“Is the Incorporation of Exotic Mathematics Necessary for a Solution of the Mind-Brain Problem?” (Whence comes Virtual Reality -As MS Word Document) (In Pdf) (NEW 8-16-08)

(This is a new and, I feel, an important addition to my ideas. It is not completed as yet, but I think the substance is there already. I think it will make it finally possible to understand my perspective and foundations based in recent developments in mathematics.)

"Virtual Reality, (Consciousness Really Explained)": MS Full Text - Word 7.0
Free Download (~800 Kbytes) (Original MS Word version) I suggest you use MS Word's "view document map" option to stay organized.

· "Virtual Reality, (Consciousness Really Explained)": MS Full Text -PDF

· Free Download (~800 Kbytes)

· Note: I am not offering an HTML version of the MS as it is impossible to preserve footnotes in that format and those are an integral part of my discussion.

Online Papers: Note: These papers are an ongoing project to expand, simplify and reformulate the major themes of my book, (available in its entirety and original form below). As such, existing papers are subject to ongoing revision, and new papers will be added when circumstances permit.

1. INTRO: The Mind-Brain Problem: An Introduction for Beginners [HTML]    (VIEW AS PDF)    (Recommended) NEW

                         An overview - not necessarily only for beginners. There are some interesting new ideas here!

2. YWHY: Mind: the Argument from Evolutionary Biology, ( Virtual Reality -A Working Model) [HTML] (VIEW AS PDF)

NEWLY REVISED AND EXPANDED (1-29-03), REVISED 1-05

***If you read nothing else on this page, please read this paper.
I believe it is the first baby step towards a scientific comprehension of
consciousness and it is the keyway to the rest of my proposed
solution of the mind-brain problem.***

This is an expansion and refinement of the first chapter of my book, (accessible below).

3. HOW: A Shortcut to the Problem: Consciousness per se ! [HTML] (Recommended) (VIEW AS PDF)

(The Logical Problem)

Note: This and the paper immediately preceding it are the two most crucial papers on this site, (other than the book itself). They define two
very different paradigms which, when combined, identify my proposal.

This is an expansion and refinement of the second chapter of my book, (accessible below).

(Adobe PDF reader 7.0.8) (free from Adobe )

Summary: See “In a Nutshell” below

The Book:

Precis, ("20 Minutes and a Blackboard") [HTML] (Recommended)
A Few Graphical Illustrations, ( PDF hyperlinks)

Outline of Argument - (i.e. Abstract. Recommended for Philosophers only!) [HTML]
(Most others would probably do better by starting with the Precis, and then the two online papers (above) which correspond to Chapters 1 and 2 of the Book respectively. From there you had best go to the end of chapter 2 and go on in the book.
The link at the top of the page is the original book, (1995), and embodies my original conception. I have not had the time nor the energy to revise it. The "Online Papers" listed above represent substantial and important expansions to the concept and constitute a sort of ongoing revision. P.S. I am currently working on a second edition. We will see how it goes.

Table of Contents, (Book):   (all sections in PDF format).
             (Note: Except for the highlighted, hyperlinked listings, this is "list only".    The former will need Acrobat Reader (c), (Adobe PDF reader), free-linked just above.
            The full MS is available above.

Introduction	4
Preface to Chapter 1, (on Realism as a Non-representative Model)	12
Chapter 1. Why? The Biological Problem: Part One	18
Preface to Chapter 2: the Logical Problem -and Realism Again	37
Chapter 2. How? The Logical Problem of Consciousness	48
Introduction to Chapters 3,4 and 5, (Towards a Resolution of the Paradox)	81
Chapter 3. Biology Part II: Towards the Where and the What? (Maturana)	84
Preface to Chapter 4	112
Chapter 4: Cognition and Experience: Quine and Cassirer	113
Preface to Chapter 5, (the Final Step)	149
Chapter 5: What? The Substance of Mind	150
Chapter 6: Conclusions and Opinions	156
Chapter 7: Epilogue	161
Appendix A, (Information and Representation)	165
Appendix B, (Isomorphism and Representation)	170
Appendix C, (Mind-Body and Artificial Intelligence: Hubert Dreyfus)	173
Appendix D: (Roger Penrose)	183
Appendix E: Dogmatic Materialism and Reality	187
Appendix F: Dennett and "the Color Phi"	190
Appendix G: An Outline of the Semantic Argument, (for Philosophers)	198
Appendix H: Extended Abstract	205
Afterward: Lakoff, Edelman, and "Hierarchy"	208
Appendix I: A Few Graphical Illustrations	233
Appendix J: An Elaboration of the Discussion of Chapter 1	237
Bibliography	243

