Joint referees #2 Jonathan Opie & Gerard O'Brien

lehar's article is welcome, and raises issues which cognitive science has lately neglected or ignored. his approach is, to our knowledge, quite novel. let us say at the outset, therefore, that we believe this material warrants bbs treatment. it is likely to generate a significant amount of critical reaction and commentary across a broad range of disciplines. at the same time, there are some weaknesses in the article which we would like to see addressed before its eventual publication. some of these are relatively minor, others concern the clarity and coherence of the argument.

minor issues forgive us if some of these seem a little pedantic, but they are offered in a constructive spirit.

1. title. why use the definite article in the article's title ("...the subjective conscious experience...")? one is inclined to ask: "which subjective conscious experience?". surely, it is better to use "... the primacy of subjective conscious experience".

This is a question of emphasis. In this paper I emphasize that conscious experience is not some ethereal entity existing in some abstracted space, but it is a very real and solid physical entity that resides in the physical brain. Attaching the definite article to the subjective conscious experience serves to objectify the concept, to suggest that it is something concrete and real. As to which conscious experience, I can only report on the only one I know, which for me is indeed The subjective conscious experience.

2. section 1, par.4 lehar's interpretation of contemporary materialism as "psychophysical parallelism" is wrong on two counts. first, contemporary materialist philosophers don't subscribe to this view, and second, psychophysical parallelism is really a form of dualism.

a better way of characterizing contemporary materialism is by reference to "token physicalism", which is general enough to subsume variants such as functionalism and the identity theory. lehar's "psychophysical parallelism" is a minority position in the contemporary philosophy of mind (sometimes ascribed to nagel and chalmers, for example). this is not intended as a criticism of the point lehar makes in the latter half of the paragraph, which we regard as important.

The term "psychophysical parallelism" has been removed from the new version.

3. section 2.2 lehar overstates the "incredible" nature of indirect realism when he claims that it flies "in the face of everything we know about neurophysiology". here lehar has not taken sufficient account of the recent work in neurocomputation (such as that of paul churchland and o'brien & opie) which explicitly aims to bring the phenomenology of conscious experience together with the details of neural network information processing. lehar should demonstrate a greater appreciation of this work. (see also 17. below.)

The response to this critique is included in the response to point 17 below.

4. section 2.4, par.1 lehar says that psychology is the "science of the...subjective side of the mind/brain barrier". we agree that conscious experience is a significant (and neglected) explanandum of psychology. however, intelligent behaviour is also an explanandum of psychology. it would be better to say: "psychology is not only the science of human behaviour, but also the science of the psyche...".

I am making an emphatic point here on the origins of psychology, which was indeed defined originally as the science of the psyche [thus the name "psyche-ology"], i.e. the science of conscious experience. Now since behavior is also part of the conscious experience, it would naturally be included in the science of psychology. But then so would sensation, perception, and cognition, not to mention language, motivation, emotion, development, learning, memory, etc., which are all part of the conscious experience and therefore are properly part of psychology. However my intent is to focus here on the original thrust of the science of psychology, which was the investigation of the subjective conscious experience.

the expression "mind/brain barrier" which is used in several places, is also a bit problematic. if the mind is the brain, or a particular kind of activity of the brain, then it is not really apt to speak of a "barrier" (by analogy, presumably, with the blood-brain barrier). why not simply say "...the subjective side of the brain" or "the subjective aspect of brain activity" or simply "conscious experience"?

This is a stylistic issue, attempting to put additional emphasis on a particular concept for the sake of the argument. The word "barrier" denotes not only a physical barrier, as is the case with the blood-brain barrier, but there are also conceptual barriers. And there is indeed a formidable barrier between mind and brain. For although we can explore another person's brain in neurosurgery, we cannot ever directly explore the mind that resides inside that brain. Conversely, we can only see the world itself through the medium of our conscious experience. So we can never get in to another man's mind from the outside, and we can never get out of our own mind from the inside. This is as formidable a barrier as any that science has encountered.

5. section 2.4, par.2 a page reference for the searle 1992 is needed.

The page reference has been provided.

6. section 2.4, par.3 is doesn't strike us as appropriate to describe the objects of experience as the "`product' or `output' of consciousness". these objects, understood as phenomenal objects (and not as the things in the world to which those phenomenal entitites refer) are among the *components* of conscious experience -- *part of* consciousness, not something consciousness *produces* (unless lehar thinks of consciousness as a process that produces a bunch of conscious experiences).

This is a stylistic turn of phrase chosen to make a particular point. In this case the point is to emphasize the reversal of information flow between direct v.s. indirect perception. The word "output" was isolated in protective "quotation marks" to indicate that it should not be interpreted literally, but figuratively, or metaphorically.

