The Geometry of Vision and the Mind Body Problemby Robert E. French

Philosophical Review

The Geometry of Vision and the Mind Body Problem by Robert E. FrenchReview by: David HilbertThe Philosophical Review, Vol. 100, No. 2 (Apr., 1991), pp. 293-297Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2185307 .

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BOOK REVIEWS

At the end of the introduction to Fodor's earlier book, RePresentations, he describes the form of much contemporary philosophical theorizing.8 Such theories, he says, frequently assert: "Let's try looking over here." When the Fodorian searchlight shines, the looking is always fruitful. Rea- soning from generally sound premises, Fodor inevitably finds a route to the unexpected, sometimes to the incredible, often to the insightful. The effect is always thought-provoking, and his influence is important even when one works to refute it. Psychosemantics deserves a wide and con- tinuing readership as a clear vision in a murky field.

DAN LLOYD Trinity College

8RePresentations (Cambridge, Mass.: The MIT Press, 1981).

The Philosophical Review, Vol. C, No. 2 (April 1991)

THE GEOMETRY OF VISION AND THE MIND BODY PROBLEM. By ROBERT E. FRENCH. Bern, Switzerland, Peter Lang, 1987. Pp. 193.

The spatial character of the immediate objects of vision is a problem that has occupied a number of the most distinguished philosophers of the modern period. To take an example particularly relevant to the work under review, George Berkeley, in his Essay towards A New Theory of Vision, defends the thesis that the spatial characteristics of the immediate objects of vision can be described using only two dimensions. That is to say there is no depth to what we see, only length and width. Berkeley's thesis has not lacked both defenders and critics in the two and a half centuries since the publication of the Theory of Vision, and at first glance the central thesis of the book under review, that visual space is two-dimensional, seems like a simple restatement of Berkeley's view. That Robert E. French is not de- fending Berkeley, however, becomes abundantly clear when he acknowl- edges that we have immediate visual perception of something like depth. French's theory in a nutshell is that the immediate objects of vision, although two-dimensional, are not flat, and it is his attempt to reconcile the claimed two-dimensionality of visual space with the acknowledgment that we have something like immediate perception of depth that provides most of the interest and novelty in this book.

Unfortunately the structure of visual space is not the only topic dis- cussed by French and the beginning and end of this rather short book are concerned with quite different topics. The book opens with an attempted refutation of naive realism and an attempted defense of the legitimacy of introspection as a methodology for uncovering the characteristics of the

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objects of vision. The book ends with the discussion of the mind body problem promised by the title; I will turn to this later. The first chapter argues for a version of the causal theory of perception and is by and large a litany of familiar examples that are supposed to force a distinction between the immediate objects of perception and physical objects. The dia- lectical aim of this section is to defend a distinction between physical space and visual space and so open the way for the author's subsequent claim that visual space and physical space have different geometrical properties. If there really is the inconsistency the author claims between the properties of visual and physical space, however, then it seems that this would be all the argument that is necessary for distinguishing the two. If there is not, the rather murky presentation of the argument from illusion and accompanying "rational reconstruction" of perceptual language is not going to convince anyone.

Chapters Two and Three provide the author's analysis of the geometry of visual space. In Chapter Two the primary aim is to establish the two- dimensionality of visual space. The author here makes use of a topological criterion according to which, "a continuum has n dimensions when it is possible to divide it into many regions by means of one or more cuts which are themselves continua of n - 1 dimensions" (p. 49). In other words if it is possible to divide a space into multiple regions using a closed curve then that space is two-dimensional, and if it is not possible the space possesses three or more dimensions. It is important to note that on this definition the surface of a sphere, for example, is two-dimensional as well as is a plane. A solid sphere is, of course, three-dimensional on this definition since it is not possible to divide a sphere into two regions using a line, although it is possible using a plane. Using this definition of what it is to be two-dimensional the author argues that it is possible to divide visual space into regions using lines or closed curves. Again, it is important to keep in mind that the sense in which visual space is two-dimensional is compatible with its being curved, and the author argues that it is in fact the case that visual space is curved.

The author, contrary to Berkeley, argues that something like depth is immediately perceived. There are two different ways to reconcile the immediate perception of depth with the two-dimensionality of visual space, and both involve supposing that the immediate objects of vision constitute a curved surface or surfaces. The obvious way to combine the two-dimensionality of visual space with the immediate perception of depth is to take visual space to be composed of surfaces at varying distances from the perceiver. The immediate object of vision would resemble a rubber sheet fitted over the objects in the field of view. Such a surface would be two-dimensional, although different parts of it would lie at different distances from the perceiver. Notice, however, that the two-dimensional surface is

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characterized in terms of its embedding in a space of higher dimension. This approach characterizes the two-dimensional surface in terms of its embedding in a three-dimensional space. This embedding may suggest that although the objects of vision are two-dimensional, visual space itself is three-dimensional. After all, what is this embedding space if not visual space itself? Although we only ever see surfaces and not solids these surfaces are located in a three-dimensional space.