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IN A NUTSHELL:

(1) From the physicalist perspective, what I propose is that mind is specifically a function of the organization of behavior, not a function of knowledge. Loosely stated, I propose that the brain/mind is the evolutionary result (by a multicellular organism) of an optimization process -the self-organized evolutionary optimization of blind behavior per se. In that process, our naive physical "objects" are non-representative, purely behavioral artifacts, but stable ones. (This, though biologically plausible, is a very radical hypothesis, but I believe it is the only viable scientific pathway to the solution of the other leg of the problem.)

These artifacts/"objects" are re-used in the "intentional arc", (Merleau-Ponty), to test our (behavioral) hypotheses -i.e. scientific and non-scientific. They are the ground for the whole of cognition. But these artifacts, (our naive objects), need not correlate hierarchically to absolute reality. (see W.J. Freeman for instance). It is necessary only that they be locked into the re-entrant loop between action and perception which passes we know not where. (Note how closely this perspective of “circular causality” fits with modern quantum theory -i.e. in the Schroedinger equation vis a vis "measurement"!

“But there is something very odd about the relation between the time-evolved quantum state’, (the Schroedinger equation), “and the actual behaviour of the physical world that is observed to take place. From time to time –whenever we consider that a ‘measurement’ has occurred – we must discard the quantum state that we have been laboriously evolving, and use it only to compute the various probabilities that the state will ’jump’ to one or another of a set of new possible states.” Penrose, 1989, pps. 226-227) But each new instance of a measurement causes yet another “loop”! The mind is a probability machine. It must countenance each “measurement” against our biologically innate object/artifacts and then recompute its overall picture. This is what cognition is.

I maintain that our mental “objects” are the evolutionary yardstick we carry. They function to crystallize and organize our input, and to crystallize and organize our output. But they must be maintained! I argue that they are organizational artifacts only. This is the answer to the question of how a non-hierarchical mapping, (e.g. Walter Freeman's chaotic dispersive mapping, or Edelman's non-topological "global mapping"), could function in cognition. I think it also gives a very pointed clue to Penrose’s problem.

"In particular, Maurice Merleau-Ponty in "The Phenomenology of Perception" [2] conceived of perception" [itself] "as the outcome of the "intentional arc", by which experience derives from the intentional actions of individuals that control sensory input and perception. Action into the world with reaction that changes the self is indivisible in reality, and must be analyzed in terms of "circular causality" as distinct from the linear causality of events as commonly perceived and analyzed in the physical world." W.J. Freeman, 1997 {22}

This thesis supplies the perspective of biology and the brain. It is our very own "cave of shadows", (Plato), -but it need not even be projective! I propose that it is the evolutionary result of a self-organized and virtual optimization of pure response. It is a GUI, (graphic user interface), rather than a “shadow”. Our "objects" are deep metaphors of process, they are not objects, (even indirectly), of representation.

(2) Mind as the functional organization of behavior gives us the first viable answers to the other profound questions of mind. It gives answers to the "homunculus" problem, to the "Cartesian theatre" problem, to the problem of "meaning", and to Leibniz's pentultimately profound question: how can the one know the many? These answers are found in the specifically operative application of David Hilbert's mathematical thesis of "implicit definition". Implicit definition allows an operative knowledge specifically of functioning itself, (sans a homunculus): it does not allow "representative knowledge". But this is "knowing" in all the crucial aspects we need! This is the perspective of "mind" itself and constitutes my second and central hypothesis. We can know our "objects" -if, (and only if), they are specifically (and purely) operative objects! This is the whole sense of Hilbert’s sally. Mathematics has already solved this problem!

