 2 does not give us conditions sufficient for outer experience, nor does it require space in the familiar, physical sense, only space in the abstract, mathematical sense.

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Still, there is a kind of argument here for the necessity of spatial concepts to objective experience. Bennett writes that Strawson’s argument “tends to show that outer experience must be of a spatial world” and that “objectivity concepts have work to do, it seems, only in worlds which are ‘spatial’ in a fairly strong sense” (Bennett 1966, p., 41). The argument, I suppose, only “tends to” show its conclusion because it is based on induction from a single case (the Sound world), rather than a deductive argument. Bennett’s understanding of the purpose of the “Sounds” chapter is clearly different from Strawson’s. Strawson makes a point of stating that his “real concern is with our own scheme” and that his speculations about the Sound world are “models against which to test and strengthen our own reflective understanding of our own conceptual scheme” (Strawson 1959, p. 86). Bennett’s mistake, however, points out a couple of questions that are relevant for our own project. To begin with, what is the nature of Strawson’s claim? In Chapter 1 of Individuals, he is quite clear that he is only after the structure of our own conceptual scheme as it actually exists. Thus, he considers questions about what sorts of concepts we do actually have. These sorts of claims are not really appropriate targets for philosophical criticism. They are empirical claims best left up to the psychologists to decide. In Chapter 2 of Individuals, however, Strawson moves to a somewhat stronger claim: that in order to have certain features of our actual conceptual scheme, creatures must necessarily have others. Here the argument is that, in order to have the concept of re-identifiability, creatures must necessarily have the concept of dimensions of independent

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variation (i.e., a concept of space in the abstract, mathematical sense). Strawson’s Chapter 3 makes a similar claim: that in order to have a distinction between inner and outer (a concept we actually have), a creature must have the concept of a person and therefore the concept of a material body (i.e., a concept of space in the everyday, material sense). Both the conclusion and the argument of Chapter 3 are stronger than in Chapter 2. The conclusion is stronger because it does not argue for merely a mathematical notion of space (as was sufficient in Chapter 2), but for a full-blown physical notion of space. The argument is stronger because it is deductive, as opposed to inductive. Bennett points out that Strawson’s theory “is roughly equivalent to Kant’s theory that outer experience must be of things in space” (Bennett 1966, p. 41). While the theories (that is, the conclusions) are equivalent, the arguments for them are quite different. Moreover, Bennett argues that their epistemological status differs. Bennett writes, “It is hard to avoid the conclusion that Strawson’s theory is analytic if it is true at all” (Bennett 1966, p. 42). Bennett thinks this because Strawson’s argument depends on tracing the implications of meaningrelationships between terms such as “objective” and “spatial”. Strawson would surely agree that his arguments in Chapters 1 and 3 are analytic. That his argument in Chapter 2 is analytic is hard to justify, because it is, as I have pointed out, speculative and inductive. Bennett does finally acknowledge these facts about Strawson’s argument in Chapter 2:

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It may be noted that the argument [Bennett has given] proves only that spatiality is sufficient for objectivity: in relation to the converse of this, i.e. in relation to Strawson’s theory, the argument is inconclusive. I suggest that Strawson’s theory is of a kind which cannot be proved conclusively. It is sometimes the case that, in arguing that condition C must obtain if distinction D is to have work to do, one must rest content with showing that C does obtain in certain situations where D does have work to do, and urging that one’s examples have covered all the relevant territory (Bennett 1966, p. 43). This reinforces my claim that Strawson’s argument in Chapter 2 of Individuals is “inductive”. However, it also misses the point of Strawson’s Chapter 2: that “spatiality” in the weak, mathematician’s sense, is not sufficient for objectivity, even though it is sufficient to permit particular re-identification. For full objectivity, both representation in abstract space and representation in everyday material space are necessary. It is important to point out that Bennett’s view that Strawson’s argument is analytic if it is true does not mean that Strawson’s conclusion is unfalsifiable. As I mentioned earlier, Bennett’s view that the theory is analytic is based on the structure of the arguments Strawson uses, that “they consist in certain ways of assembling facts about meanings” (Bennett 1966, p. 44). Bennett thinks that Strawson’s arguments are analytic (which only means of a certain form) but not that Strawson’s conclusion is analytic. The conclusion is only analytic if it is true. If the conclusion is analytic, then it would be a priori, because all analytic judgements are a priori. And if it were a priori, then it would be unfalsifiable, because that is the meaning of a priori in Bennett’s interpretation of Kant.

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However, because Strawson’s conclusion is not analytic (unless it is true), it is not a priori, and so not unfalsifiable. What about Kant’s theory that outer experience must be of things in space? Kant’s theory, as Bennett states it, is that “the outer sense of every human is such as to guarantee that the outer world which he experiences will always conform to the theorems of Euclidean geometry” (Bennett 1966, p. 15). Bennett is not impressed with Kant’s argument, and anyway is mainly concerned with determining whether it really is synthetic a priori, and what that could possibly mean. Consequently, he does not explain Kant’s argument. We must look elsewhere for useful exegesis of the Kantian argument that material bodies are necessary for the concept of objectivity. 5.3

Wiggins David Wiggins uses an argument similar to Bennett’s. He writes: if I cannot allude to my commerce with other persisting things, I cannot say where I am, where I have been or, it seems, anything. Even supposing I could say what I am thinking and have been thinking, others might have had the same thoughts. So no definite description of me would have been achieved. Self-knowledge without the possibility of reference to any other thing than myself either collapses into the tautology that I = I or, dubiously, into a statement about my inner life which does not determine who I am (Wiggins 1963, p. 181).

By putting the argument in a somewhat different form, this quotation may perhaps allow us to get a grasp on it. For Wiggins’ “self-knowledge” we may substitute Strawson’s “experience”. We may then read the argument as follows: experience

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without the possibility of reference to anything else either collapses into the knowledge that there is experience, or into a statement about a life of experience that does not determine who the experiencer is. It does not determine who the experiencer is because, as Wiggins points out in the first part of the quotation, others might have had the same experience. 5.4

Pears Further evidence that I have correctly interpreted Strawson’s argument

may be found by comparing my interpretation with those of other commentators. For example, in an early review of Individuals, David Pears paraphrases the conclusion: “It follows that the concept of a person as a particular to which we can ascribe both states of consciousness and physical characteristics is one that we must possess, and must possess as a primitive concept, if we are to maintain nonsolipsistic consciousness” (Pears 1961, p. 177). Pears’statement of the conclusion is clearly a statement about a matter of fact: in order to have objectivity, a subject must have the concept of a particular to which both states of consciousness and physical characteristics may be ascribed. It follows that, in order to have objectivity, a subject must have the concept of a particular to which physical characteristics may be ascribed; and thence must have the concept of a physical object. To have the concept of a physical object, a subject must be capable of representing material space. This is unarguably a matter of fact. It is empirically testable (falsifiable). Provided we can test whether or not a subject has objectivity and whether or not a

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subject has the concept of a physical object, we could falsify the claim if we could find a subject that has objectivity but not the concept of a physical object. Strawson’s claim amounts to the assertion that such a subject cannot be found. Pears himself has doubts about the necessity of the claim: Mr. Strawson’s conclusion… rests on an elaborate Kantian argument, which seeks to demonstrate that our conceptual scheme has a very rigid structure, in which non-solipsistic consciousness necessitates the concept of an embodied subject. But it may be that the argument succeeds in showing only that nonsolipsistic consciousness makes it natural to have this concept, or even very unnatural not to have it (Pears 1961, p. 178). This suggestion is followed by an argument against Strawson’s conclusion. We must consider this argument in detail, because, if Strawson’s conclusion can be shown a priori to be false, there would be no need to look at empirical data to test it. Pears considers the argument strictly the way Strawson presents it in the text, in the dialectic context of an argument against skepticism about other minds. Pears’version of Strawson’s argument is that “philosophical doubt about other minds… destroys the concept of one’s own possession of states of consciousness, and thus removes the necessary condition of its own statement” (Pears 1961, p. 179). The aspect of skepticism that Strawson sees as problematic is the concept of a person as a compound of two components, the consciousness and the body. For Strawson’s argument against skepticism to fail is for his argument for the

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primitiveness of the concept of persons to fail. The question is thus: has Strawson defeated the skeptic? Pears jumps into Strawson’s argument at precisely the point where we struggled so much to interpret Strawson. Strawson, as we have seen, claims that I could not have the concept of my ownership of states of consciousness if I did not have the concept of another’s ownership of states of consciousness. This is the anti-skeptical claim. The skeptic’s claim is that my concepts of my ownership of states of consciousness and another’s ownership of states of consciousness are independent. In other words, the claim is that I could have the concept of my ownership of states of consciousness without having the concept of another’s ownership of states of consciousness. Pears poses a dilemma. Supposing that I do have the concept of another’s ownership of states of consciousness, then either my ascription of consciousness to another must “go beyond the maximum amount of evidence that I could acquire” (Pears 1961, p. 181), or it must not. If my ascription of consciousness to another does not go beyond the maximum amount of evidence that I could acquire, Pears claims, Strawson’s argument could not “even begin to work” (Pears 1961, p. 181). If my ascription of consciousness to another does go beyond the maximum amount of evidence that I could acquire, Pears claims, Strawson’s argument “seems to break down almost as soon as it begins” (Pears 1961, p. 181). We must first of all inquire as to what it means for my ascription of consciousness to another to “go beyond the maximum amount of evidence that I

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could acquire”. I take it that for this to be the case would be for my beliefs in another’s ownership of states of consciousness to be unjustifiable. That is, it is another statement of the skeptic’s claim and, as such, a statement Strawson would clearly wish to deny. So let us assume that Strawson holds that my ascription of consciousness to another does not go beyond the maximum amount of evidence that I could acquire. Pears has four separate responses to this horn of the dilemma: (1) that it is implausible; (2) that Strawson does not hold it; (3) that if Strawson did hold it, the argument he uses against the skeptic would be invalid; and (4) that if Strawson did hold it, another argument Strawson uses would show that the conclusion of the present argument was false. That is an imposing set of responses, but let us consider them in turn. The first argument is that the hypothesis (that my ascription of consciousness to another does not go beyond the maximum amount of evidence that I could acquire) is implausible, or, as Pears puts it “exceedingly hard to believe” (Pears 1961, p. 183). This is the weakest of the responses. The limits of Pears’belief system hardly seem relevant to the topic at hand. Moreover, if, as I suggested above, the proposition that my ascription of consciousness to another goes beyond the maximum amount of evidence that I could acquire is a statement of skepticism, then Pears’response begs the question. No doubt, for the (honest) skeptic, a non-skeptical position is “exceedingly hard to believe”. Pears second elaboration of this horn of the dilemma is that Strawson does not hold the claim that generates it (that my ascription of states of consciousness

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to another does not go beyond the maximum amount of evidence that I could acquire). Pears writes: the only thing that might suggest that Mr. Strawson believes it is his corollary, that we must sometimes possess criteria for the ascription of states of consciousness to others that are, in some sense, logically adequate. But this corollary is at least capable of being interpreted in a less sweeping way, and everything else in his treatment points to the opposite belief (Pears 1961, p. 183). Pears does not say what is the “less sweeping way” in which Strawson’s assertion (that we must sometimes possess criteria for the ascription of states of consciousness to others that are, in some sense, logically adequate) may be interpreted. Nor does Pears elaborate on what he means by “everything else in his treatment”. As a consequence, the only way I can think of to evaluate his claim is to consider how Strawson himself interprets the proposition Pears demeaningly labels a “corollary”. Strawson does not take it so lightly. He restates the assertion several times, in only slightly different forms, and spends a number of pages defending it. In fact, the version Pears quotes is only the first and by far the most tentative: “in the case of at least some P-predicates, the ways of telling must constitute in some sense logically adequate kinds of criteria for the ascription of the P-predicate” (Strawson 1959, p. 105). Subsequent statements are more unequivocal: “What I have said is that one ascribes P-predicates to others on the strength of observation of their behavior; and that the behavior-criteria one goes on are not just signs of the presence of what is meant by the P-predicate, but are criteria of a logically

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adequate kind for the ascription of the P-predicate” (Strawson 1959, p. 106). Strawson subsequently calls this the “doctrine that the criteria on the strength of which one ascribes P-predicates to others are criteria of a logically adequate kind for this ascription” (Strawson 1959, p. .107). Here there are no wishy-washy corollaries about some ascriptions being adequate in some sense. Instead, there is the unqualified doctrine that the criteria for ascribing states of consciousness to others are logically adequate. As if the unequivocal statements Strawson gives of his own position were not enough, he also interprets it himself in a way that clearly shows that he believes that the criteria for my ascription of states of consciousness to others do not exceed the maximum amount of evidence I could acquire. To begin with, the criteria Strawson has in mind as logically adequate, as he clearly states in the quotation from page 106, are observations of behavior. Surely, observations of behavior do not exceed the maximum amount of evidence I could acquire. This comes out clearly in his discussion of the example of the predicate “depression”. If we allow a logical gap to open between the criteria on the strength of which we say that another is depressed, and the actual state of being depressed… then it swallows not only his depression, but our depression as well. For if the logical gap exists, then depressed behavior, however much there is of it, is no more than a sign of depression. But it can only become a sign of depression because of an observed correlation between it and depression. But whose depression? Only mine, one is tempted to say. But if only mine, then not mine at all (Strawson 1959, p. 109).