7. section 3 lehar appears to accept chalmers' pessimistic analysis of the "hard" problem of consciousness. this is surely premature when there is a large literature that has responded to chalmers' diagnosis of the situation. some reference to this literature would be helpful. (note, the singular of qualia is "quale".)

I am not aware of any paper that convincingly counters Chalmers' analysis, which in my view is both insightful and unimpeachable. Chalmers himself tells me that he has not heard any convincing counter-arguments. Furthermore, the reviewers themselves (O'Brien & Opie 1999 Section 5.4 "The Explanatory Gap") cite Chalmers to make the same essential point, without reference to the "large literature" supposedly refuting Chalmers' argument.

8. section 3, par.3 o'brien and opie's (1999) vehicle theory is a *connectionist* vehicle theory. thus, it aims to explain consciousness in terms of the vehicles of explicit representation as these are understood by connectionists. lehar gives the impression that this approach commits one to a naive first-order resemblance account of mental representation (a square shape in the world represented by a "square shaped region of activation in the brain"). no such commitment attaches to a vehicle theory. see the author's reply in the same issue.

The offending section has been removed from the paper.

9. section 4 in this section lehar initially claims that his perceptual modeling approach "avoids" and "sidesteps" the traditional philosophical problems inherent in neural models of perceptual experience. however, later in this section he admits that his approach really only "postpones" these problems. the former language is thus obviously too strong and should be toned down. (by the way, it is "nagel" not "nagle".)

Perceptual modeling does indeed "avoid" or "sidestep" philosophical problems inherent in neural models of perceptual experience, and it does so by not addressing the neurophysiological issues at all. Therefore the perceptual model is a complete solution to modeling perception, although it is only an interim solution to the larger neurophysiological modeling question. So I stand by the statement that the perceptual model avoids and sidesteps the philosophical problems. (The spelling error has been corrected.)

10. section 8, par.3 lehar says: "the extrinsic constraints are those defined by the visual stimulus, whereas the intrinsic constraints are those defined by the structure of the percept. the configuration of the input encodes the extrinsic constraints, while the stability of the perceptual representation encodes the intrinsic constraints."

wouldn't it be more appropriate to say that the structure of the percept is *determined by* constraints intrinsic to the computational mechanism. it doesn't really make sense to say that the intrinsic constraints are "defined" by the structure of the percept. rather, it is the former, however they might be physically implemented, that determine the latter. of course, the constraints are in some sense implicit in the final structure of the percept, but they aren't defined by it.

The suggested correction has been made in the new version.

similarly, the stability of the perceptual representation is *a result of* the intrinsic constraints, it doesn't "encode" those constraints. at best it displays them.

The suggested correction has been made in the new version.

incidentally, talk of "the most stable configuration" or the configuration with "the greatest simplicity, or pragnanz" (next par.) doesn't actually explain much. a principle like pragnanz is kind of a higher-order gestalt principle that itself stands in need of some explanation in terms of a computational mechanism. lehar, as he admits, offers no such mechanism.

It is a common criticism that Gestalt theory fails to specify the higher order Gestalt principles like prägnanz and emergence in terms of a computational mechanism. Actually Wolfgang Köhler (1924) showed that there is no magic in emergence or prägnanz, they are common properties of certain kinds of physical systems, such as the soap bubble taking on its spherical shape, or water seeking its own level in a vessel. As Köhler pointed out, that equilibrium state tends to exhibit simple regular patterns, as seen in the spherical shape of the soap bubble, and the flat surface of water, and that simplicity of the equilibrium state is itself the property of prägnanz. So it is perfectly meaningful to talk of "the most stable configuration" and "the greatest simplicity or prägnanz", when talking about a dynamic system model. All that remains to be established is exactly what kind of dynamic system might be active in perception, and exactly how it might work. The only valid criticism of Gestalt theory is its failure to provide that specific mechanism, not its failure to define the meaning of prägnanz. And to provide a specific mechanism behind visual perception is exactly the objective of the Gestalt Bubble model. In fact the real value of the Gestalt Bubble model is exactly that it offers one example of how a perceptual model can be built to exhibit the properties of emergence and prägnanz, with the final percept corresponding to the equilibrium state of the system. The objective of the Gestalt Bubble model therefore is exactly to provide "an explanation in terms of a computational mechanism" of the elusive Gestalt principle of prägnanz.

The mechanism which I explicitly avoid discussing in this paper is not the computational mechanism of perception, but rather the neurophysiological embodiment of that computational mechanism as expressed in the physical brain. In fact I have suggested exactly such a neurophysiological theory to account for the Gestalt properties of perception elsewhere ( Lehar 1999). However in the present paper I have elected to confine the discussion to perceptual modeling issues, independent of neurophysiological considerations.

11. section 8.1 we think it would be appropriate at this point to reiterate that the neural implementation of the "volumetric block or dynamic computational elements" need not be a topographic or topological isomorph of this model, but need only be, in lehar's terms "functionally isomorphic". this will decrease the risk of mis-interpretation regarding the model.