3) From there, my thesis gets harder, but justifiably so, I think. Employing Ernst Cassirer's "Theory of Symbolic Forms", I argue a case of ontic indeterminism as a legitimate extension of Kant's work, and propose that this is the only plausible answer for what it is that we must consider ourselves, (finally, that is, scientifically) -as purely biological organisms. Organisms, (aka mechanisms), do not know, organisms do -organisms are "triggered", (after Maturana)! Or rather, the only "knowing" of which we are capable is an operative knowing! Ontology is, and must always be, an indeterminate.

I believe the very act of the presentation of any adequate solution to this problem is probably the hardest (technical) writing problem that has ever existed. There are so many preconceptions and prejudices, so many "prior certainties", so much confusion over even the basic beginnings, that it is almost impossible -and the resulting emotional reactions sometimes actually emotionally violent. There is also, I feel on the other hand, a built-in biological prejudice against a real answer. (Absolute dedication to the innate algorithm is clearly biologically essential.) I need, (and anyone with a similar case needs), active participation from my, (his), reader -and the realization of the necessity for a bravery to believe differently. The problem demands it. My book states my basic case, but there are crucial later advancements in my online papers, A Very Different Kind of Model: Mind, The Argument from Evolutionary Biology , and A Shortcut to the Problem: Consciousness per se ! (Chapter 3, Chapter 4, and Chapter 5 taken together contain my finished answer.) I will ask that you examine my whole case before rendering a judgement. I start out with extreme abstractness, but reach very concrete and specific answers. I think it is the shortest and easiest path between this profound problem and its solution.

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Dogmatic Materialism’s perspective on the Mind-Brain problem:

I think that most of the force of the materialist argument lies in the “bragging mode”, (i.e. “Put up or shut up!”), rather than in logical argument! The argument for this particular viewpoint on the subject of mind, i.e. the materialist viewpoint, is based on continued and crushing demonstration and new and important confirmations. By this, I mean that materialists can point to the fact that at every moment, new confirmations of their fundamental thesis arise -from new PET scan procedures to new antibiotics, to the discovery of new atomic particles – or to seeing your own heart during a sonogram -and an integration of just about everything in between. It goes on and on and is eminently successful –and they expect it to stay that way. They can and do retort to any argument by demonstration, not primarily by a resort to logic. Their perspective is so “perfect” that logic is largely irrelevant! I tried to make this point in my book. (There are holes in their position –mainly in what they will not look at—see Gleich, Van Fraasen, etc.)

It seems to be largely overlooked, however, that it is only by the ongoing and progressive change of the very terms, the concepts at the very bottom of their conception, (by changing the rules of the game), that it sustains its viability. Materialists would probably answer that the reductions are hierarchical, each embedding and preserving the prior conception. But does this really match what has actually happened? What could Galilean relativity, (even ignoring the harder case of Einsteinian relativity), have in common with the direct acceptance of things as and where they are –even considering the aspect of scale. What could quantum theory have to do with such a view of "things"? What is it that ultimately exists for these deepest theories of materialism? Answer: purely probabilistic particles in a purely probabilistic “space”, (the Schroedinger equation), and purely relativistic space itself, (not an aether!).

At this point I can only argue with them logically, but at some point, I hope to be able to argue with them on their own cherished ground -i.e. in terms of results and new "toys". The one place where I think their theory actually fails has always been at the center of my attention -a theory of the mind. How can a spatially and temporally discreet process, (which is the essence of materialism), produce a unified mind. Nowhere in that scenario is there room for the most important qualities we associate with consciousness – i.e. “knowing”, “the Cartesian theater”, …… For these are what lays at the foundations of “mind” in the sense we normally mean by the word. Dennett says they are impossible within materialism. The only choice that remains then is an antiscientific dualism which is little more than wishful thinking. How can a scientist tolerate such an inconsistent pluralism?