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The conclusion of this argument is that we cannot allow a logical gap to open (that is, that there is no logical gap) between the criteria on the strength of which we say that another is depressed and the actual state of being depressed. Moreover, the criteria are clearly behaviors. Pears must be wrong on this count. Strawson clearly does believe that my ascriptions of states of consciousness do not go beyond the maximum amount of evidence that I could acquire, because they do not go beyond my observations of others’behavior. What about Pears’third argument, that if Strawson did hold that my ascriptions of states of consciousness do not go beyond the maximum amount of evidence that I could acquire, then Strawson’s argument against the skeptic would be invalid? Pears argues that it could not even begin to work, because “its starting-point is the concept of another person’s ownership of states of consciousness, and in this concept it will not be including anything that the skeptic wants to reject” (Pears 1961, p. 181). Let us try to make sense of this claim. Recall that the assertion under question is whether my concept of my ownership of states of consciousness is independent of my concept of another’s ownership of states of consciousness. The skeptic asserts that it is, while Strawson denies that it is. In particular, Strawson asserts that I can ascribe states of consciousness to myself only if I can ascribe states of consciousness to another. The skeptic denies this conditional. It is possible, according to the skeptic, that I can ascribe states of consciousness to myself without being able to ascribe states of consciousness to another. Pears reads Strawson’s argument that this is

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impossible just as I do: “if I did not already possess the concept of another’s ownership of states of consciousness, I could not understand the phrase ‘my states of consciousness’, because I could not see any difference between the meaning of this phrase and the meaning of the phrase ‘all states of consciousness’” (Pears 1961, p. 180). What does Pears mean when he asserts that the “starting point” of this argument is the concept of another person’s ownership of states of consciousness? I take it that he is alluding to the supposition that I do not already possess the concept of another’s ownership of states of consciousness. I think the idea behind Pears’argument is that the skeptic would accept the claim (that I can have the concept of my ownership of states of consciousness only if I can have the concept of another’s ownership of states of consciousness) as long as my concept of another’s ownership of states of consciousness only involves the maximum amount of knowledge that I can have. The skeptic can agree to the conditional that I can ascribe states of consciousness to myself only if I can ascribe states of consciousness to others without more than the maximum amount of evidence that I can acquire. It’s just that, in these circumstances, the skeptic thinks that we have an impoverished notion of consciousness, that the states of consciousness that I ascribe to others must be somehow less than the states of consciousness that I ascribe to myself. However, this argument trades on an ambiguity in “states of consciousness” in the statement of the argument. There are two possibilities: either my states of consciousness are the same kinds of things as others’states of

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consciousness, or they are not. If they are, then the conditional under dispute may be written: I can have the concept of my ownership of states-of-consciousness-1 only if I can have the concept of another’s ownership of states-of-consciousness1. If my states of consciousness are not the same kinds of things as others’states of consciousness, then the conditional must be written something like: I can have the concept of my ownership of states-of-consciousness-2 only if I can have the concept of another’s ownership of states-of-consciousness-3. Strawson is clearly defending the first version of the conditional. In one statement of the argument, he writes “it is a necessary condition of one’s ascribing states of consciousness, experiences, to oneself, in the way one does, that one should also ascribe them, or be prepared to ascribe them, to others who are not oneself. This means… for example, that the ascribing phrases are used in just the same sense when the subject is another as when the subject is oneself” (Strawson 1959, p. 99). Even in the case where I can ascribe states of consciousness to others on the basis of only the available evidence, the skeptic does not accept this claim. For the skeptic must believe, if he is to remain a skeptic, that in this case, the states of consciousness I ascribe to others are different from the states of consciousness I ascribe to myself. So Strawson’s argument against the skeptic is not invalid on the grounds Pears claims it is. But Pears’final argument is that another argument (one which incidentally Strawson himself uses in another context) shows that the conclusion of Strawson’s argument against the skeptic about other minds is false. This second

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argument begins with the supposition that led to this horn of the dilemma: that my ascription of states of consciousness to others does not go beyond the maximum amount of evidence that I could acquire. Then the skeptic denies that I can ascribe states of consciousness to myself only if I can ascribe states of consciousness to others without going beyond the maximum amount of evidence that I could acquire. The argument Pears considers is that the skeptic’s “doubt is senseless, or could not be stated by him, because it goes beyond the best available criteria” (Pears 1961, p. 179). It goes beyond the best available evidence because it claims that I can ascribe states of consciousness to others only if I exceed the maximum amount of evidence that I could acquire. But this excess cannot be expressed, so the skeptic must phrase his doubt as follows: I can understand the concept of my ownership of states of consciousness only if I can understand the concept of the “not altogether reliable signs of another person’s states of consciousness” (Pears 1961, p. 179). In this case, writes Pears, “the skeptic could not have been charged with rejecting our conceptual scheme, and recommending another. For he could not have been represented as recommending anything more than a change of words” (Pears 1961, p. 179). That is, the skeptic recommends replacing our talk about other peoples states of consciousness with some vague talk about the doubtful signs we have of those signs of consciousness. But this recommendation is consistent with Strawson’s claim that I cannot understand the concept of my ownership of states of consciousness unless I understand the concept of others’ ownership of states of consciousness. Or, as Pears puts it, “such a verbal

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recommendation could not possibly have any repercussions on the concept of one’s own possession of states of consciousness” (Pears 1961, p. 179). Pears calls this argument the “direct” argument. Pears calls the argument that Strawson actually uses the “indirect” argument. Pears’final word about all of this is that, if the direct argument can be used, “the conclusion of the indirect argument could not be correct” (Pears 1961, p. 181). Pears apparently thinks that the significant conclusion is that the skeptic is rejecting the conceptual scheme in which his own doubts make sense. But that is not the conclusion of Strawson’s argument. It is only a step along the way. The conclusion Strawson draws is just the condition we have been considering all along: that I can understand my ownership of states of consciousness only if I can understand others’ownership of states of consciousness. The direct argument does not show that this conclusion is false. It only shows that, on one interpretation, the skeptic agrees with it. But we cannot take the skeptic’s concession to Strawson’s argument to be a victory for the skeptic. So, let us allow that Strawson has made his case that identification of states of consciousness (experiences) depends on identification of persons. By the first few steps of the argument I rehearsed above, this shows that objectivity depends on identification of persons. How does Strawson get from there to the conclusion that objectivity depends on spatial representation? He does so in part by arguing that persons are both material bodies and experiences. Since persons are material bodies, identification of persons must

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depend on identification of material bodies. Identification of material bodies depends on spatial representation. That is rather fast. Why is the identification of persons dependent on the identification of material bodies? The last step in Strawson’s argument that objectivity requires materialbody identification is simple. Because identification of subjects of consciousness requires identification of persons, to which both predicates ascribing experiences and predicates ascribing corporeal characteristics are applicable, identification of subjects of consciousness entails the ability to identify at least some material bodies: those that are parts of persons. And, he has argued, because material bodies constitute a system of spatial relations, the ability to identify material bodies requires the ability to represent spatial relations. 5.5

Rorty Richard Rorty also sees Strawson’s persons argument as an argument for

the thesis that objectivity requires spatial representation. In a paper primarily on Strawson’s arguments in The Bounds of Sense, Rorty writes that “Strawson has available an additional argument” for the claim “that if you don’t know what the distinction is between seeming and being, you won’t know what an experience is, whereas if you do know what this distinction is, you automatically know what a physical object is” (Rorty 1970, p. 212 and note 5). Before I go on to show that Rorty’s interpretation of Strawson’s argument is similar to mine, I want to point out that Rorty has the conclusion wrong. To begin with, Rorty conflates two theses that Strawson is careful to keep separate: (1) that objective experience is

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necessary for any kind of experience; and (2) that experience of physical objects is necessary for objective experience. Second, Rorty takes Strawson to hold a conclusion that I am not sure he does, that is, that objective experience is sufficient for experience of physical objects. In any case, the “additional argument” is: the argument familiar from the “Persons” chapter of Individuals— to the effect that you don’t know what an experience is unless you know what a person is, and that a person must be thought of as something that has physical-object characteristics as well as “mental” characteristics (Rorty 1970, p. 212, n. 5). Rorty’s summary is just a telescopic version of the argument as I presented it in Chapter 3. In fact, Rorty gives a somewhat lengthier version of the argument later in the body of his paper: “to have the concept of a ‘state of consciousness’one has to have the concept of the subject of such a state, and that one can have the latter concept (the concept of a person or a self) only if one can use physical-object concepts to distinguish one person from another” (Rorty 1970, p. 221). In Rorty’s paper “Strawson’s Objectivity Argument,” he had summarized Strawson’s argument as follows: “to have the concept of a ‘state of consciousness’one has to have the concept of the subject of such a state, and… one can have the latter concept (the concept of a person or a self) only if one can use physical-object concepts to distinguish one person from another” (Rorty 1970, p. 221). We might diagram Rorty’s version, at the same time connecting it with objectivity, as follows:

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(1)

a subject can have the concept of an objective state of consciousness only if he can have the concept of a state of consciousness

(2)

a subject can have the concept of a state of consciousness only if he can have the concept of a subject of a state of consciousness

(3)

a ‘subject of a state of consciousness’ is a ‘self’

(4)

therefore, a subject can have the concept of a state of consciousness only if he can have the concept of a self

(5)

a subject can have the concept of a self only if he can use physical-object concepts to distinguish one self from another

(6)

therefore, a subject can have the concept of an objective state of consciousness only if he can use physical-object concepts to distinguish one self from another

Rorty considers a criticism of this argument based on the claim “that we could have a conceptual scheme which would enable us to think about states of the self without thinking of them as states of the self” (Rorty 1970, p. 221). What part of the argument is this supposed to contravene? Apparently, it is (4). The objector’s claim seems to be that a subject can have the concept of a state of consciousness (a state of the self) without having the concept of a self. Rorty does not give us much help in clarifying the issue. His first attempt is the following confusing passage: “Such an opponent might grant… that someone who had no physical-object concepts would not have our concept of a state of the self, but could nevertheless grasp a concept which he applied just on

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those occasions, when, e.g., we would apply the concept of ‘sensation of something red’” (Rorty 1970, p. 221). It is clear that the imagined subject has a concept of a state of consciousness, and also that he does not have physical-object concepts. Thus it is clear that the objection denies that a subject can have the concept of a state of consciousness only if he has physical-object concepts, that is, that it denies the conclusion of the argument. It is unclear from the example, however, just whether Rorty’s objector denies proposition (4) of the argument or some other part of it. Rorty’s second attempt at explication is not any more helpful. He writes that the “suggestion is that there might be terms in a solipsistic language which had the same extensions as terms signifying states of consciousness in our language, but not the same meanings, and that the use of these words would provide concepts which would make experience possible— but not an experience which satisfies the objectivity thesis” (Rorty 1970, p. 221). Let us try to follow this version through. A subject whose language included terms which had the same extensions as terms signifying states of consciousness could at least refer to states of consciousness. So the subject can refer to states of consciousness. However, his terms do not have the same meanings. Wherein lies the difference? Rorty’s first gloss on the objection was that the subject could “think about states of the self without thinking of them as states of the self.” On the face of it, this does not make much sense. The concept of a self is, according to the version of the argument Rorty himself gives, the concept of a subject of a state of

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consciousness. By substitution, the claim is that the subject can think about states of a subject of a state of consciousness without thinking of them as states of a subject of a state of consciousness. How does this match up with his later explication, the one we just considered, in which he asserts that the subject can refer to states of consciousness? The only explanation I can think of is that he means that the subject can refer to states of consciousness even though he cannot refer to the subjects of states of consciousness. That is, the subject can refer to states of consciousness even though he cannot refer to selves. So construed, the claim has some affinity with a denial of (4), but it is not really a denial of (4). A full-blown denial of (4) would assert that a subject can have the concept of a state of consciousness even though he does not have the concept of a self. Our objector has only argued that a subject can refer to a state of consciousness even though he cannot refer to a self (a subject of a state of consciousness). Therefore, in a strict sense, the objector has not even really presented an objection to Strawson’s persons argument. He has instead presented an objection to the following argument: (2*) a subject can refer to a state of consciousness only if he can refer to a subject of a state of consciousness (3)

a ‘subject of a state of consciousness’ is a ‘self’

(4*) therefore, a subject can refer to a state of consciousness only if he can refer to a self

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(5*) a subject can refer to a self only if he can use physical-object concepts to distinguish one self from another (6*) therefore, a subject can refer to a state of consciousness only if he can use physicalobject concepts to distinguish one self from another The point is that these are two different arguments. In particular, the difference lies between: (2)

a subject can have the concept of a state of consciousness only if he can have the concept of a subject of a state of consciousness

and (2*) a subject can refer to a state of consciousness only if he can refer to a subject of a state of consciousness We have on our hands a suggestion for a kind of counterexample to (2*). We have to ask two questions at this point. First, can we really provide a counterexample? Second, even if we do provide a convincing counterexample, does the falsity of (2*) entail the falsity of (2)? Rorty doesn’t give us any help here. In fact, he confuses matters even further by claiming that his argument would deflate not only Strawson’s argument, but also “any which has the form ‘The concept X presupposes the concept Y, and therefore to experience X’s presupposes being able to experience Y’s” (Rorty 1970, p. 221). To begin with, we should not assume that the argument we have been considering, the argument derived directly from Rorty’s own statement of Strawson’s persons argument, does not have this form. In particular,

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it does not even mention experience. Suppose we try to reframe the argument in such a way as to show how it fits this framework: (2**)

the concept of a state of consciousness presupposes the concept of a subject of a state of consciousness

(3)

a ‘subject of a state of consciousness’ is a ‘self’

(4**)

the concept of a state of consciousness presupposes the concept of a self

(5**)

the concept of a self presupposes the concept of a physical object

(7)

therefore, the concept of a state of consciousness presupposes the concept of a physical object

(8)

therefore, to experience a state of consciousness presupposes being able to experience a physical object

Rorty’s objection to this argument is that “an opponent can grant that to experience X’s as X’s would require a grasp of the concept Y, but nevertheless insist that X’s may be experienced under another description, and that a grasp of the terms used in formulating this new description does not presuppose an ability to use the term ‘Y’” (Rorty 1970, pp. 221-2). Let us look at another version of such an argument to get a grasp on what Rorty means. Suppose someone argued that “The concept morning star presupposes the concept morning, and therefore to experience the morning star presupposes being able to experience the morning”. Now, as Rorty suggests, we can grant that to experience the morning star as the morning star would require a grasp of the concept of the morning, but