In point 14 (below) the reviewers request clarification on the issue of structural v.s. functional isomorphism. In response to that request I have inserted additional explanation in section 5, including a new figure, to clarify this issue. That additional explanation obviates the need for a re-iteration here.

12. section 8.6 the move here, if we understand it, explains subject reports under "objective instruction" conditions (sect.6.3). we wonder if it would be appropriate to make explicit mention of how the model handles subject reports under "projective instruction" conditions.

The reviewers seem to have missed the whole point. The curious aspect of size perception that demands explanation is the fact that distant objects are perceived to be both smaller (by perspective), and yet at the same time to be undiminished in size, as if size perception were a dual phenomenon, encoding simultaneously two different values for the perceived size of the perceived object.

The Gestalt Bubble model proposes a new and original explanation for this phenomenon in the form of a kind of double representation which incorporates that duality in the representation itself. Although distant objects are actually represented as smaller in this model (i.e. they occupy less space in the representational matrix itself) the scale of the representation also shrinks with distance from the egocentric point (i.e. the center of the perceptual sphere) so that although distant objects are smaller, they are measured against a shrunken reference grid, and therefore they are judged to be undiminished in size.

So this model handles "objective instructions" by measuring the size of percepts relative to the shrinking objective-size scale, and it also handles "projective instructions" by the actual size of percepts in the representational matrix.

13. section 10, final par. to speak of having "direct experience" of the "internal effigies" of objects in the world is rather odd. we understand lehar's point of course, namely, that our access to objects in the world is indirect, and mediated by internal perceptual states. even so, it would be better to say that our experience is comprised of internal effigies of objects in the world, rather than of the objects themselves.

There are some who claim that phenomenal experience is mediated by "the vehicles of explicit representation in the brain", but at the same time the experience itself corresponds to the contents of those vehicles, rather than the vehicles themselves. This kind of double explanation which has the vehicles as neurophysiological entities, but their contents as subjective phenomena, invites the dualistic interpretation that leaves unanswered the question of how the vehicles are related to their contents. The language chosen above, by contrast, emphasizes the unity of the subjective experience and the corresponding neurophysiological mechanism in the brain. They are different aspects of the same underlying structure, viewed from the internal subjective context v.s. the external objective context. Therefore there is no ontological difference between the "vehicle" and its "contents", they are one and the same thing. The Gestalt principle of isomorphism highlights this unity, because the isomorphism is not some incidental quality that compels the subjective and objective percepts to conform to each other, but rather they cannot help but be isomorphic, because they are different manifestations of the same essential structure, viewed from two different perspectives. I stand by the statement that the internal effigies in perception are directly experienced.

major issues below are some issues which we consider to be of greater significance.

14. section 6.1 this section is quite problematic. having gone to considerable trouble to establish that the model being presented does not directly bear on the neurophysiological correlates of conscious experience, but merely codifies or systematises the information content and structure of consciousness, lehar here raises what appear to be problems for a theory of the neural correlates.

the reply to the homunculus problem is fine, as far as it goes. lehar rightly notes that this is just as much a problem for a symbolic conception of mental representation as for an analog conception, but is in fact no problem at all, because the threatened regress can be contained by assuming mental processes that are sensitive to the symbolic or analog structure of the representations.

the trouble is, lehar in effect admits here that his theory is (to some extent) a theory of the neural vehicles of consciousness. he describes them as "full spatial analog[s]" of the environment and "explicit spatial representation[s]". those assertions appear to speak to the nature of the vehicles, rather than their contents.

to make matters worse, in the latter part of the paragraph lehar reverts to talking about the contents of the vehicles in defense of his view. he says that the "existence and fully spatial nature [of percepts] in my internal perceptual world is beyond question". this is surely a claim about the contents of visual experience.

talk of "explicit spatial representation" and "spatial nature of the perceptual representation" now becomes quite ambiguous. is it the vehicles that are spatial (and hence topologically isomorphic with what they represent), or do they merely *represent* spatial properties.


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A whole new section has been added to section 5 in the paper, clarifying the relation between structural and functional isomorphism, complete with the new Figure 1 to illustrate the concept. I suspect these reviewers will be unhappy with this explanation, as it highlights the fact that I do indeed advocate a "Picture-In-The-Head" theory of spatial representation, a position that they argue against in their own paper.

O'Brien & Opie (1999 Sect. 5.3) argue that "We don't expect the green of grass to be represented by green-colored neural vehicles. Why, therefore, should we expect spatial properties of the world to be represented by corresponding spatial properties of the brain?"