French does not, however, adopt this characterization of the geometric structure of visual space. Rather than characterizing the curvature of the seen surface in terms of its embedding in a higher space he characterizes it in terms of its intrinsic curvature. Via an excursion into differential geometry French shows how what we might have naively called the immediate visual perception of depth can instead be expressed in terms of changes in the metric structure of the two-dimensional surface that is immediately seen. The phenomenal experience of seeing surfaces at different depths is, according to French, really the phenomenal experience of seeing surfaces with different internal metric structures. Space limita- tions prohibit a discussion of the technical details but the essential point is statable without them: differing physical depths are represented in visual space not in terms of phenomenal depth but in terms of the varying intrinsic curvature of the surfaces occupying visual space. We do not need to embed the two-dimensional surfaces that are the immediate objects of vision in a three-dimensional space in order to account for the immediate visual perception of depth and its consequences such as size-constancy.

There are obvious technical worries with regard to applying the tech- niques of differential geometry to visual space. The differentials and inte- grals that this theory makes use of would seem to give the immediate objects of vision a richness and determinateness that they do not possess. Consequently, and as he himself admits, some of the assumptions necessary for French's analysis to apply do not seem to admit of any introspec- tive test. Leaving these issues aside, however, a fundamental question remains. Suppose that we can do as French suggests and reinterpret the phenomenology of depth perception as the phenomenology of intrinsic curvature; we are still left with the question of what we gain by doing things in this way. Nothing in his argument suggests that we cannot, as we are naively inclined to do, characterize the immediate objects of vision as lying at various phenomenal depths. It does not seem more plausible to claim that we have immediate awareness of intrinsic curvature than that we have immediate awareness of depth. If anything the reverse seems true. We are given no argument that the visual facts are any better ac- counted for on his theory than on one in which two-dimensional surfaces are located at varying distances in a three-dimensional space. French presents us with wvhat seems like an interesting result but then fails to give

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us any account of what its philosophical consequences are for our under- standing of vision. The results have a certain intrinsic interest and it seems like they should have consequences but French does not aid us in discov- ering what they are.

French does think his theory has implications, although not for the un- derstanding of vision itself. The implications occur in his discussion in the final chapter of the book of how there can be causal connections between mind and body. In the course of this discussion we are told a number of rather amazing things: visual space is located in physical space, in fact somewhere inside the brain (p. 166); "visual space moves with respect to the visual cortex" (p. 167); "the mind is not only spatially extended, but also spatially coextensive with physical space" (p. 172); and finally "at least one of the differentiating characteristics between the mind and the body is topological; that the mind, one portion of which being phenomenal space, exists in a two-dimensional format, whereas physical entities possess at least three spatial dimensions" (p. 172). The final conclusion of French's investigation of the mind-body problem as it applies to visual space is that "phenomenal space is a two-dimensional surface which either remains sta- tionary or revolves with respect to a series of regions of the brain, and which, while not actually occupying any points of the brain occupied by physical entities, such as electrons, nevertheless passes sufficiently close to these entities so as to enter into causal relationships with them" (p. 174). The driving force behind this theory is the contention that in order for two things to interact causally they must be spatially contiguous. Since according to French visual space is the causal result of events in the brain it must be spatially contiguous with them. Thus we derive the view that that part of the mind which is visual space is a two-dimensional surface that meanders among the neurons of the visual cortex.

It is hard to know quite what to say about this theory. First there is the claim that visual space is part of the mind and that part of the mind is as a consequence spatially extended and two-dimensional. In making visual space a part of the mind French is refusing to acknowledge the traditional distinction between acts of awareness and the objects towards which those acts are directed. The objects occupying visual space could depend on acts of awareness for their existence without being part of the mind itself. There may be grounds for not wishing to draw such a distinction but French does not tell us what they are and seems unaware that this well- known distinction has ever been drawn. Second, there is the location of visual space within the visual cortex. This move seems to be motivated by the thesis that causation requires contiguity coupled with the assumption that it is the occupants of visual space that are the causal results of brain events and not merely our awareness of these occupants. Notice that if the neural locations that account for the visual perception of space are not

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arranged in a topologically similar way to the spatial perceptions of which they are the putative cause, then on French's view those neurons cannot really be the cause of those perceptions. This seems an implausibly strong a priori constraint on the representation of space in the brain. The brain may work this way but French's argument requires that it could not have worked in any other way. These two problems, of course, do not exhaust the difficulties facing a theory which describes dizziness as the rotation of visual space with respect to the brain.

In addition to its philosophical difficulties the book is poorly written and poorly edited. There are numerous typographical errors, and the footnote numbers for the first chapter following note 6 are all off by one. Arguments are rarely clearly stated and the reader is typically left with the formidable task of reconstructing arguments for apparently implausible positions with little knowledge of either the premises or the precise form of the conclusion.

DAVID HILBERT

California Institute of Technology

The Philosophical Review, Vol. C, No. 2 (April 1991)

MEANING AND FORCE: THE PRAGMATICS OF PERFORMATIVE UT- TERANCES. By FRANcOIS R&CANATI. Cambridge, England, Cambridge University Press, 1987. Pp. x, 278.

Sentence (la) below can be literally used to perform the speech act mentioned in (lb):

(1) a. Go ahead b. I order (permit, defy) you to go ahead

What is the difference, if any, in the way they work? What is the role of the italicized prefixes in (lb), and how is the "serious" utterance of (la) (Austin's "implicit" or "primitive" performatives) related to the serious utterance of (lb) (Austin's "explicit" performatives)?'

Two approaches can be traced to Austin's work on performatives. On the first view the performative prefix "adds nothing to the representa-

'See J. Austin, "Performative Utterances," in J. Austin, Philosophical Papers (Ox- ford, England: Oxford University Press, 1961).

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The Geometry of Vision and the Mind Body Problemby Robert E. French