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nevertheless insist that the morning star may be experienced under another description (for example, as the evening star), and that a grasp of the terms used in formulating this new description does not presuppose an ability to use the term ‘morning’. Resorting to such an overworked example is unfortunate, but it does accomplish an important goal: showing how the argument as Rorty phrases it in this, general, version is related to the argument as he so confusingly presented it in the original. It also helps us to see the central ambiguity in the argument. The ambiguity lies in the word “experience”. I can experience the morning star as the morning star only by seeing Venus in the morning. On the other hand, I can experience the morning star without seeing Venus in the morning (for example, by seeing it in the evening). The difference is, as Rorty had said, between experiencing the common referent under one description (in one sense) as opposed to another. Another way of putting the same point is that it is the difference between being able to identify the referent of a term and grasping the sense of the term. The question is whether Strawson’s persons argument requires that we should merely be able to identify the referent of the term “state of consciousness” or that we should moreover be able to grasp the sense of that term. The language in which Rorty himself phrases the argument (to have the concept of a ‘state of consciousness’) suggests that we must be able, not merely to identify the referent, but also to grasp the sense. Moreover, Strawson’s own emphasis on selfconsciousness suggests that he would also insist that we must be able to grasp the

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sense of a state of consciousness, that is, to experience it as a state of consciousness. But is this really necessary for Strawson’s argument? In fact, it is not. Rorty has misstated Strawson’s argument, and, although he has possibly found an objection to the argument he gives, I do not believe that he has found an objection to the argument Strawson gives. For, as the reader will recall from our exegesis of that argument, Strawson’s claim is not that one can “have the concept” of a state of consciousness only if one can “use physicalobject concepts”. Rather, the argument is that one can identify, or ascribe, states of consciousness only if one can identify material bodies. That is, Strawson’s argument is based purely on the ability to refer to the things in question, not on an ability to experience them in a particular sense. Strawson’s conclusion is not that one can experience a state of consciousness only if one can experience a physical object, but rather that one can identify a state of consciousness only if one can identify a physical object. Because Rorty’s argument is not Strawson’s argument, Rorty’s criticism of his argument is not a criticism of Strawson’s argument. Strawson’s claim, being weaker, is easier to defend. Rorty writes about an objection to Strawson’s persons argument that: since our only test for relations of presupposal among concepts is whether a given word could be said to be properly used by someone who could not use some other word, to have a given concept must be identified with (or at least have as a necessary condition) the ability to use a given word, or a given group of words. Thus nothing will be said to have experience which is not a language-user (Rorty 1970, p. 222).

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This assertion raises several issues we must address directly. (1) Is it true that our only test for relations of presupposal among concepts is whether a given word could be said to be properly used by someone who could not use some other word? (2) When can we say that a given word can be properly used by someone? (3) Is it a conceptual or an empirical issue whether a given word can be properly used by someone who could not use some other word? (4) Should we identify having a concept with being able to use a given word? (5) Is the ability in question counterfactual or actual? (6) Is it even plausible that nothing which is not a language-user could have experience? In addition, we must ask about any transcendental argument that we presume to test empirically whether it is based on relations of presupposal among concepts. Rorty makes his point again in somewhat different language a couple of pages later: “unless we both restrict the application of the term ‘experience’to language-users and restrict the concepts they can employ to those signified by words which they can use, we will have no basis whatever for offering transcendental arguments about the possibility of experience” (Rorty 1970, p. 224). He also relates this general thesis about transcendental arguments directly to Strawson: “Arguments of the Strawsonian type rest on considerations of which words can be understood independently of which other words. The relevance of these considerations vanishes if we admit the possibility of a being who could experience something as an X but could not use the word ‘X’nor any equivalent expression” (Rorty 1970, p. 224).

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So far, I have argued that Rorty misconstrues Strawson’s argument, and that as a consequence, he has not given a compelling criticism of it. Do Rorty’s remarks on transcendental arguments in general hold their force, despite his error in that particular case? Rorty does give us the beginning of an answer to questions (2) and (5) above. He writes that: in order to be correctly said to have a given concept one must have at some time or another applied it— used it in forming judgment (true or false) about some real or imagined entity. If a man’s conceptual repertoire is so limited that the only sorts of judgements he can make are reports of observation or introspection, then it will necessarily be the case that if he has the concept “X”, then he will have experienced something as X; he will, that is, have judged something or other (truly or falsely) to be X. This is not a remark about a psychological mechanism. It is not to say that he needed the experience of an X in order to “abstract” the concept “X” from it. Rather, it is a remark about our criteria for crediting a man with the grasp of a concept (Rorty 1970, p. 226). Rorty thinks that one of the conditions on someone’s having the ability to use a given word (that is, having the concept expressed by that word) is that he should actually have exercised that concept in judgement. It is thus not a counterfactual, but an actual issue. Rorty also clearly thinks that his version of transcendental argument is the only kind of transcendental argument possible. He writes that “All that transcendental arguments— a priori arguments about what sort of experience is possible— can show is that if you have certain concepts you must have certain other concepts also” (Rorty 1970, p. 231). We should consider whether this claim

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is true, especially in light of the fact that Strawson’s persons argument, at least, does not appear to have this form. Rorty’s claim about the nature of concepts is based on a Wittgensteinian epistemology. Rorty writes that “as long as concepts are discrete mental contents— representations— there is no clear way in which relations of presupposition between them can be discerned. It is only when the Wittgensteinian interpretation of concepts is adopted that we are able to give arguments for one concept presupposing another— arguments of the form: ‘No one who did not know how to use the word ‘...’would know how to use the word ‘— ’’” (Rorty 1970, p. 237). If Strawson’s argument does in fact turn upon such a Wittgensteinian interpretation of concepts, it is open to critique from that angle. Rorty begins with an argument from The Bounds of Sense from the necessary unity of experience to the objectivity thesis. Strawson’s own conclusion is that the minimum implied is that some at least of the concepts under which particular experienced items are recognized as falling should be such that the experiences themselves contain the basis for certain allied distinctions: individually, the distinction of a subjective component within a judgement of experience (as “it seems to me as if this is a heavy stone” is distinguishable within “this is a heavy stone”); collectively, the distinction between the subjective order and arrangement of a series of such experiences on the one hand and the objective order and arrangement of the items of which they are experiences on the other (Strawson 1966, p. 101).

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This, particularly the latter statement about the possibility of distinguishing objective order and arrangement from subjective, is, as we have seen, merely a statement of the objectivity thesis. Rorty, however, misreads Strawson here. Rorty’s interpretation of Strawson’s argument in general is that “if you don’t know what the distinction is between seeming and being, you won’t know what an experience is, whereas if you do know what this distinction is, you automatically know what a physical object is” (Rorty 1970, p. 212). So, Rorty’s version of the argument is that you can have experience only if you can have objective experience (if you know what the distinction is between seeming and being), and you can have objective experience if and only if you can experience physical objects. In fact, Strawson is only saying that one would not know what an experience was if one did not know how to distinguish the subjective ordering of experiences from the objective ordering of their causes. The argument that this, in turn, requires a representation of spatial relations, and, in fact, the conception of a physical object, comes later. Rorty has, like Kant, conflated arguments for the objectivity thesis with arguments for the spatiality thesis. Rorty makes the same mistake on the very next page. He begins by citing a different passage from Strawson: What is meant by the necessary self-reflexiveness of a possible experience in general could be otherwise expressed by saying that experience must be such as to provide room for the thought of experience itself. The point of the objectivitycondition is that it provides room for this thought. It provides room, on the one hand, for “Thus and so is how things objectively are” and, on the other, for

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“This is how things are experienced as being”; and it provides room for the second thought because it provides room for the first (Strawson 1966, p. 213). This passage is, on my reading, simply a statement of, and advertisement for, the objectivity thesis. Rorty, however, takes it a step farther (indeed, I would argue, a step farther than it actually goes): The point that Strawson is making here is that you don’t know what “experience” means if you don’t know what “seems to me… ” means, that you don’t know what that means unless you know that something can seem to me to be X and not be X, and that if you know that something can seem to me to be X and not be X, you know what it is for something to be a physical object. So anybody who can say to himself: “This is the way it seems to me now” can also say to himself: “This may be how certain physical objects are now” (Rorty 1970, p. 213). I take no issue with the part of Rorty’s exegesis that construes Strawson as here arguing that the possibility of experience requires an objective-subjective or “seems-is” distinction. But Rorty makes the mystifying statement that “if you know that something can seem to me to be X and not be X, you know what it is for something to be a physical object”. Strawson does not mention “physical” objects anywhere in the passage. In fact, he does not even mention “objects”. He writes instead in the extremely general terminology of “things” which, as any careful reading of the text shows, he is careful not to conflate with “physical objects”. Although Strawson does indeed make arguments about the relation of physical objects to the objectivity condition, he does not do so in the passage Rorty cites. Moreover, even when Strawson does connect physical objects (that is,

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objects in space) with objectivity, Strawson’s claim is that representation of objects in space is necessary for the fulfillment of the objectivity condition. Strawson’s claim is not, as Rorty would have it, that the fulfillment of the objectivity condition is sufficient for the representation of physical objects. Rorty does at least acknowledge that someone might propose to drive a wedge between the objectivity thesis and the spatiality thesis. In a footnote, he writes that “It might be objected at this point that one could grasp the contrast between ‘seems’and ‘is’even if one lacked the concept of a physical object by making a distinction between veridical and nonveridical, trustworthy and untrustworthy, sense data, on the basis of the coherence or incoherence of some sense data with others. But what would it mean to say that a sense datum was nonveridical save that it did not properly represent the characteristics of some physical object?” (Rorty 1970, p. 213). This is an element common to several criticisms of Strawson, one that I must admit I do not understand. Strawson’s conclusion is that, in order to have objective experience, I must always and continuously represent a spatial framework. It is not that, in order to have developed the idea of objective experience in the first place I should have first had to have represented a spatial framework. Bennett, for example, apparently misunderstands this point when he writes: “there is evidence in Individuals… that Strawson really is prepared to argue genetically, basing philosophical conclusions on principles of the form “If P, then Q earlier”… .Perhaps he is entitled to, but the literature which argues that

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he is not deserves an answer” (Bennett 1968, p. 345). Strawson does not make such an argument, and we should not criticize him for doing so. Rorty at least recognizes this much. In a discussion of “the puzzling claim that we can, by a priori argument, demonstrate something about the order in which we must have had certain sorts of experiences” (Rorty 1970, p. 211), Rorty agrees with Bennett that a “‘genetic’claim is just not the sort of claim that can possibly result from an investigation of relations of presupposal between concepts” (Rorty 1970, p. 229). Rorty, however, correctly notes that “the point of the objectivity argument is not to establish a genetic order, but to refute a claim about such an order— viz., the claim that we could have some other concepts before we had any physical-object concepts. This argument does not imply anything about the order in which experiences must come” (Rorty 1970, pp. 22930). This position has an intuitive appeal, and it has also been supported by more contemporary arguments. The most visible proponent of this thesis in the contemporary literature is Gareth Evans. He writes, for example, that: The places which we think about are differentiated by their spatial relations to the objects which constitute our frame of reference… . Hence a fundamental identification of a place would identify it by simultaneous reference to its relations to each of the objects constituting the frame of reference. A place would be thought about in this way if it was identified on a map which represented, simultaneously, the spatial relations of the objects constituting the frame of reference. This identification has a holistic character: a place is not identified by reference to just one or two objects,

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and so the identification can be effective even if a few objects move or are destroyed. Our identification has this holistic character whenever we rely, in our thinking about places, upon what has come to be called a ‘cognitive map’: a representation in which the spatial relations of several distinct things are simultaneously represented. It is essential to the existence of a genuine concept of space, and of objects existing in space independently of perception, that the thinker have the capacity to form and employ representations such as these… .To say that the fundamental level of thought about the spatiotemporal world— the level of thought to which all our other thinking directs us— is thought which would be sustained by a cognitive map of that world is to stress that our fundamental level of thinking is, in a certain sense ‘objective’. Each place is represented in the same way as every other; we are not forced, in expressing such thinking, to introduce any ‘here’or ‘there’” (Evans 1982, pp. 151-2). In this passage, Evans clearly asserts that an allocentric representation of spatial relations is necessary for an objective model of the world. Charles Parsons’summary of these points is useful: “space is in some way prior to objects, in the sense that objects are experienced as in space, and in the sense that experience does not reveal objects, in some way not intrinsically spatial, that stand in relations from which the conception of space could be constructed” (Parsons 1992, p. 72). We need not get involved in the tendentious debate over Kant’s transcendental idealism. It does not matter for us whether Kant thought that objects themselves could have spatial properties, only that it is clear he thought that to perceive them (and thus identify them) we must necessarily locate them in space.