But if "greenness" is not a property of the brain, where does that green color come from? It cannot be a property of the world itself, because it is a subjective quale, i.e. a kind of arbitrary mapping used in the internal representation of the brain to represent light of median wavelengths. The green color is itself a property of the physical mechanism of the brain, not of the external world. Although the neurophysiological correlate of this green quale has yet to be identified, we already know for a fact that it is green, because we can see it "from the inside". That does not mean it will look green to an electrode that measures the activation of particular cells in the brain, nor that those cells would appear green under microscopic examination. The greenness can only be experienced internally, but that does not make it any the less green, or any the less a characteristic quality of certain physical processes in the physical brain.

On the question of the spatial properties of the phenomenal world, if the representation subserving that phenomenal experience is not itself spatial, then why would it appear spatial phenomenally? There are many non-spatial ways to represent spatial information. For example it can be expressed in the form of mathematical equations that describe spatial structures, or spatial structures can be expressed in a Fourier code. But if our brain were to employ either mathematical equations, or Fourier descriptors as its representation of spatial structure, then our subjective experience would itself necessarily appear in the form of mathematical equations, or of Fourier descriptors. The fact that the world of experience takes the form of a spatial structure is direct evidence for a spatial representation in the brain.

I do not expect the reviewers to be convinced by this argument, this is a central paradigmatic issue around which the whole paper revolves. It is the inevitable consequence of taking an Indirect Realist view of perception, which shows that the properties of the phenomenal world are properties of the brain first and foremost, and only in secondary fashion are those properties also reflective of certain properties of the external world. It is curious that O'Brien & Opie join Atkins (1996) in calling Isomorphism a "Naive Theory of Perception". In fact it is their own view which is the one consistent with Naive Realism, because they seem to accept without question that the world appears spatial, although they deny a spatial representation in the brain, as if we were viewing the world directly, instead of by way of the medium of the representational mechanism in the brain.

If, at the end of the day, Lehar does subscribe to a "PICTURE-IN-THE-HEAD" APPROACH to visual perception, he MUST DO MORE TO DEFEND IT AGAINST THE NUMEROUS OBJECTIONS IT FACES. There is A VOLUMINOUS PSYCHOLOGICAL/ PHILOSOPHICAL LITERATURE ON THIS PROBLEM, with which Lehar should show at least some familiarity. A good place to go, for example, is the volume "IMAGERY" EDITED BY NED BLOCK. Of particular interest to Lehar will BE FODOR'S WELL- KNOWN REPLY to the "infinite regress of observers within observers" criticism that Lehar ascribes to Dennett, O'Regan and Pessoa et al.

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As far as I can tell, the "numerous objections" faced by the Picture-In-The-Head theory amount to one single objection, and that is the tired-old homunculus argument, which has already been dispatched many times over. This is the worst kind of critique to receive in a review because it is so open-ended, it is hard to address. If there really were so many objections, why don't the reviewers mention one or two of them so I would know what they are talking about? I understand that the reviewers may think that there are numerous objections, but that is only because this alternative is so rarely given any serious consideration that the reviewers haven't heard it defended before. The reviewers casually point me to Ned Block's "Imagery". But that book contains eight different articles by eight different sets of authors! Any hint as to which of these authors supposedly delivers the coup-de-grace for the Picture-In-The-Head hypothesis? Or do I have to go through the entire book to address this reviewers objection?

Ned Block himself offers the answer right in the introduction, on page 2:

"But no one writing in this book (nor any other serious participants in the debate) thinks that people can literally see and manipulate real internal pictures. Brain scientists have found no pictures in the brain, and even if they had, the presence of pictures wouldn't explain the phenomena unless the brain contained an internal eye to view them and an internal flashlight and internal hands to manipulate them etc. (And even if we postulate an internal eye, would there still be another eye in that eye's brain? So we have a problem: the obvious explanation is blocked."

So the "formidable objection" by Ned Block is nothing more than the tired old homunculus argument! Block does however explain why this alternative seems so incredible, and that is because "brain scientists have found no pictures in the brain". This either means that there are no pictures in the brain, or that modern neuroscience is in a state of serious crisis, because it cannot find the pictures in the brain that we know must be there. And the evidence for the presence of those pictures is right before our eyes, if only we can see beyond the naive realist illusion and recognize the phenomenal world for what it really is.

Chapter 1, by Roger Brown & Richard Harrnstein offers no arguments against the Picture-In-The-Head hypothesis.

Chapter 2, by Daniel Dennett, offers the following objection: (page 52)

"For an image to work as an image there must be a person (or an analogue of a person) to see or observe it ... we shall have to design a perceiver- analogue to sit in front of the image, and yet another to sit in front of the image which is the end product of perception in the perceiver-analogue, and so forth ad infinitum."

So its the tired old homunculus argument being dragged out again! On page 56 Dennett discusses the question of hallucinations, and the phenomenal space in which they are observed, using the example of a "freak" visual experience caused by electrical stimulation of the cortex...