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I should point out that, even if some of those arguments that I have rejected were to be valid, they would not in themselves establish that we must represent space, but only that a spatial framework must exist. Strawson and Kant solve this problem in the same way. They both argue that, even if some fundamental spatial framework exists, we cannot perceive it in and of itself. Therefore, we must be capable of representing it. Strawson summarizes Kant’s Analogies as follows: The fundamental thought of the Analogies is that of the connection between the objectivity of experience and unity of the spatio-temporal framework of experience. To this is added the clear realization that there is no question of pure objective Space-Time itself being an object of perception to which we can directly relate other objects of perception. And from these two thoughts together there follows the general conclusion that the necessary unity of Space-Time must somehow be represented by a system of connections between our ordinary empirical perceptions (Strawson 1966, p. 147). This most general version of the argument shows the indirectness of its progress. Objectivity requires a spatio-temporal framework. Because we cannot directly perceive any spatio-temporal framework, the one that grounds objectivity is a representation of the connections between the objects of our perceptions. (I point this out only to be clear about the argument. I do not intend to challenge it here.) Indeed, Kant’s own argument for this conclusion, in the Refutation of Idealism, makes a bit more sense. He begins, “I am conscious of my own existence as determined in time. All determination of time presupposes something

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permanent in perception” (Kant 1781/1787, B275). This is a much clearer statement than Strawson’s claim that, in order to make sense of a subject’s awareness of himself as having an ordered series of experiences, we need a system of temporal relations that includes more than the experiences themselves. It is clearer because it makes explicit what we discovered only after detailed examination of Strawson’s argument: that we need something above and beyond the experiences themselves, something constant or permanent, in order to make sense of the passage of time. Kant’s proof, as amended in the preface, continues: “But this permanent cannot be an intuition in me. For all grounds of determination of my existence which are to be met with in me are representations; and as representations themselves require a permanent distinct from them, in relation to which their change, and so my existence in the time wherein they change, may be determined” (Kant 1781/1787, Bxl). That is to say, whatever is the constant against which I measure the succession of my experiences, it cannot itself be one of my experiences (“an intuition in me”). The reason why none of my experiences is adequate to serve as a constant against which the succession of my other experiences may be measured is clear enough from the end of Kant’s next sentence: as an experience itself, any purported constant experience would itself require something constant and distinct from it, against which its change could, in turn, be measured. None of my experiences can constitute the permanent constant against which my experiences are measured, because each one would require something else constant against which it could be measured. Whatever is the

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constant against which the succession of my experiences are measured, it must be something other than one of my experiences. That much is clear enough. Kant, however, is at least in danger of making the same, apparently unjustified, slide from the established fact that the constant must not be one of my experiences to the claim that it must not be me, or in me. His last sentence begins, “all grounds of determination of my existence which are to be met with in me are representations”. I can see no way to interpret this except as the claim that I consist entirely of my experiences. There is nothing but my experience to latch on to in me, so to speak, except experience itself. The claim that I consist of nothing but my experiences is surely open to debate. In particular, if we consider it in light of Strawson’s own argument that a person consists not only of experiences but also of the body that has them, then we may say that my body is, in a sense, “in me”. Therefore, my body is available as a constant by which I may measure the succession of my experiences. This is precisely the sort of claim I was getting at in relation to Strawson’s argument above. It seems that Kant may be susceptible to this objection as well. For, his argument continues, “perception of this permanent is possible only through a thing outside me and not through the mere representation of a thing outside me; and consequently the determination of my existence in time is possible only through the existence of actual things which I perceive outside me” (Kant 1781/1787, B275,-6). Kant has slipped from the claim that the “permanent cannot be an intuition in me” to the claim that it must be a “thing outside of me”. (It is

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significant that in the unamended proof the revised portion begins “This permanent cannot, however, be something in me” and not “this permanent cannot be an intuition in me”, as it does in the revised version. Kant saw the tension, although he never quite got rid of it.) The conclusion that Kant’s argument properly warrants is that there must be something permanent other than my experiences against which I may judge their succession. If we find it necessary to add that this permanent is not “in me” that can only mean that it is not merely an experience of mine. It cannot, however, be taken to mean that the existence of my own body is inadequate as a grounds for the succession of my experience. Regardless of whether Strawson has properly interpreted Kant here, it is clear enough that Strawson holds this proposition to be true. What is his argument for it? Strawson gives this argument several times, in several forms, in Chapter 3 of Individuals. In its first presentation, it is a generalization of a reflection about the sound world. Strawson has concluded that the experiencer in the sound world cannot distinguish himself from other possible subjects of experience, and he wonders why: “Would it not seem utterly strange to suggest that he might distinguish himself as one item among others in his auditory world, that is, as a sound or sequence of sounds? For how could such a thing— a sound— be also what had all those experiences?” (Strawson 1959). Keeping in mind that in the sound world (the “no-space” world), there are nothing but sounds, this seems

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eminently plausible. From this consideration about the sound world, Strawson generalizes to any possible experiencer: [for someone] to have the idea [of a self] at all, it seems that it must be an idea of some particular thing of which he has experience, and which is set over against or contrasted with other things of which he has experience, but which are not himself. But if it is just an item within his experience of which he has this idea, how can it be the idea of that which has all of his experiences? (Strawson 1959) Strawson asserts here that the idea of a self cannot be merely an experience, a particular state of consciousness, because the self is supposed to be that which has all experiences. An experience seems not to be the sort of thing that can have experiences, so the self is of a different logical kind than experiences. The self must be something above and beyond mere experience. Strawson does identify some aspects of the more complex argument as originating in Kant’s writings, especially the Refutation of Idealism and the Analogies. In particular, there is a more full discussion of the step that puzzled us in our exegesis of the step in Strawson’s argument which claimed that, in order to identify my own consciousness, I must be able to identify other consciousness. Strawson traces this argument to the Refutation of Idealism, and in particular the claim that “The consciousness of my existence is at the same time an immediate consciousness of other things outside me” (Kant 1781/1787, B 276). Strawson also gives a version of the persons argument on pp. 126-7 of The Bounds of Sense. He begins: “Suppose we think first simply of a temporal series of representations or experiences.… We may… think of the members of the series

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as temporally ordered in relation to each other, as having each a determinate temporal position in the series relatively to the others” (Strawson 1966, p. 126). This is the idea I used before of an ordering of experiences, for example: Now Strawson asserts that “what we really mean by an experience’s membership of such a series is really nothing different from its being an experience of a potentially self-conscious subject” (Strawson 1966, p. 126). It seems at first that what is meant by this is that we must take the notation I used above as shorthand for something like: S experiences [A], then S experiences [B], then S experiences [C] However, Strawson asserts that the “internal temporal relations of the members of the series are quite inadequate to sustain or give any content to the idea of the subject’s awareness of himself as having such-and-such experience at such-andsuch a time (i.e. at such-and-such a position in the temporal order” (Strawson 1966, p. 126). This, it seems, makes more of the self-consciousness of the subject than I did in my gloss above. For it seems that what is really required is that the notation be shorthand for something like: S experiences [himself as experiencing [A], then [B], then [C]]. Perhaps a better, or at least a simpler, way of writing the same thing is: S experiences [[A], then [B], then [C]].

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That is, the subject himself must be aware of the temporal order of the representations he experiences. The next question to ask is why the internal temporal relations of the members of the series are inadequate to give content to the idea of the subject’s being aware of himself as having the experiences in that order. This question allows us to return directly to the more relevant problem: why are the internal temporal relations of the members of the series inadequate to give content to the subject’s awareness of his having experiences in a given order? The answer is, I think, to be found in comparing the different interpretations I gave of the series. They were: (1)

S experiences [A], then S experiences [B], then S experiences [C].

(2)

S experiences [himself as experiencing [A], then [B], then [C]].

(3)

S experiences [[A], then [B], then [C]].

(1) was inadequate because it did not capture the self-consciousness of the subject. It might just as well have been paraphrased as: S’ experiences [A], then S’’ experiences [B], then S’’’ experiences [C]. since there is no self-awareness of the subject as a subject to connect the three experiences. I offered (3) as a simpler, meaning shorter, version of (2), but we can now see that it is inadequate, because only (2) makes explicit S’s selfconsciousness: his experience of himself as experiencing. To make this fully explicit, we should really interpret our ordering as:

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S experiences [S experiences [A]] then S experiences [S experiences [B]] then S experiences [S experiences [C]]. In this formulation, there is a clear identity of the subject, S, across all three of the experiences. Another way of accomplishing the same thing would be to include S’s individual experiences in the temporal ordering, naming them by their positions in the ordering: If we had written the ordering that way in the first place, we could have simply interpreted it as: S experiences 1, S experiences 2, S experiences 3 So, when Strawson writes that the internal temporal relations of the original series cannot give content to the idea of the subject’s awareness of himself as having experiences in a given order, it seems that he means that only the temporal relations of the more complete series could give content to that idea. This explanation has the virtue of making sense of Strawson’s next few remarks, beginning with the claim that to “give content to this idea we need, at least, the idea of a system of temporal relations which comprehends more than those experiences themselves” (Strawson 1966, p. 126). As usual, Strawson puts the point in as general terms as possible. In particular, it seems that he means that

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we need the idea of a system of temporal relations which comprehends those experiences as the experiences of the very same self-conscious subject. That is, we need the idea of a system of temporal relations which includes the subject himself. “But,” Strawson writes, “there is, for the subject himself, no access to this wider system of temporal relations except through his own experiences” (Strawson 1966, p. 126). This is the obvious point that the subject has no direct access to the world, but only to his own representations of it. Therefore, he concludes, the subject’s experiences “must be taken by him to be experiences of things (other than the experiences themselves) which possess among themselves the temporal relations of this wider system” (Strawson 1966, p. 127). That is, on this interpretation, the subject’s experiences must be taken by the subject to be the experiences of the subject, that is, different states of one and the same subject; and these states of the subject (the “wider system”) have temporal relations among themselves. 5.6

Conclusion We have seen that, despite detailed and voluminous argument, Strawson

does not convincingly establish in either Individuals or The Bounds of Sense that “spatial representation,” in any unequivocal sense, is the fundamental form of representation. Properly interpreted, however, his arguments do lead to two very significant conclusions. First, representing spatial relations in an abstract, mathematical sense is sufficient for reidentifying particulars and predicating things of them (i.e., conceptualizing them). Second, our representations of actual

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material objects in three-dimensional physical space provides both an additional, more natural way of designating objects in thought and a kind of guarantee of quantitative uniqueness for those objects we do identify in thought. This is so simply because two material objects cannot be in the same place at the same time. Although these are not the precise conclusions that Strawson himself claims to have established, they are very important. What Strawson’s arguments (again, properly interpreted) have given us ultimately is a new way of understanding the fundamental nature of representation. The lesson we should take away is that the fundamental form of representation is not the linguistic, syntactic, logical, computational kind of representation that we see in language and traditional artificial intelligence. Rather, the fundamental form of representation is spatial representation: identifying objects by, and representing their properties as, locations in space. In the case of material object identification, this is our everyday, three-dimensional, physical space. In the case of categorization and, in general, predication (ascribing properties to objects) it is representation in a high dimensional, abstract, mathematical space. As we shall see in the next chapter, this kind of representation is very naturally implemented in the kinds of systems that compose our brains: neural networks.

Chapter 6 Representational Similarity 6.1

Abstract If Connectionism is to be an adequate theory of mind, we must have a

theory of representation for neural networks that allows for individual differences in weighting and architecture while preserving sameness, or at least similarity, of content. In this paper we propose a procedure for measuring sameness of content of neural representations. We argue that the correct way to compare neural representations is through analysis of the distances between neural activations, and we present a method for doing so. We then use the technique to demonstrate empirically that different artificial neural networks trained by backpropagation on the same categorization task, even with different representational encodings of the input patterns and different numbers of hidden units, reach states in which representations at the hidden units are similar. We discuss how this work provides a rebuttal to Fodor & Lepore’s critique of Paul Churchland’s state space semantics. 6.2

Introduction Since Putnam’s papers on Turing-machine functionalism in the 1960’s,

computational functionalism has been the dominant theory of mind. On this view, mental states are tokenings of morphologically identifiable “symbols” at an abstract (“functional”) level of description. The meaning, or “content,” of a

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mental state is determined by the symbols tokened in that state, the rules governing the tokenings of symbols in the system, and the relations between the symbols tokened inside the system and objects outside of the system. This is the fundamental view underlying computational models of cognition, i.e., Good Old Fashioned Artificial Intelligence (GOFAI) models. In keeping with convention, we will refer to it as the “Classical” view. The advantage of the Classical view over the various “identity” theories of mind that proliferated before Putnam’s work is that it allows for the multiple reliability of mental states. On identity theories, mental states are identical with the physical substrates in which they are realized. Therefore, identity theories rule out the possibility of the same mental state being realized in systems composed of different substances. However, many of us have the strong intuition that machines could, at least conceivably, think the same kinds of thoughts that we do. By individuating mental states at a functional level, rather than a physical level, the Classical view makes room for this intuition: different systems, perhaps even systems composed of such different substances as carbon and silicon, could realize the same functional description and so be in the same mental state. While Classical models of cognition performed well at abstract, logical tasks, they tended to do less well at more primitive sensory-motor tasks. Classical models were often too sensitive to small variations in starting conditions, or to the environment in which they operated. They also tended to degrade ungracefully in the face of minor damage.

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The rebirth of connectionism, and especially the development of the backpropagation learning algorithm in the 1980’s, seemed to offer an alternative. Connectionist models were robust in the face of damage and minor changes in initial conditions or environment, and excelled at the kinds of sensory-motor tasks that had been the bane of Classical models. Paul Churchland soon proposed that Connectionism was not only a new kind of cognitive modeling but also a new theory of the mind. On Churchland’s view, mental states consist, not in the tokening of symbols, but in the activation of hidden units in a connectionist network. Churchland writes, “the brain represents various aspects of reality by a position in a suitable state space” (Churchland 1986, p. 78). He makes the same point in another work: fleeting facts get represented by a fleeting configuration of activation levels in the brain’s many neurons.... The overall pattern of neuronal activation levels at any given instant constitutes the brain’s portrait of its local situation here and now (Churchland 1995, p. 6). The position in activation space occupies the same role in the Connectionist theory of mind as the tokening of symbols does in the Classical view. On the Classical view, an occurrent representational state just is the tokening of certain symbols. On the Connectionist theory of mind, an occurrent mental state just is the activation of certain nodes. The content of the qualitative experience of seeing a particular color, for example, is a specific pattern of neural activation:

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a visual sensation of any specific color is literally identical with a specific triplet of spiking frequencies in some triune brain system (Churchland 1986, p. 104). Any humanly perceivable color...will be a distinct pattern of activations across...three types of downstream opponent process neurons (Churchland 1995, p. 25). One of the notable virtues of Churchland’s pattern-of-activations theory is that it explains the introspective (and psychophysical) datum that qualitative experiences within perceptual modalities exhibit robust similarity relations. As Churchland writes, if the pattern of activations theory is true: then the similarity of two color sensations emerges as just the proximity of their relative state-space positions (Churchland 1986, p. 104). Coding each color with a unique triplet of neural activation levels provides not only for phenomenological similarities...but for other phenomenological relations as well. Intuitively, orange is between yellow and red, as pink is between white and red. And that is exactly how they are positioned within the coding space (Churchland 1995, pp. 25-6). Color categorization, of course, lends itself to network modeling. Language imposes categories on many properties of the qualitative states that comprise our consciousness. We categorize colors, for example, by chroma (red, orange, yellow, green, blue, or violet), by brightness (light or dark), by saturation (deep or pale), and in other ways. The qualities of our awareness, however, transcend the categories we use to communicate their properties. We perceive sets of relative similarity relations between our qualitative states, both within and across the

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categories we use to describe them. For example, for any three reds we can distinguish, we will be able to say which of two is more like the third, even if we cannot describe the difference precisely. Given the similarities we perceive among our qualitative states, we can order them along the dimensions of the properties we perceive as ordered. Where the dimensions are orthogonal, we can construct spaces that map our qualitative states into points in a low-dimensional space, points that reflect by relative proximity the similarities we perceive between the qualitative states. The problem of constructing such spaces is the ordering problem, the problem of constructing “for each category of qualia, a map that will assign to each quale in the category a unique position and that will represent relative likeness of qualia by relative nearness in position” (Goodman 1951, pp. 217-8). The field of psychophysics has for the past hundred and fifty years taken the solution of the ordering problem as its fundamental task. It has proceeded by eliciting from human subjects large numbers of judgments of the relative similarities between stimuli in various qualitative modalities, and mapping these similarity judgments into spaces using the techniques of multi-dimensional scaling. The procedure has been fruitful. For example, it has given rise to the CIE uniform color space specification (anonymous 1976a; Wyszecki and Stiles 1982), which maps human color similarity judgments into a three-dimensional Euclidean space such that human judgments of similarity between color stimuli correspond as closely as possible to similarities in the color space.

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As a result of the successful solution of the ordering problem for many domains of qualitative experience, psychophysics has generated an enormous set of data on the similarity structure of qualitative experiences. This point has been made before. Austen Clark writes, for example, that “there is no need for a new discipline of ‘objective phenomenology’— of objective characterization of the modes of appearance of the world— for psychophysics already is that discipline” (Clark 1985a, p. 505). As Clark points out: qualia are...those properties [of sensations] which enable one to discern similarities and differences: they engage discriminations. The way in which qualia have been thought to do this is isomorphic to the way critical properties engage an internal discriminal process. Items identically encoded yield qualitatively identical presentations, and differences at that stage occasion differences in qualia. In short, qualitative content can be identified with those properties of encodings which engage the discriminal process (Clark 1985b, p. 392). Hence, we should expect the structure of qualitative content to be reflected in the structure of neural representations at various stages of sensory processing. Qualitative experiences, for all their touchy-feeliness, are contentful states. While the contents of our qualitative experiences transcend our conceptualizations of them, the experiences are nevertheless contentful. One of the virtues of Connectionism is that it accounts not only for the conceptual aspects of qualitative content, but also, and equally naturally, for their nonconceptual aspects — the subtle similarities and other relations among them for which we have no names or

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ready concepts but which we are nevertheless capable of distinguishing when confronted with or asked about them. Although some philosophers might be resistant to the idea of associating content with qualitative state, there is no reason to suggest that the qualitative contents on which Churchland bases his examples are not contentful in the fullest sense of the word. As Wittgenstein pointed out, and as linguists have voluminously documented, the contents of many if not all of our concepts are rather more like qualitative contents than many philosophers have acknowledged. Psychophysics— objective phenomenology— has not yet got around to all of our concepts, but the work has only just begun. However, in contrast with Clark, we believe that items need not be identically encoded in order to yield qualitatively identical presentations. Rather, we believe that items with the same relative positions in state space will yield qualitatively identical presentations. Small changes in the way that a particular item is encoded, provided that they do not change its position relative to the encodings of other items, will not, we claim, change its qualitative presentation. This is, we feel, also a problem with Churchland’s strict identification of content with a specific position in state space. It is well known that networks with different numbers of hidden units can solve the same problem. It is at least plausible that what is represented at the hidden layers of two such networks is the same. (It is only that the information is distributed over more nodes in one network than in the other.) It is also a fact that two different human beings can

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have the same belief, even though it strikes us as highly unlikely that such beliefs are ever represented by exactly the same levels of activation over exactly the same numbers of neurons in two people’s brains. On the position-in-activationspace view of occurrent representation that Churchland advocates, the criterion for representations in two different individuals having the same content is clear: they must have exactly the same levels of activation over exactly the same numbers of neurons. Even if the representations are not identical, their similarity is easy to compute, for example by taking the dot products of the respective activation vectors. There is a problem, though: dot products (and other standard measures of association like correlation) are only defined for vectors of equal length. However, different numbers of units can carry the same information. (Connectionist nets can solve the same problem with different numbers of hidden units, and human beings can hold the same beliefs despite presumable differences in the numbers of neurons in their respective brains.) Therefore, the position-inactivation-space view leaves us at a loss as to how to determine when two systems represent the same information with a given pattern of activation. We cannot take the dot product, compute correlation, or use any of the other standard tools for determining similarity between two vectors, because we might be dealing with vectors of different lengths. There is no corresponding problem for the Classical view, because an occurrent mental state on the Classical view is just the tokening of certain symbols, and two individuals (with sufficiently powerful

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architectures) can token the same symbols regardless of how many transistors, or whatever, they have. The same problem arises when we consider latent representations. On the Classical view, latent information is represented by the set of rules that govern the manipulation and tokening of symbols. Classical systems of many different sorts can embody the same sets of rules. It is tempting to identify the representation of latent information in a Connectionist network with its position in weight space, i.e., the particular set of weights that determines which of its units will be activated in a given circumstance. Churchland espoused this view at one time: “An individual’s overall theory-of-the-world...is a specific point in that individual’s synaptic weight space.... a configuration of connection weights” (Churchland 1989b, p. 177). This position-in-weight-space view of latent information in Connectionist networks faces the same sort of problem as did the position-in-activation-space view of occurrent information. Networks with different weights may in fact react very similarly to their inputs. Differences in certain weights may be compensated for by differences in other weights in such a way that differently weighted networks exhibit similar, if not identical, responses to the same inputs. Churchland himself acknowledged this problem, putting the point in terms of the partitioning of activation vector spaces: “differently weighted systems can produce the same, or at least roughly the same, partitions on their activationvector spaces” (Churchland 1989b, p. 177). (A partitioning of activation-vector

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space is a particular mapping between input activations and hidden-unit activations.) The point is not limited to artificial neural networks. Different people may know the same things even though it would be highly surprising to find that even small areas of their brains were wired in exactly the same ways. Because we want our theory of mind to allow for the fact that different people, who presumably are not wired identically, can share knowledge, the position-inweight-space view is unacceptable. It suffers from the same sort of chauvinism the position-in-activation-space conception of occurrent representation does: individuating representation states too finely makes it impossible for subtly different individuals to be in the same representational state. If Connectionism is to be an adequate theory of mind, we must have a theory of representation for neural networks that allows for individual differences in weighting and architecture while preserving sameness of content. An evident solution would be to identify latent information not with specific patterns of connection strengths, but rather with characteristic groupings of activation patterns, the partitions of activation space that the specific connection weights determine. The way networks partition their hidden layer activation spaces is a better criterion for evaluating their semantic similarity than is their exact position in weight space. The partitioning view allows different individuals to represent the same latent information without having identical networks. Churchland also considered this possibility: we might try to abstract from the idiosyncratic details of a system’s connection weights, and

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identify its global theory directly with the set of partitions they produce within its activation-vector space. This would allow for differently weighted systems to have the same theory (Churchland 1989b, p. 177). As soon as Churchland made this suggestion, however, he dismissed it on the grounds that it would preclude lawful explanations of learning: While differently weighted systems can embody the same partitions and thus display the same output performance on any given input, they will still learn quite differently in the face of a protracted sequence of new and problematic inputs...because the learning algorithm that drives the system to new points in weight space does not care about the relatively global partitions that have been made in activation space. All it cares about are the individual weights and how they relate to apprehended error. The laws of cognitive evolution, therefore, do not operate primarily at the level of the partitions...rather, they operate at the level of the weights. Accordingly, if we want our “unit of cognition” to figure in the laws of cognitive development, the point in weight space seems the wiser choice of unit. We need only concede that different global theories can occasionally produce identical short-term behavior (Churchland 1989b, pp. 177-8). It is not obvious to us that the “unit of cognitive significance” really must figure in the laws of cognitive development. The “unit of cognitive significance” is presumably that feature in terms of which we give our explanations of how behaviors happen. The laws of cognitive development, on the other hand, are explanations of how behaviors change. As long as the laws of cognitive development adequately explain changes in behavior, we see no reason why they must do so in ways that refer to the mechanisms of behavior themselves.

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Admittedly, we do not now have rigorous theories of how the partitions of neural networks will change given new inputs, while we do have algorithms such as backpropagation for determining how the weights in artificial networks should change in order to learn particular tasks. In the case of artificial networks, though, the algorithms themselves give us perfectly good explanations of how learning changes the weights. While the mechanisms of learning in biological neural systems are not yet completely understood, we expect that neuroscience will eventually discover the laws that govern the ways synaptic connections change in the face of new experience. Changes in the weights determine changes in the partitions. Presumably, therefore, laws could be developed that would explain changes in partitions in terms of learning. At least, we do not see any reason in principle why this is not so. Churchland (1989a) also seems to have adopted the view that the partitions are the fundamental unit of cognitive significance, however important the weights may be in the explanation of learning: While the weights are of essential importance for understanding long-term learning and fundamental conceptual change, the partitions across the activation space, and the prototypical hot-spots they harbor, are much more useful in reckoning the cognitive and behavioral similarities across individuals in the short term. People react to the world in similar ways not because their underlying weight configurations are closely similar on a synapse-by-synapse comparison, but because their activation spaces are similarly partitioned (Churchland 1989a, p. 234).

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This latter view seems to have stuck. In his most recent book, Churchland asserts that: the general and lasting features of the external world are represented in the brain by relatively lasting configurations of synaptic connections (Churchland 1995, p. 5). This might suggest that Churchland has reverted to his earlier position-in-weightspace account of knowledge. However, he also writes that the cluster diagram of NETTalk’s hidden-layer activations “is the conceptual framework that learning has produced within NETTalk” and that it “displays the system of interrelated categories or concepts whose activation is responsible for NETTalk’s sophisticated input-output behavior” (Churchland 1995, p. 90). Thus, Churchland’s considered view seems to be that knowledge corresponds to a partitioning of activation space, not to a point in weight space. The main consideration in favor of the partitioning-of-activation-space conception of latent information in networks is the desideratum that different individuals be able to share mental states. It is a fact that many different human beings— at least some of whom presumably have differently weighted connections between neurons in their respective brains— often share beliefs. Taking category structure to be identical to the weighting of network connections would force us to say that two individuals whose brains were wired even slightly differently had different categories, even if their categorization behaviors were identical. This is a very good reason for preferring a partitioning-of-activationspace view of latent representation in neural networks to a position-in-weight-

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space view: it allows us to account for the representational similarities between individuals who have different weights and architectures. The position-in-weightspace view, on the other hand, relegates the pervasive correspondence between the similarity judgments of different individuals to mere accident. We therefore believe that we must reject the position-in-weight-space view of neural representation (where latent representations are identical if and only if they are implemented in neural systems with identical connection strengths). Instead, we favor of a partitioning-of-activation-space theory of neural representation (where latent representations are similar insofar as they partition the activation space in similar ways). To meet Churchland’s objection about the lawfulness of cognitive development, we must begin to formulate laws of cognitive development that operate over partitions rather than activations, but that is a project for another paper. Adopting the partitioning-of-activation-space view about latent information also suggests a complementary solution for the corresponding problem with the position-in-activation-space view of occurrent information. Rather than associating content with absolute position in activation space, we advocate associating content with relative position in the partitioning of activation space. On our view, occurrent representations in different neural networks should be compared not by the absolute positions of the representations in the networks’ activation spaces, but rather by each representation’s location relative to other possible activations in the same network.

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There is, however, a significant problem with the partitioning-ofactivation-space view: how do we assess when two networks with differently weighted connections or different numbers of hidden units partition their activation space the same way? Taking the partitioning of activation space to be the representational vehicle requires that we find a way of comparing partitionings. On the position-in-weight-space view, it was easy (theoretically, anyway) to determine whether two different individuals represented their experiences the same way: we simply determined whether they had the same connection strengths between their neural units. Things are not so easy on the partitioning-of-activation-space view. In order to make the partitioning-of-activation-space theory of neural representation viable, we must solve this problem. The position-in-weight-space view has an easily computable measure of representational similarity between two individuals: two individuals’neural representations are similar in proportion to the correlation between the connection strengths (or synaptic weights) between their neural units. The association between two vectors of equal dimensions is easy to compute using vector inner products. However, because the inner product between two vectors is defined only if the vectors have the same number of components, the technique of computing simple correlation between representations is not applicable to the partitioning-of-activation-space model of representation. The partitioning-of-activation-space model is designed

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specifically to account for similarities across individuals with different neural architectures, but it seems to leave us with no way of measuring those similarities. Fodor and Lepore (1996a; 1996b) have voiced precisely this objection in response to Churchland’s theory of state-space semantics. In short, the argument is that a Connectionist theory of mind, because of the way it individuates mental states, cannot give a satisfactory account of different individuals being in the same mental state. Fodor and Lepore argue that the viability of Churchland’s view of state-space representation depends on his having a robust criterion for content identity, a project whose prospects they view as dim. They raise the same problem that we have about the identity of content across individuals with different architectures: If the paths to a node are collectively constitutive of the identity of the node...then only identical networks can token nodes of the same type. Identity of networks is thus a sufficient condition for identity of content, but this sufficient condition isn’t robust; it will never be satisfied in practice (Fodor and Lepore 1996a, p. 147). The condition will never be satisfied in practice because different individuals are bound to have at least slightly different connections among nodes. Any theory of mind must have a substantive notion of inter-individual content similarity that is not dependent on a strictly psychophysical mode of explanation. A Connectionist explanation, based on neurophysiological measurements, would be in a position to give precisely such an explanation only if Connectionism had an adequate account of inter-individual sameness (and hence difference) of content.