"Having a visual hallucination is ... just being aware of the content of a non- veridical visual `report' caused by such a freak discharge. And where is this report and what space does it exist in? It is in the brain and exists in the space taken up by whatever event it is that has this non-veridical content, just as my description of hallucinations takes up a certain amount of space on paper. Since spatiality is irrelevant to descriptions, freak descriptions do not require ghostly spaces to exist in.

If the neurophysiological "description" of the hallucination is not expressed as a spatial pattern in a spatial medium, what is it that transforms the phenomenal correlate of that description into the spatial pattern that we experience? How did phenomenal experience settle on a spatial format for presenting the non-spatial information in the brain? Why would it not, for example, appear phenomenally as a Fourier descriptor, or as a mathematical formula? And where does the transformation from non-spatial to spatial take place if not in the brain? And what is the algorithm of that transformation? And where is the spatial percept stored or registered? In truth, the fact that the phenomenal world appears as a spatial pattern is direct evidence for a spatial representation in the brain.

In Chapter 3 page 63 Jerry Fodor offers his own "fatal blow" to the Picture-In-The- Head theory by announcing that he is...

"unsympathetic about the empirical basis for the existence of stagelike changes in modes of internal representation ... because I think it would be appalling if the data really did somehow require us to endorse that kind of view. I am, in fact, strongly inclined to doubt the very intelligibility of the suggestion that there is a stage at which cognitive processes are carried out in a medium that is fundamentally nondiscursive."

So Fodor's whole argument is that he finds the idea incredible! He then goes on to present a caricature of a simplistic image-based "language" which he calls "Iconic English", and demonstrates how this simplistic concept is inadequate as a model of thought. For example if "John" is represented by an image of John, and "green" is represented by a green tile, then the sentence "John is green" could not be meaningfully constructed out of those elements. So Fodor succeeds in shooting down his simplistic straw man theory of imagistic thought, and thereby supposes he has put an end to the notion altogether.

Chapter 4 is written again by Daniel Dennett. This time he "defeats" the notion of mental imagery by constructing a fanciful analogy. He asks the reader to imagine that anthropologists have discovered a native tribe that believes in a hitherto unheard-of God of the forest, named "Feenoman" (this will stand in for the supposedly fictitious "phenomenal experience" whose existence Dennett so forcefully denies). Some of the anthropologists begin to believe in Feenoman as an objectively real deity (the "Feenomanists"), while others retain their scientific rigor, and study the native religion while remaining agnostic themselves (the "Feenomanologists"). On page 102 Dennett concludes that:

"Phenomenal space is Mental Image Heaven ... [mental images] can reside, with Santa Claus, in the logical space of fiction."

But analogies only work when the analogy is analogous. In this case nobody has ever actually seen Feenoman, and therefore it is reasonable to question His existence. The phenomenal world on the other hand is right before our eyes, if only we can recognize it for what it is. Dennett's argument works better against mental imagery than perception, because it is easier to deny the existence of those...

"...entirely mythical species of mental images: the various non-physical, phenomenal or epiphenomenal, self-intimating, transparent to cognition, unmisapprehensible, pseudo-extended, quasi-imagistic phantasms that have often been presented as mental images in the past." (page 104)

However this argument does not work so well against perception. For to deny a spatial representation in the brain is to deny the vivid spatial structure so plainly evident in the world we see around us.

Chapter 5 is provided by Robert Schwartz, who launches into a minute analysis of exactly what images might be, and by what principles they differ from other forms of representation. His only serious challenge to the Picture-In-The-Head theory is his complaint that the concept of isomorphism is too vague, because it uses the concept of "similarity" between the picture and the object it represents. But since similarity is itself a rather vague term, Schwartz objects that

"the unqualified claim that a picture resembles its referent is vacuous."

Does Schwartz suggest that any statement about the similarity between items is also vacuous? Surely scientific discourse can meaningfully employ terms such as similarity even in the absence of a rigorous definition. In any case this objection is only valid when the claim is unqualified. In my own discussion of isomorphism I have qualified the concept of similarity by invoking information theory, and specifying that the information content of the subjective experience cannot be any greater than the information content of the corresponding neurophysiological state. The use of information theory to quantify the otherwise vague notion of similarity is a significant and original formulation of the issue of isomorphism, and this one step makes my own discussion of isomorphism impervious to many of the objections raised against this much-maligned notion.

Chapter 6 is provided by Kosslyn, Pinker, Smith, & Schwartz. As mental imagery advocates they offer no challenge to the Picture-In-The-Head hypothesis.