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As we have seen, there are lots of reasons why Connectionism needs a robust criterion of inter-individual content similarity. Because the position-inactivation-space and position-in-weight-space views are inadequate for the task, we have argued that two individuals’neural representations are similar in proportion to the correspondence between the partitionings each produces over the set of possible inputs. But how can we evaluate that correspondence? The units in an artificial neural network (neurons in a biological network) can be seen as determining dimensions in an abstract space. The vector of activations over the units at a particular time is a point in this space. Hence, the network’s representation of every object is a point in activation space. Objects that the network represents as alike will be nearby in this space (fall into the same partition), whereas objects that the network represents as different will be distant (in different partitions). Groups of similar objects form clusters in the space. For example, a network’s representations of trees might form one cluster and its representation of animals might form another. The problem of measuring the representational similarity of two different networks is the problem of measuring the similarity of the clusters in one network’s activation space with the clusters in the other network’s activation space. The way a single network partitions its activation space may be visualized using cluster analysis. In the application of cluster analysis to networks, patterns of activation at the hidden units are measured for each input, and then the patterns are progressively matched with each other according to their proximity. The result

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is a dendogram, or tree structure, which graphically displays the relative proximities of the input patterns as they are represented at the hidden layer. In the first application of cluster analysis to representation in artificial neural networks, Sejnowski and Rosenberg (1987) showed that similarities among hidden-layer representations in their NETTalk network matched the phonological similarities that humans perceive in spoken phonemes. For example, hard-’c’and ‘k’sounds were grouped together, and at the highest level, consonants were grouped together, as were vowels. We can use cluster analysis to visualize the partitioning of activation space within a single network. However, cluster analysis produces a dendogram, and we know of no accepted way to compare different dendograms. If we think, for example, of the complex dendogram representing the clustering of inputs in NETTalk, it is unclear how we could measure the similarity of that tree with a different one. Furthermore, there are myriad ways to cluster data, with differing results. Thus, “cluster analysis” itself is an ambiguous term at best. 6.3

A Modest Proposal We have argued that having a method for comparing the relative positions

of concepts in one state space to the relative positions of concepts in another state space is critical for state space semantics. The method we propose here works well for neural networks, and may be generalizable to animals and robots. The basic idea is to collect the activation patterns evoked by inputs and compute all possible distances between these representations. The distances between

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representations capture the structure of representational space. We then compute the correlation between the distances between representations in one state space and the distances between representations in the other state space. This procedure can be used to measure the similarity between any two neural representations (be they from natural or artificial networks, from input, output, or hidden-unit representations, from the same or different networks, with the same or different numbers of units). Walking through the application of our measure to a simple problem is the easiest way to explain it. Suppose we consider the representation of three things, “A”, “B”, and “C”, in a network with one hidden unit. Say the network represents these things with the following levels of activation: A=, B=, C= We will call such a representation a vector coding. In this case, the vector has only one dimension. The network’s representations fall on a line:

Figure 4

A one-dimensional vector coding

Suppose also that another network, this one with two hidden units, represents the same three things with the following vector coding: A=, B=, C= In this case, the points form a triangle in two-dimensional space:

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Figure 5

A two-dimensional vector coding

Our problem is to measure the similarity of these two shapes. We start by taking distances5 in each network between each of its representations and each other, giving two symmetric matrices: Distances Between Representations 1-Unit Network 2-Unit Network A B C A B A 0 50 100 A 0 42 B 50 0 50 B 42 0 C 100 50 0 C 80 58 Table 1

C 80 58 0

Comparison of distances between points in two different vector encodings.

Taking distances between the representations has two advantages. First, it achieves invariance to global translation, rotation and mirror inversion, since for any set of points in n-dimensional space, the set of distances between them will remain constant through uniform translation, rotation, or inversion. Second, taking distances between the representations allows us to use standard

5

We use Euclidean distance, but it would be possible to use other distance measures.

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mathematical measures of similarity to compare the representations. Since the distance matrices for both networks are symmetric and we are measuring the representations of the same number of things in each network, the distance matrices each have n(n-1)/2 unique elements, where n is the number of representations being compared. If we lay the unique elements for each network out in a vector, we have two vectors of length n(n-1)/2. In our toy case: We then compute the correlation (Pearson’s r) between these two vectors. (Correlation measures the extent to which the values in one data set can be predicted from values in another data set. Values close to 0 indicate that it is impossible to predict the values in one set from the values in the other, whereas values near 1 indicate that one set can be predicted almost perfectly from the other.) In this toy example, the correlation is 0.91, suggesting that they are similar structures. This corresponds to our intuition, in that both spaces place B “between” A and C. (In realistic cases, of course, we would want to compare many more observations.) Using correlation also achieves a third criterion that we believe should be met by any solution to this problem, namely scale invariance, because correlation is insensitive to the magnitude of the vectors being compared. In summary, our measure evaluates to 1 for two individuals who have identical representations (modulo differences in global scale, rotation, translation and inversion), to -1 for individuals whose representations are maximally dissimilar

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(anticorrelated), and to 0 for individuals whose representations are completely uncorrelated. This is the essence of our solution to Fodor & Lepore’s challenge— by computing the similarity of the distances between points in two representational spaces, we provide state space semantics with a criterion for semantic similarity while eliminating the need to match the dimensions of the two spaces. Our technique has a number of desirable properties as a measure of representational similarity. Because it compares distances between representations, it allows for comparisons between networks with different numbers of units, and it is insensitive to differences in global rotation, translation and inversion. Because it uses correlation (which is not sensitive to magnitude) as a measure of association, it is also insensitive to differences in global scaling. Global differences of scale merely reflect uniform differences in activation levels. If one network has activations that range between 0 and 1 and another network has activations that range between 0 and 100, the scale of their representations will be different. Nevertheless, if the shapes of their representations are similar, we would want to judge them as similar. Similar arguments hold for translation and rotation: translational differences correspond to differences in which part of the range of activation the neurons use the most; rotational and inversion differences correspond to differences in which neurons are used to represent which factors in the representation.

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In the following, we present two experiments that demonstrate the use of our measure on neural networks that learn to classify colors. In the first experiment, we show that neural networks with different “sensory apparati” learn internal representations that are quite similar by our measure, and that neural networks with the same sensors learn nearly identical representations. In the second experiment, we show that even neural networks with different numbers of hidden units (in this case, an excessive number) also learn nearly identical representations by our measure. 6.4

Experiment One As an example of how our technique for measuring similarities in network

representations can be used, we chose to model color categorization in artificial neural networks using a variety of input encodings. The different encodings might be thought of as ways in which the sensory systems of different “species” encode the impact of light at various frequencies on their bodies. The key assumption is that all of the networks agree about the category labels (i.e., they all agree that a particular stimulus is “red”). This corresponds to agreement within human subjects about color labels, which is presumably “trained”. We considered two questions. First, we were interested in the degree of agreement within a species. This addresses the question of how much you and I might agree in the content of our representations, even though we may have different synaptic connectivity and hence different actual patterns of activity (the issue of different numbers of neurons is addressed in the next section). Second,

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we were interested in the degree of agreement between species. This addresses the question of how similar the content of your representations can be to the content of my representations when at least one aspect of our “bodies”— the sensory apparatus— differs between us, even though we use the same learning mechanism and number of internal units. 6.4.1 Procedure We started with a database of reflectance spectra of color samples measured by the University of Kuopio, Finland (anonymous 1995). The database consists of 40 files, each one containing data from a particular page in the Munsell Book of Color: Matte Finish Collection (anonymous 1976b). The database contains data on 10 colors: red, yellow-red, yellow, green-yellow, green, blue-green, blue, purple-blue, and purple. For each color, there are 4 files, each containing data on the color at Munsell hue values of 2.5, 5, 7.5 and 10, respectively. Each file consists of about 30 spectra. Each spectrum is represented by 3 lines in the file. The first line for each spectrum is a label of the spectrum based on the Munsell notation. The second line for each spectrum consists of 61 elements of raw data obtained from the output of a spectrophotometer, measured from 400nm to 700nm, at 5nm intervals, represented as integers between 0 and 4095. (Some values were larger than 4095 but should, according to the Kuopio specification, be corrected to 4095.) Because the spectra were measured from 400nm to 700nm at 5nm intervals, each spectrum could be considered a 61-

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dimensional vector, of which the first component represents the reflectance intensity of a color chip at the wavelength 400nm, the second at 405nm, and so on. To generate our data set from the Kuopio set, we ignored the data for the intermediate colors yellow-red, green-yellow, blue-green, and purple-blue and used only the data on 5 colors: red, yellow, green, blue, and purple. The data had approximately the same numbers of patterns for each color for a total of 627 patterns. To make network training possible, we replaced the Munsell labels with the binary suffixes shown in Table 2 to serve as output patterns over 5 units. Color Red Yellow Green Blue Purple Table 2

Pattern 10000 01000 00100 00010 00001

Target output patterns for the 5 color categories.

To correct the errors reported in the specification of the original data set, we replaced all values greater than 4095 with 4095. To prepare for encoding the input patterns with schemes that required large numbers of units for each element, we then scaled the 0-4095 values to 0-255 values and removed all but every fifth field from the Kuopio input patterns, resulting in patterns with 12 rather than 61 elements each. This formed the complete data set for our purposes. From this base data set, we created four different encodings of the input patterns to be used in training the networks.

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1) The binary encoding was formed by representing the 0-255 integer inputs as 8-bit binary numbers. Thus, each pattern had 96 (=12x8) input elements in the binary encoding, each element valued either 0 or 1. 2) The real encoding was formed by scaling the 0-255 integer inputs to decimal representations between 0 and 1. Thus, each pattern had 12 input elements in the real encoding, one for each of the elements in the integer data set, each element a rational number between 0 and 1. 3) The gaussian encoding was formed by dividing the interval between 0 and 255 into quarters, and using five units to represent the endpoints of the intervals. A particular value was coded as a Gaussian “bump” on this interval, with a standard deviation of 32 and mean and the point to be represented. (See Table 3 and Table 4.) Element Value Table 3 Value 0 127 128 255

1 0

2 63.75

3 127.5

4 191.25

5 255

Mean value of each element in the gaussian encoding. Element 1 1 0.000380 0.000335 0

Element 2 0.137462 0.141791 0.133233 0

Element 3 0.000357 0.999878 0.999878 0.000357

Element 4 0 0.133233 0.141791 0.137462

Table 4

Some examples of gaussian encodings.

Element 5 0 0 0.000380 1

4) The sequential encoding was formed by numbering the patterns sequentially with 3-digit decimal numbers from 001 to 627. Each 3-digit number was then represented by a single unit with activation between 0 and 1. (See Table

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5.) While this might seem completely arbitrary, in fact like colors were grouped together in the pattern file, so this representation does contain enough information to solve the problem. Pattern Number 1 627 Table 5

Element 1 0 0.6

Element 2 0 0.2

Element 3 0.1 0.7

Some examples of sequential encodings.

Next, we created a set of holdout data and a set of training data for each representation, by taking every sixth line for the holdout set (104 patterns) and leaving the rest for the training set (523 patterns). Because we were not exploring generalization in this experiment, we did not use a separate testing set. Using backpropagation, we trained 3-layer networks, each with 3 hidden units, on each input encoding for a maximum of 10,000 cycles using a learning rate of 0.25. Training was stopped before epoch 10,000 if the root mean-squared error of the holdout patterns had not declined in as many epochs as taken to reach the previous low. For example, if a minimum root mean-squared error was reached after epoch 2,500 and no subsequent epoch had a lower error, then training would be stopped after epoch 5,000. For each encoding, the experiment was repeated with 5 networks, each starting with a different set of initial random weights. About half of the networks stopped training before epoch 10,000. However, those networks that trained fewer than 10,000 epochs tended to perform less well on the categorization task. Nevertheless, most networks achieved 90% or greater accuracy on both the training and holdout sets.

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Using the best learned weights from each network, we computed the activations at the hidden nodes for each network on each input pattern, thereby obtaining each network’s internal representation of the input patterns at its hidden layer. We then computed the Euclidean distances between all patterns for that network. Now, to compare two networks, we can compute the correlation between their corresponding distances. This technique can be applied to any level of any layered network. We can also use it to compare the distances induced by the input patterns themselves, treated as activation patterns, to the distances induced by another input encoding. In this way, we can determine whether our input encodings are really “different” in their structure. Furthermore, it would be uninteresting if the hidden layer representations just reflected a structure that already existed at the input. Thus, we used our technique to compare the structure of each input encoding with the structure learned at the hidden layer of networks trained on that encoding. For visualization purposes, we also computed cluster diagrams for some layers, using standard hierarchical cluster analysis with Euclidean distance. 6.4.2 Results In order to visualize the input encoding structure, we performed a hierarchical cluster analysis on the input vectors. Figure 6 displays a cluster diagram of a subset of the colors for the “real” encoding. Note that his clustering appears disorganized, and does not match very well with our qualitative

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perceptions of color similarities. The colors are mixed together; for example, “Green 300” and “Blue 380” are clustered together. The cluster diagrams for the “binary”, “gaussian”, and “sequential” encodings are similarly disordered. _________________|----------> Yellow-200 | |__________|--------> Red-60 | |--------> Purple-500 | _______|---> Purple-440 | |---------| |---> Purple-460 -| | |-------> Red-540 | | |--> Yellow-180 | | |--| __|-> Green-240 | | | |--| |-> Green-320 |-----------------| |------| |--> Blue-360 | | | __|-> Red-20 | | | | |-> Red-40 | | |--| _|-> Green-300 | | | |-| |-> Blue-380 | | | |--| |-> Blue-400 |---------| |--| |-> Purple-420 | |--> Blue-600 | _____|---> Green-260 | | |---> Green-280 | | ____|---> Blue-340 |------| | |___|---> Red-100 | | |___|--> Yellow-160 | | |__|-> Yellow-120 |-----| |-> Yellow-560 | ___|---> Red-80 | | |___|--> Yellow-140 |----| |--> Yellow-220 |___|---> Purple-520 |___|--> Green-580 |__|-> Purple-480 |-> Purple-620

Figure 6

Representative clustering of input patterns in the “real” encoding (31 of 627 patterns shown).

We then compared the input encodings using our technique. To our surprise, the binary, real and gaussian input encodings were highly correlated with each other (see Figure 7). The correlation between the real and gaussian encodings was nearly 1, and the binary encoding had a correlation of about 0.8 with both the real and the gaussian encodings. The sequential encoding, on the other hand, was almost completely uncorrelated with the other encodings.