Chapter 7 is contributed by Zenon Pylyshyn, who is an ardent opponent of mental imagery. His argument is that what people report as properties of images, are actually properties of the objects they represent, not of the images themselves. For example when a mental image of a table is observed to have spatial extent, Pylyshyn argues that spatial extent is not a property of the mental image, it is a property of the table itself. Only a Naive Realist could possibly accept this argument because an Indirect Realist realizes that none of the properties of the objective external world can possibly penetrate into conscious experience except by way of explicit representations of them in the brain, mediated by sensory input. If the mental image did not have spatial extent, then no spatial extent would be experienced for that image. Pylyshyn argues as if the quality of spatial extent can somehow bypass the sensory interface to the world and penetrate directly into the experience of the imaging subject, without leaving an impression in the subject's brain.

The final chapter, Chapter 8, is written again by Stephen Kosslyn, who as a strong advocate of mental imagery offers no argument against the Picture-In-The-Head theory. However he does hazard to say on page 207 that

"Although no serious researcher today maintains that images are actual pictures in the head, some still find it reasonable to posit quasi-pictorial representations that are supported by a medium that mimics a coordinate space."

I find this statement puzzling, since the notion of quasi-pictorial representations supported by a medium that mimics a coordinate space is exactly what I consider to be "actual pictures in the head". So I am at a loss as to whether I am in agreement or disagreement with Kosslyin on this point. But in any case he offers no explanation for why no serious researcher believes in pictures in the head.

So, after poring through the "voluminous literature" in the recommended tome, all I have come up with is the homunculus argument! This is what I really hate about these journal reviews. At the casual mention of a "voluminous literature" and a vague pointer at a book, the humble supplicant for publication has to rush off to the library and plough through a mass of irrelevant material only to find that the reviewers did not know what they were talking about! I can understand why they may have had the impression that this book contained "numerous objections" to the notion, and that is because the notion was never even considered as a serious alternative by any of the parties to the debate. But that is all the more reason why it deserves that consideration now.

Daniel Dennett makes the insightful observation that although this issue remains unresolved, and that nobody really knows with any certainty whether there are pictures in the brain, (page 30)...

"A curious feature of the debate is the passion it evokes, which is unlike the normal passion of scientific controversy ... everyone, it seems, has a fiercely confident opinion about the nature and existence of mental images. This manifests itself in remarkable ways: in unhesitating predictions of the results of novel psychological experiments, in flat disbelief in the integrity of recalcitrant experiments, in gleeful citation of "supporting" experimental evidence, coupled with bland imperviousness to contrary evidence."

In his summary of the debate to date, Kosslyn et al. offer the observation that...

"Not surprisingly neither arguments nor counter-arguments have been definitive, and neither seems to have had enough force to sway most people from whatever position they found most congenial in the first place."

This is a sure sign of a paradigmatic debate. The reason for the supreme confidence of the opposing camps is that they are not debating the facts of the case, as they would in a debate over more specific theories. Instead, the issue involves the paradigmatic question of whether the subjective conscious experience is a valid source of evidence for the nature of the neurophysiological representation employed in the brain. For if it is, then the existence of mental images can be easily confirmed by inspection. And that choice in turn depends on the epistemological question of whether the world we see around us is the real world itself, or whether it is merely a replica of that world in an internal representation. The only way to break the endless cycle of fruitless debate is to cut through to the paradigmatic issue hidden at the core of the debate, and settle once and for all the question of the epistemology of conscious experience. The fact that none of the contributing authors in Ned Block's book even considered a Picture-In-The- Head theory even as a theoretical possibility, and the fact that the homunculus objection crops up so often without challenge, highlights the urgent need for this paper to be published without further unnecessary delay.


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This issue is now clarified in the new extended Section 5 in the paper.

16. Section 8.6 Again, Lehar says "The most significant feature of this concept of perceptual processing is that the result of the computation is expressed not in the form of abstract variables encoding the depth and slope of the perceived rectangle, but in the form of an explicit three-dimensional replica of the surface as it is perceived to exist in the world." ARE WE TO TAKE THIS LITERALLY? OR IS THE "REPLICA" HERE SOME KIND OF FUNCTIONAL ONE?

This issue is now clarified in the new extended Section 5 in the paper.

17.On PDP models.

In Section 9 Lehar claims that "the computational transformations observed phenomenologically are implausible in terms of contemporary concepts of neurocomputation and even in terms of computer algorithms".


Even so we grant that there is some prima facie plausibility to Lehar's claims where "neuron doctrine" style theories are concerned. We are not so convinced when it comes to PDP approaches. Indeed, we would offer the suggestion that the PDP APPROACH TO NEURAL COMPUTATION, SUITABLY INTERPRETED, HOLDS OUT SOME HOPE OF *IMPLEMENTING* THE VERY PERCEPTUAL MODEL LEHAR DEFENDS.