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Figure 7

Hinton diagram showing correlation among input patterns. The areas of the boxes are proportional to the values.

The difference in correlation between the sequential input encoding and the other input encodings is due to the fact that there is little relationship between the order that a sequential pattern appears in the data file (which is grouped by color), and the actual spectral properties of the light. That this should be so is reflected in the cluster diagram of the real encoding: the real encoding is, after all, a reasonably good representation of the filter responses, but the colors are intermingled in the cluster diagram. On the other hand, since like colors appear nearby in the sequential pattern file, the sequential numbering provides considerable information concerning the color category. In particular, most colors

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that should be categorized together are nearby in the input pattern space. There are two exceptions to this. The first is that, because three digits were used to represent elements in the sequential encoding, patterns differing in the ordering by as much as 100 can be as close together as patterns differing by only one in the ordering. For example, pattern 345 (which is represented as ) is as close to pattern 245 () as 245 is to 244 (). The second exception is caused by the fact that all neighbors in the ordering are 0.1 apart in the encoding except points with a 0 element. Each pattern with a 0 element in the sequential encoding comes right after one with a 0.9 element (and hence the two are at least 0.9 units apart). For example, although patterns 458, 459, and 460 are right next to each other in the data set, the sequential representation of pattern 459 () is much closer to that of pattern 458 (), than it is to that of pattern 460 (). In order to test whether the trained networks were recoding the stimulus patterns, we compared the hidden unit structure with the input encoding structure. We also compared the hidden unit structure of each species with the input representations of the others. None of the input representations were very highly correlated with any of the hidden unit representations of any of the networks (see Figure 8). In fact, the binary networks’hidden unit patterns were more highly correlated with the real input patterns than with their own input patterns. Similarly, the gaussian networks’hidden unit patterns were more highly correlated with the real input patterns than with their own input patterns.

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Although the real networks’hidden unit patterns were most highly correlated with the real input representation, they were correlated almost as well with the gaussian input representation. The sequential networks were also most highly correlated with their own input representation. All of the networks re-encoded the data at the hidden layer, rather than simply copying the input pattern structure to the hidden layer.

Figure 8

Hinton diagram showing mean correlations of the different input pattern encodings with the hidden unit activations of 5 networks trained on each encoding. The area of each box is proportional to its value. The input patterns are represented in the columns; the hidden unit patterns are represented in the rows.

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In order to assess whether the contents of the internal representations were similar, we compared the hidden unit representations of the five networks of each “species” with each other (10 comparisons). The diagonal of Figure 9 shows the mean correlation within each species. All of the within-species correlations are greater than 0.9. Thus, networks of the same species starting from different random initial weights found similar solutions to the color categorization problem. The similarities are also reflected in their cluster diagrams, which not only show colors grouped in human-like ways, but are also similar to each other. For example, Figure 10 shows a cluster diagram of the hidden-unit activations of one of the networks trained on the real encoding, and Figure 11 shows the same type of diagram for a different network trained on the same encoding. Despite the differences in initial random weights, the cluster diagrams are similar, in that like colors are grouped together, and the same groups are placed near one another in the diagrams.

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Figure 9

Hinton diagram showing mean correlation between hidden unit activations. Shows mean correlation between hidden unit activations of 5 networks trained on each encoding and hidden unit activations of 5 networks trained on each other encoding (e.g., binary vs. real), as well as mean correlation between hidden unit activations among the 5 networks trained on each encoding (e.g., binary vs. binary). The area of each box is proportional to its value.

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______|---> Red-20 | |___|---> Red-40 |-----------| |---> Red-60 | | __|-> Red-80 | |------| |-> Red-100 |-------------| |--> Red-540 | | _____|----> Yellow-120 | | | |----> Yellow-180 | |-----------| _|-> Yellow-140 | | |--| |-> Yellow-200 | |-----| |-> Yellow-220 | |__|--> Yellow-160 | |--> Yellow-560 -| ________|--> Green-260 | | |--> Green-280 | |------------| |-----> Purple-420 | | | | __|--> Green-300 | | |--------| |-----| |--> Green-320 | | | | |__|-> Green-240 | | |-----| |-> Green-580 |-------------| | ____|-> Blue-340 | |-----| |-> Blue-360 | |____|--> Blue-400 | |__|--> Blue-380 | |--> Blue-600 | |-------> Purple-500 |------------| |----> Purple-480 |-------| |--> Purple-460 |----| __|-> Purple-440 |--| |-> Purple-520 |--> Purple-620

Figure 10

Representative clustering of hidden-unit activations in one of the five networks trained on the “real” encoding (31 of 627 patterns shown).

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______|----> Red-20 |-------| |____|--> Red-40 | | |--> Red-60 |-----------| |------> Purple-420 | |_______|--> Red-80 | |__|-> Red-100 | |-> Red-540 | ______|----> Yellow-120 |-------------| | |----> Yellow-180 | | |-----------| |-> Yellow-160 | | | | |--| _|-> Yellow-140 | | | |------| |-| |-> Yellow-200 | | | | |-> Yellow-220 | |-----------| |--> Yellow-560 | | ______|----> Green-280 | | | |____|--> Green-260 | | | |__|-> Green-240 | | | |_|-> Green-320 -| |-----------| |_|-> Green-300 | | |-> Green-580 | | ____|--> Blue-380 | |------| |--> Blue-400 | | __|-> Blue-340 | |----| |-> Blue-360 | |--> Blue-600 | _|-> Purple-440 | |--| |-> Purple-460 |-------------| |-> Purple-520 |__|--> Purple-480 |__|-> Purple-500 |-> Purple-620

Figure 11

Representative clustering of hidden-unit activations in another of the five networks trained on the “real” encoding (31 of 627 patterns shown).

The off-diagonals of Figure 9 show the mean correlation between different species’ hidden unit representations (5X5 = 25 comparisons). All are highly correlated. Correlations between hidden unit representations between the networks trained with the binary input encoding and the networks trained on the real and gaussian input encodings are nearly 1. For networks trained on the real encoding and the gaussian encoding, the results are very similar. This might be expected based on the high correlation of their input representations. More striking is the high correlation between the sequential encoding networks’ internal representations and the others. Although somewhat lower than the others, this is a

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large change from the near-zero correlation between their input encodings. This suggests that, at least for neural networks trained by backpropagation on this task, agreement in categorization labels leads to agreement in internal content, regardless of sensory coding. Given that the correlation between networks trained on the sequential encoding and networks trained on the other encodings is somewhat lower than the correlation among networks trained on the other encodings, we would expect the cluster diagrams for networks trained on the sequential encoding to be somewhat different from those trained on the other encodings. They are. Figure 12 shows the clustering of hidden unit activations for one of the networks trained on the sequential encoding. Like the clusterings of networks trained on the real encoding, the clustering of the network trained on the sequential encoding groups like colors together. However, there is a subtle difference between the clustering in real networks and in sequential networks. In the clusterings on the real networks, clusters of different colors are more distinct. For example, in Figure 11, like colors are all clustered together, with one exception (“Purple-420” is clustered with the reds). In the clusterings on the sequential networks, clusters of different colors are not as distinct. In Figure 12, for example, some greens are clustered with yellows, while some are clustered with blues. This is presumably a consequence of the unusual properties of the sequential encoding.

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______|--> Red-80 | |--> Red-100 |----------------| __|-> Red-20 | |------| |-> Red-40 |---------------------| |__|-> Red-60 | | |-> Red-540 | | ______|--> Green-240 | |----------------| |--> Green-260 | | |-----> Yellow-120 | |------| __|--> Yellow-200 | |-----| |--> Yellow-220 | |__|-> Yellow-140 | |_|-> Yellow-160 -| |_|-> Yellow-180 | |-> Yellow-560 | _____|--> Green-300 | |--------| |--> Green-320 | | |_____|-> Green-280 | |--------------| |-> Green-580 | | | _____|--> Blue-340 | | |--------| |--> Blue-360 |---------------------| |_____|-> Blue-380 | |-> Blue-600 | ____|---> Blue-400 | | |---> Purple-420 |--------------| __|-> Purple-440 | | |-> Purple-460 |----| _|-> Purple-500 |--| |-> Purple-520 |_|-> Purple-480 |-> Purple-620

Figure 12

Representative clustering of hidden-unit activations of one of the five networks trained on the “sequential” encoding (31 of 627 patterns shown).

6.4.3 Discussion It is a well-known “folk theorem” of neural net lore that different networks trained on the same problem may partition their activation spaces in similar ways. Our results quantify this intuition. Furthermore, we have also shown that it is possible for networks from different “species” (i.e., trained from different input encodings) to partition their activation spaces in similar ways. Even though the networks in our experiment were trained on different input representations, the high correlations between the hidden layer activations of the networks show that they partition their activation spaces in similar ways. Therefore, it is possible for

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the representational states of two individuals who categorize their inputs the same way to be similar, not only in spite of their having different connection strengths between neurons, but even in spite of their having different “sensory systems”, i.e., input encodings. The results with the sequential networks are equivocal, however. Although the correlations between hidden unit activations in sequential networks and hidden unit activations in networks from other species are higher than the correlations between the sequential input encoding and the other input encodings, the sequential networks are not as similar to the others as the others are among themselves. So we cannot say that the internal representations that different individuals form will be similar no matter how the input is encoded as long as they perform the same categorization task. However, the representational states of two individuals who categorize their inputs the same way can be similar despite some differences between the way the task is presented to the individuals (the way the inputs are encoded). Evidently, there must be a certain amount of similarity between input representations in order to achieve highly similar hiddenunit representations. Also, other differences may be significant. For example, in this experiment we used only networks with 3 hidden units, and only a specific learning rule. More work is needed to determine what factors most influence the relationship between hidden-unit representations in different networks.

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6.5

Experiment Two In a second set of experiments, we varied the numbers of hidden units in

the networks, using only the real encoding and the sequential encoding. The goal was to determine whether nets with different numbers of hidden units would develop similar representational structures, and to test the effect of small variations in our procedure. 6.5.1 Procedure A nice feature of the two most different input encodings, the real encoding and the sequential encoding, is that they both use a rather small number of inputs. The real encoding requires only 1 input unit per element, and the sequential encoding only 3 input units per pattern. Hence, in this experiment, we used all 61 of the input elements in the original data set. Also, having discovered in the first experiment that the networks learned the problem rather more quickly than we had expected, we implemented a mechanism for stopping training earlier. We separated the original data set into 3 sets: a training set (used for training the networks and containing 472 patterns, approximately 75% of the complete set); a holdout set (used for deciding when to stop training and containing 93 patterns, approximately 15% of the complete set); and a testing set (used for testing performance of the networks and containing 62 patterns, approximately 10% of the complete set). We also randomized the order of presentation of the patterns during each training epoch.

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For each of the two input encodings (real and sequential), we trained 3layer networks with 1 to 10 hidden units. Each network was trained for a minimum of 500 epochs, and training was stopped after the 500th epoch whenever the root mean-squared error on the holdout set had not decreased in 50 epochs. We also replicated the training regime on 10 additional networks with 5 hidden units each, in order to demonstrate that the results in Experiment 1 using networks with different initial random weights were not sensitive to our minor changes in procedure. 6.5.2 Results Figure 13 shows the performance of each network on the test set (generalization performance). Networks with 1 and 2 hidden units failed to learn, and so will not be considered further. Networks using the “real” encoding and 3 to 10 hidden units all learned the problem approximately equally well, often within 500 epochs. No network trained more than 675 epochs. Results were slightly different for the sequential encoding. Networks with fewer than 5 hidden units trained on the sequential encoding performed less well than the networks trained on the real encoding (approximately 85% correct compared with approximately 95% correct). The networks trained on the sequential encoding show more variation in both percentage of classifications correct and error over time. Also, the networks trained on the sequential encoding show a greater disparity between error on the training set and error on the holdout set (data not shown). These

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results are also presumably due to the strange nature of the sequential encoding, as discussed above.

Figure 13

Percent correct on the test set versus number of hidden units.

Regardless, with 5 or more hidden units, all but the last difference disappeared. In contrast with networks with less than 5 hidden units, those with 5 or more achieved accuracy of approximately 95% on the test set, which is better than networks trained on the real encoding (see Figure 13). In any case, networks trained on the real input encoding learned hidden-layer representations that were substantially different from the input representation, but very similar to each other, regardless of the number of hidden units in the network (see Figure 14). Correlations between hidden-unit activations and input patterns were low, but average correlations between hidden-unit activations over networks with different

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numbers of hidden units were very high. Likewise, networks trained on the “sequential” encoding learned hidden-layer representations that were substantially different from the input representation, but more similar to each other, regardless of the number of hidden units in the network (see Figure 15). Correlations between hidden-unit activations and input patterns were low, although higher than they were for the “real” encoding, but average correlations between hidden-unit activations over networks with different numbers of hidden units trained on the “sequential” encoding were still very high.

Figure 14

Number of hidden units versus correlation to input patterns and average correlation to networks with different numbers of hidden units for networks trained on the “real” encoding.

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Figure 15

Number of hidden units versus correlation to input patterns and average correlation to networks with different numbers of hidden units for networks trained on the “sequential” encoding.