The PDP approach takes seriously the intrinsic structural properties of the brain, and attempts to develop an account of both cognition and perception consistent with these properties. It identifies as a principal computational mechanism a style of processing known as relation search (or constraint satisfaction). This, we suggest, is just the kind of mechanism required to implement the kinds of dynamic, reciprocal interactions, and emergent phenomena that Lehar postulates in sections 8.2, 8.3, 8.4, 8.5 and 8.6. We think Lehar might consider this suggestion, and, at the very least, MAKE SOME COMMENT AS TO THE POTENTIAL OF THE PDP APPROACH to implement his perceptual model.

18. On originality. This follows from the previous point. We accept that PDP theorists haven't said much about the representation of space, but there have been some tentative steps in the direction of applying PDP thinking to gestalt perceptual phenomena. We commend the following papers to the author:

PALMER, S.E. (1992) Modern theories of Gestalt perception. In: G.W.Humphreys (ed.) Understanding Vision. Blackwell. (See particularly the latter part of the paper.)

READ, S.J., VANMAN, E.J. & MILLER, L.C. (1997) Connectionism, Parallel Constraint Satisfaction Processes, and Gestalt Principles: (Re)Introducing Cognitive Dynamics to Social Psychology. PERSONALITY AND SOCIAL PSYCHOLOGY REVIEW Vol.1(1):26- 53 (Not focussed on perception, but a nice discussion of PDP and gestalt theory).

OPIE, J. (1999) Gestalt theories of cognitive representation and processing. Psycoloquy 10(021)

[Note: Caps above indicate sections highlighted by the editor for particular importance to address.]

The reviewers are obviously advocates of PDP models and therefore naturally reluctant to accept the limitations of their paradigm without specific proof that it is wrong. But it is impossible to prove a negative- i.e. I cannot demonstrate that no possible future PDP model could ever be formulated to address the Gestalt phenomena discussed in the paper. The onus is on the PDP advocates themselves to demonstrate the capabilities of their paradigm. However there is good reason to believe that the neural network paradigm has some serious limitations with respect to the phenomena specifically addressed by the Gestalt Bubble model.

The Gestalt Bubble model was formulated as a perceptual model, but the computational functionality that it performs can be readily expressed in PDP terms. However the result is a combinatorial explosion of receptive fields so great as to seem completely implausible to the author. That is why I chose to present it as a perceptual model rather than a neural network model, and that is why I stand by my statement that "the computational transformations observed phenomenologically are implausible in terms of contemporary concepts of neurocomputation". Now this is admittedly a personal judgement, as plausibility judgements necessarily are, so I cannot prove definitively that PDP models are implausible. But there is good reason to believe that they are implausible for the class of perceptual computation addressed by the Gestalt Bubble Model.

The reviewers point out correctly that PDP models of Gestalt phenomena have been proposed, that exhibit the Gestalt properties of emergence and prägnanz. That's all well and good, but those models happen to be irrelevant to the specific perceptual phenomena addressed by the Gestalt Bubble model, i.e. the perceptual transformation from a two-dimensional stimulus to a three-dimensional volumetric perceptual structure.

In fact some of the models the reviewers cite actually highlight the limitations of the PDP approach by the parts of the problem which they pointedly avoid addressing. For example Palmer (1990 p. 316) presents a PDP model to account for the ambiguous percept of an equilateral triangle as an arrow pointing in one of the three directions indicated by its corners. Palmer presents a simple dynamic neural network model in the form of three nodes with mutually inhibitory connections, resulting in a winner- take-all behavior. The activation of the winning node represents a percept of the triangle as an arrow pointing in the corresponding direction. This is an excellent demonstration of Gestalt dynamics in a perceptual model. But now consider what kind of architecture would be required to make those three nodes operate as advertised in response to a given visual stimulus. For it is here at the lower end of the visual hierarchy that neural network theory runs into a combinatorial mess. Let us begin with a functional description of what that processing must do. We need a circuit which can read a visual image, and identify the presence of one or more equilateral triangles in the stimulus. For each equilateral triangle the system must set up a triangle of mutually inhibitory nodes with dynamic behavior as described by Palmer. Forget the rest of the problem, like the question of how the final activation of the winning node for each triangle becomes a percept of a directed arrow. Even the computational functionality outlined above already poses a formidable challenge for PDP theories. We know how to make edge detectors out of neurons with spatial receptive fields, so we begin with edge detectors at every location across the visual field, replicated at every orientation. But the next problem of finding the triangles already begins to leap into combinatorial territory. For we now need "angle detectors" tuned to respond to pairs of lower-level edge detectors spanning a 60 degree angle. Like the edge detectors themselves, the angle detectors must be replicated at every location across the visual field, where they are also replicated at every possible orientation, and wired to the appropriate pair of edge detector cells. There are several ways to proceed from this point, but all of them are ugly. We could now posit "triangle detectors" tuned to respond to the presence of three "angle features" in a triangular configuration. These "triangle detectors" would also have to be replicated at every location across the visual field, at every orientation, and through a range of spatial scales, so as to be able to detect triangles independent of their rotation, translation, and scale. We could then equip each of these innumerable triangle detectors with the three nodes of Palmer's circuit to perform the competition between perceptual interpretations. If the reviewers do not find this architecture already completely implausible, consider the problem of generalizing the model to detect other types of triangles besides equilateral triangles, or other shapes such as squares or rectangles, each of which would require a whole different combinatorial set of feature detectors for each different shape!

There are neural network models out there which address lower level visual processing in Gestalt terms, for example Grossberg & Mingolla (1985, 1987) and Zucker et al. (1989). But these models themselves run headlong into the combinatorial problem as soon as they dare to tread beyond simple collinear completion. Zucker et al. (1989) posit curvature detectors at every location, orientation, and through a range of curvatures across the visual field. Grossberg & Mingolla (1987) briefly court with the idea of cells with receptive fields configured to respond to right-angled corners in the stimulus. But no mention is made of the combinatorial explosion hidden in that pandora's box, because explicit curvature or corner detectors suggest also detectors for other detectable features, such as acute and obtuse angle detectors, not to mention detectors tuned to vertex types composed of more than two edges, for example "T" or "Y" or "X" vertex detectors. For each of those specialized detectors would also have to be replicated at every location, orientation, and through a range of spatial scales across the visual field. Note that this is a problem not only with "feature detector" or "grandmother cell" models of visual representation, for the models of Grossberg & Mingolla, and of Zucker et al. are specifically dynamic neural network models, i.e. models that employ dynamic patterns of activation across the neural substrate to encode perceptual structure. But all those different receptive field types are still required just to control or channel the patterns of activation required for the functionality of the model, as I explain in detail in Lehar (2001). And the Gestalt Bubble model extends the required functionality into three dimensions, requiring three- dimensional volumetric receptive fields replicated at every location in three dimensions, and at every orientation in three dimensions and through a range of spatial scales.

I have explained elsewhere ( Lehar 1999, 2001) that the Achilles heel of neural network theory lies in the principle by which it encodes spatial structure, i.e. the neural receptive field that is anchored to the tissue of the brain. For the receptive field is no different than a template theory, a concept whose limitations are well known. And yet this idea is so deeply entrenched in contemporary neuroscience that it will take a profound paradigmatic revolution to uproot it.

But it is impossible to prove a negative- plausibility arguments are necessarily based on intuitive appeal, or on the perceived promise (or lack of it!) of a theoretical approach which has not yet been fully demonstrated. So I do not expect the reviewers to be convinced by this plausibility argument, because the plausibility issue cannot be resolved definitively by argument and evidence alone. And that is why I felt that a discussion of the limitations of neural network theory would only distract from the principal message of the paper, which is not on the limitations of the older paradigm, but on the promise of the new one.

To conclude, let us reiterate that we think this is an insightful and valuable paper. We look forward to seeing it in print.

I would like to see how these reviewers review a paper they do not like!


Atkins K. (1996) Lost the Plot? Reconstructing Dennett's Multiple Drafts Theory of Consciousness. Mind & Language 11 1-43.

Grossberg, Stephen, & Mingolla, Ennio (1985). Neural Dynamics of Form Perception: Boundary Completion, Illusory Figures, and Neon Color Spreading. Psychological Review, 92, 173-211.

Grossberg, Stephen, & Mingolla, Ennio (1987). Neural Dynamics of Surface Perception: Boundary Webs, Illuminants, and Shape-from-Shading.. Computer Vision, Graphics and Image Processing, 37, 116-165.

Grossberg, Stephen, & Todorovic, Dejan (1988). Neural Dynamics of 1-D and 2-D Brightness Perception: A Unified Model of Classical and Recent Phenomena" Perception and Psychophysics 43, 241-277.

Köhler W. (1924) Die Physischen Gestalten in Ruhe und im stationären Zustand: Eine naturphilosophische Untersuchung. Erlangen: Verlag der Philosophichen Akademie.

Lehar S. (1999) "Harmonic Resonance Theory: an Alternative to the `Neuron Doctrine' Paradigm of Neurocomputation to Address Gestalt properties of perception." Rejected Psychological Review November 1999. Resubmitted to Behavioral & Brain Sciences- not accepted for review because only one paper allowed per customer at a time (!) Available at

Lehar S. (2001) "Directional Harmonic Theory: A Computational Gestalt Model to Account for Illusory Contour and Vertex Formation". Submitted Perception & Psychophysics, August 2001. Also available at

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Palmer S. E. (1990) Modern Theories of Gestalt Perception. Mind & Language 5 (4) 289-323)

Zucker, S. W., Dobbins, A., & Iverson, L. (1989). Two Stages Of Curve Detection Suggest Two Styles Of Visual Computation. Neural Computation, 1, 68-81