For networks with 5 hidden units, 10 replications starting from different initial random weights confirmed that networks with different weights trained on the same encoding found very similar solutions to the problem. Average correlation among the 10 different networks trained on the real encoding was 0.93, and average correlation among the 10 different networks trained on the sequential encoding was 0.93. In other words, networks with different weights trained on the same encoding found very similar solutions to the problem regardless of which encoding they used. Average correlation between the hidden unit activations of the 10 5-unit networks trained on the sequential encoding and

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the sequential encoding itself was 0.33. Average correlation between the hidden unit activations of the 10 5-unit networks trained on the real encoding and the real encoding itself was 0.23. In other words, the hidden unit representations, while not completely unrelated to the input patterns, were not simply copies of the input patterns. 6.6

Discussion We have proposed correlation over the distances between hidden-unit

activations as a robust criterion of content similarity. Our simulation results show that our criterion is robust, at least to changes in input encoding, number of connections, and specific connection strength. However, Fodor and Lepore had originally demanded that a robust criterion of content identity was necessary. Is similarity enough, or should we concede that connectionism cannot give an account of content because it cannot give an account of content identity? Fodor and Lepore offer a series of arguments against the very possibility of a theory of content based on similarity rather than identity. The first argument is that any criterion of state space similarity presupposes a notion of state space identity. Thus, they write: What Churchland has on offer is the idea that two concepts are similar insofar as they occupy relatively similar positions in the same state space. The question thus presents itself: when are S1 and S2 the same state space? When, for example, is your semantic space a token of the same semantic space type as mine? (Fodor and Lepore 1996a, p. 152)

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Formally speaking, our method can be used to compare measurements from any two state spaces. In fact, however, in the experiments reported in this paper, we imposed additional constraints on the state spaces we compared. The spaces were generated by presenting identical stimuli to subjects who “spoke similar languages” (all of the network “subjects” were trained with the same labels on input stimuli). Using feedforward connectionist networks, it was both possible to conduct such experiments and reasonable to assume that activations caused by identical stimuli were comparable. Nevertheless, the fact that we imposed those constraints might give rise to a number of objections, which we discuss below. A first objection is that our technique is not applicable to biological nervous systems because it depends on having large numbers of highly accurate, simultaneous single-cell recordings over an extended period of time. Of course, the real world is messier. Given the technology we have today, it would be impossible to conduct an experiment like ours on human beings. We agree that it would be impossible to use our technique on biological nervous systems given current technology, but we suspect that the technology will someday be available to record the sort of data that would be necessary for applying our technique to real nervous systems. In fact, one could apply the technique to the results of fMRI experiments, which provide a low-resolution view of neural activation. In any case, our point does not depend on it. We have argued that our technique provides a robust criterion for inter-individual concept similarity. The fact that such a criterion exists is theoretically important because it means that state space

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semantics cannot be rejected on the grounds that it has no such criterion. It is not necessary to make that theoretical point that we provide a method for evaluating the criterion that is universally and easily applicable. In fact, we have provided a method that is universally and easily applicable to artificial neural networks, and we have also argued that it is universally, though not easily, applicable to biological neural networks. A second objection is that our technique is not applicable to recurrent networks, where state is preserved between stimulus presentations. The neural networks in real brains are far more complex than the simple three-layer feed forward networks used in the experiments we report here. By using discrete time feed forward networks, we constrained the systems in our experiments to be passive receptors of their inputs. It is likely that even humans sitting on a couch watching TV are not such perfectly passive receptacles. Rather, they bring internal state to the processing of input. Indeed, this is the point of priming experiments. Recurrence introduces a significant new level of complexity by allowing the possibility of storing information in the state of the network that is not directly caused by the current sensory stimulus. In most recurrent networks (not to mention real nervous systems), it is not reasonable to assume, as we did in the experiments above, that states caused by identical stimuli are comparable. Two people watching the same television are likely to be thinking very different things, but our technique seems to presuppose that they are thinking the same thing.

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Although the experiments in this paper used feedforward networks, we believe that it is also possible to compare representations in recurrent networks using our technique. Other methodologies that inspect brain states, such as ERP’s or PET scans, suffer from the same problems. Those that use such methodologies tend to average over many stimulus presentations, and sometimes over different subjects, in order to smooth out such variations. We would do something similar. A third objection is that our technique is too formal, in the sense that it could judge as highly similar two networks that represented completely different things but happened to have stumbled upon similar internal representations. It is theoretically possible that two networks presented completely different categories of input stimuli might have very similar activation space structures, and so be judged by our mathematical measure to be semantically similar as well. However, in addition to the purely formal technique of correlating distances between representations, our technique also depends on matching stimuli. (In the case of recurrent networks, it furthermore depends on matching multiple presentations of the same stimulus, potentially in different contexts.) Hence, it is not purely formal. Indeed, the finding that two different categories of input stimuli had similar activation space structures would be an interesting finding about conceptual structure. A fourth objection is that we do not take into consideration the possibility of thinkers who have different numbers of concepts. Indeed, with our theory or without it, counting concepts is a difficult business. How many concepts do you

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have? Is it the same number as I have? If you have 40 and I have only 3, how is it possible to compare our representational states? We haven’t said much about what concepts are on our theory, and we don’t feel that we need to in order to make our point. We have proposed a criterion for similarity of the content of representational states across individuals that does not depend on individuating concepts. We do, however, want to say three things about what concepts are not. First, concepts are not stimuli. One might assume that we equate concepts with stimuli on the basis of the fact that we use identical stimuli to match points in the activation spaces of different networks. As we discussed above, however, this is not an intrinsic part of our theory; it is only a methodological convenience. Second, concepts are not “dimensions in state space,” at least insofar as “dimensions in state space” is taken to refer to the dimensions the space happens to have (e.g., the number of units in the hidden layer of a neural network in the case of an activation state space). In fact, it has been one of our primary points that networks with different numbers of units (and hence state spaces with different dimensionalities) can still be meaningfully compared. Third, concepts are not terms in a language. We did not impose the “same language” constraint on our networks in order to ensure that they had the “same concepts”. Although we used exactly the same output representations in all of our networks, we might have mixed up the output units in such a way that the networks all made the same categorizations while using different output units to label them. Such networks would have spoken “different languages” in the sense

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that they would have had different terms for their categories. Nevertheless, they would have had the same number of categories and would have agreed on which stimuli belonged to a particular category. Although we did not run such an experiment, we would not expect it to change our results. There is also a stronger sense in which our networks might have spoken “different languages”. There are many psychological results showing that people categorize the world in very different ways (see Goschke and Koppelberg 1990 for a review) and many philosophical arguments to the effect that figuring out what someone is saying is at least as hard as figuring out what they are thinking (e.g., Quine 1960). Our networks might have had more or fewer categories in their repertoire; some might have been trained to distinguish only two colors, others to distinguish six or more. If that had been the case, would it have made sense to compare representational similarity between networks with different numbers of categories, and what would the results have been? Because we have not yet done the experiments, we cannot report the results. We do, however, think that it would have made sense to compare the networks. We would hypothesize that the representational similarity between networks trained on different numbers of color terms would be rather low, since networks that had to learn more categories would also have to create more partitions in their hidden unit activation spaces. A fifth objection is that we tacitly assume a hopelessly naïve form of empiricism – that any concept may be elicited simply by the presentation of some

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stimulus. This objection, like the third one, arises from a misinterpretation of the fact that we match representations according to stimuli in the experiments we report here. Since we present the same stimuli to each network, it is easy to think that we assume that a thinker has one concept for each stimulus;. However, even the reader who understands that we do not identify concepts with stimuli might still be puzzled about how we would measure representations of abstract concepts like love, truth, beauty and justice. What possible stimulus could reliably elicit a thought employing such a concept from any subject? We don’t believe that there is any such simple stimulus (although showing the subjects those words themselves, or sentences that contain them, would be a good start). Nevertheless, we believe that it is reasonable to assume that some concepts (color concepts are a good example) are primarily (though clearly not entirely) perceptual, and that we can get at representations of the more abstract concepts by using what we know about the representations of more perceptual concepts as landmarks in the representational space. We can start by matching such mostly-perceptual concepts as best we can across large numbers of contexts. The structure of higher-level, more abstract, less perceptual concepts can then be explored by locating them relative to the conceptual “landmarks” we have identified for more perceptual concepts, again across many contexts. By finding patterns of activation that are not the same as known perceptual representations but which are in similar relative positions across large numbers of contexts, we can locate the representations of abstract concepts in activation space. (Which concepts they are will have to be

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determined by other means, since we do not purport to have a means of determining what a person is thinking, only a criterion for when two people are thinking similar things.) Such representations, although they would be located relative to more perceptual representations, would not necessarily have perceptual representations as logical parts or final causes. Our theory is not mere empiricism, as can be seen from the fact that the metric of content similarity we advocate can be used to measure similarity of internal representations regardless of how inputs are encoded. In fact, as we have demonstrated empirically, it is even possible for systems with very dissimilar input representations to have internal representations that are more similar than their inputs. The mention of similarity in the previous paragraph raises a final issue we must address. Fodor and Lepore’s challenge to state space semantics was to provide a criterion for content identity. Although we have given a criterion of content identity (perfect correlation), our experiments as well as our intuitions tell us that it will be met only very rarely. Is our theory, which depends in most cases on similarity, not identity, good enough to meet the objection? We think it is. Fodor and Lepore are, we feel, unduly concerned with the identity of concepts: clearly a necessary condition for the identity of state spaces is the identity of their dimensions; specifically, identity of their semantic dimensions, since the current proposal is that concepts be located by reference to a space of semantically relevant properties (Fodor and Lepore 1996a, p. 152).

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We have shown that it is possible to compare state spaces of arbitrarily differing dimensions, as long as we are willing to be satisfied by a measure that reaches identity only in the limit. Contra Fodor and Lepore, we are not “faced with the question when x and y are the same semantic dimensions” (p. 152). The question simply does not arise, because we are not comparing similarity along dimensions. Instead, we are comparing relative distance between activations, and distance can be computed in any number of dimensions. Fodor and Lepore anticipate this kind of argument. They write: Perhaps it will be replied that semantic similarity doesn’t, after all, require concepts to be adjacent in the very same state space; perhaps occupying corresponding positions in similar state spaces will do. That a regress has now appeared is, we trust, entirely obvious (p. 152). On our view, semantic similarity does not consist in concepts occupying similar relative positions in identical state spaces. Moreover, neither does semantic similarity consist in concepts occupying similar relative locations in similar state spaces. Rather, semantic inter-individual concept similarity consists in concepts occupying similar relative locations in the state spaces of the two individuals, however similar or different those state spaces may be. Our measure of content similarity is robust and well defined for any state space. The question of statespace similarity does not arise. Hence, there is no issue of a regress.

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6.7

Conclusions Our goal here has not been to defend a particular theory of what semantic

content is or how it is determined. Rather, we have defended Connectionism in general, and state space semantics in particular, against the charge that they are incompatible with any theory of content because they preclude the very possibility of determining identity of content across individuals. In response to Fodor and Lepore’s challenge to state space semantics, we have argued that representational similarity can be measured by correlation between inter-point distances in any two activation state spaces. Thus, we have shown that state space semantics does have a way of measuring similarity of content (and, in the limit at least, identity of content). It can be used to measure similarity of internal representations regardless of how inputs are encoded and regardless of number of hidden units or neurons a network might have. Furthermore, we have shown empirically that the measure of content similarity we advocate for state space semantics is robust under several conditions, by using it to demonstrate that different individuals, even individuals with different “sensory organs” and different numbers of neurons, may represent the world in similar ways. 6.8

Acknowledgement The text of this chapter is joint work with Garrison Cottrell. The

dissertation author was the primary author, and the co-author (Garrison Cottrell) directed and supervised the research that forms the basis for this chapter.

Chapter 7 Conclusion 7.1

Summary Over the previous six chapters, I have defended the thesis that spatial

representation is a fundamental constituent of thought in two different ways. First, we identify and refer to individual particulars either by directly locating physical objects in material space with respect to ourselves or by analogous processes in the case of abstract objects. Second, the means by which our brains represent and categorize these objects is as points in a neural activation space. This theory of representation is rather different from the sort of linguistic and computational theories that have dominated philosophy in this century. However, it is not without precedent in the history of philosophy, as I argued in Chapters 3 through 5. The spatial theory of representation advocated in this dissertation owes its origins to Strawson and, ultimately, to Kant. Moreover, it is part of the continuous dialog about the nature of mind in which philosophers have been engaged since the dawn of civilization, as evidenced in Chapter 3. The technique for comparing internal representations in neural networks reported in Chapter 6 is, on the one hand, a useful tool in the arsenal of cognitive modelers. As demonstrated in the experiments reported in Chapter 6, it can be used fruitfully to study the properties of network models. On the other hand, the specific technique is really only one product of a far more general view of representation, one which grounds representation in the spatial abilities of the

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cognizer and the spatial properties of his brain. The author hopes that this more general theory, not just the specific tools and experimental results presented in Chapter 6, will ultimately be the legacy of this work. 7.2

Directions for Future Research Although this dissertation has not solved all of the problems considered in

Chapter 2, it has solved the one central problem: to give an account of the essential constituents of thought that is compatible with physicalism. The author believes, as stated in Chapter 2, that this problem is at the heart of the largest questions in the history of philosophy. Although that claim will remain unjustified here, it is obviously fertile ground for future work! As stated in the Introduction, this dissertation presents a theoretical framework that depends ultimately on a wide range of psychological and neuroscientific literature. One direction for future research would be to do a careful analysis of whether the results reported in this literature really support the thesis of this dissertation. Is it psychologically plausible that a representation of physical space is necessary for identifying and referring to individual objects? That reference is a generalization of or metaphorical extension of the grasping of material objects? That predication is the location of objects in a high-dimensional mental space in which the dimensions and the proximities of any given activation to others is psychologically significant? As an example, one specific question is whether material-object identifications are dependent on cognitive maps. In particular, one would like to

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know whether damage to the hippocampal or parietal lobes that impairs cognitive mapping ability also necessarily impairs object-identification. The goal would be to give the most charitable version of an Evans-style argument for the dependence of material-body-recognition on allocentric representation of space, and then to evaluate it in light of developmental, behavioral, and physiological evidence about the relation between physical object identification and cognitive mapping. Another fertile area is the question of whether egocentric representation of space is necessary for allocentric representation. It does seem that, if we use an allocentric frame of reference or a cognitive map, we must somehow place ourselves in it. However, the fact that we can find dissociations between allocentric and egocentric spatial skills in cases of brain damage in other species suggests that this a priori theory might not hold up. Finally, the material in Chapter 6 cries out to be extended in many ways. To begin with, it would be interesting to compare the effects on representational similarity of varying the “languages” the networks speak (i.e., their categorization behaviors). It would also be interesting to compare networks with more than two processing layers, in order to evaluate the similarity between representations at different stages of processing. In addition, it has been suggested that we should find a measure of similarity that allows for nonlinear as well as linear mappings between the representations in one network and those in another. Last but not least, the author is particularly interested in the problem of comparing representational similarity over time in recurrent networks..

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