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In the early days of any science, art is as important as calculation. This is because conception must occur before calculation or confirmation are even possible. Without the beginnings in a plausible conception, there is nothing to calculate, nothing to confirm. I believe we are in the very early days of the science of the mind. I believe we are in a position in regards to the mind-brain problem comparable to that of scientists in the early Copernican era regarding the problems of physics and cosmology. There was no viable conception at that time.

Copernicus reoriented the universe from the model of Ptolemy, and, as his contemporaries could clearly see, it resulted in a profound simplification of astronomical calculations. But consider the dilemmas this reorientation imposed on the rest of the science, (and on the scientists), of the time. What were its implications for the physicists’ understanding of ordinary motion, for instance? Was it falsifiable? Was it even comprehensible? (See Thomas Kuhn quoting Copernicus himself on this issue. "The Copernican Revolution", Kuhn, e.g. pps: 150-151).

The physics of the time was Aristotelian, founded and appropriate in the worldview of Ptolemy. Man stood at the center of an absolute, spatial universe. Ordinary motion was absolute and rectilinear, and gravity was trivial, (things simply found their natural level as regards the center of the Earth). With Copernicus however, mankind supposedly rode a corkscrew through space. Why did rocks therefore describe their simple paths when hurled? Why was it not an impossibly difficult task to simply tie one’s shoe in this purported cosmological dance? Within the Aristotelian physics of the time, and under the Copernican hypothesis, even the laws of simple motion should be different on the face of the moon than here –or there –or anywhere. That is, they should be different, (under geometric translation), if, in fact, they were universally translatable at all. (The curve described by a thrown rock on the moon, (assuming Aristotelian physics), ought to obey the dynamic laws of its twin on earth, but this would require an accounting of the motion of the moon itself – hence its path would, in fact, be a corkscrew for an astronaut there.) This situation is easily visualized using another of Kuhn's examples -i.e. the mathematical equivalency between the Copernican and the (earth centered) Tychonian cosmological models. Kuhn argues very lucidly that a purely mechanical model of the one can be turned into a model of the other by simply attaching the earth to the model's base rather than the sun -i.e. it is an exact mathematical "transformation"! All relationships necessarily translate exactly because of the mechanical nature of the model!

It took Galileo’s further radical concept of the relativity of motion, (Galilean relativity), to fix this problem, (mostly), and lead to his beginnings of dynamic laws applicable to anywhere, anytime. It is an old calumny against the Pope, I believe, that he charged Galileo to accept Copernicus’ view as a calculational device only. This is generally accepted as a religious and solely selfish edict, (in support of the bible), but, in the context of the times, it might more correctly be understood as a necessity of the needs of the physics – the Aristotelian physics –then current. Galileo’s relativity was as radical a reorientation as was Copernicus’. It still “goes against the grain” somewhat, but –it works! It still had to go through multiple stages, (each a work of art) –through the conceptions of Kepler, et al, and finally through those of Newton before it became the “obvious truth” we accept today. It took two centuries before Copernican theory became viable.

The situation on the mind-brain problem today reminds me very strongly of James Gleich's description of the beginnings of "Chaos Theory", ("Chaos", James Gleich, pps. 36-37):

"Then there are revolutions. A new science arises out of one that has reached a dead end. Often a revolution has an interdisciplinary character - its central discoveries often come from people straying outside the normal bounds of their specialties. The problems that obsess these theorists are not recognized as legitimate lines of inquiry. Thesis proposals are turned down or articles are refused publication.....Every scientist who turned to chaos early had a story to tell of discouragement or open hostility. Graduate students were warned that their careers could be jeopardized if they wrote theses in an untested discipline....Some journals established unwritten rules against submissions on chaos....

New hopes, new styles, and, most important, a new way of seeing. Revolutions do not come piecemeal. One account of nature replaces another. Old problems are seen in a new light, and other problems are recognized for the first time. Something takes place that resembles a whole industry retooling for new production. In Kuhn's words, 'It is rather as if the professional community had been suddenly transported to another planet where familiar objects are seen in a different light and are joined by unfamiliar ones as well.' "

But isn't the latter just a reiteration of Kant's famous words?

"If in a new science which is wholly isolated and unique in its kind, we started with the prejudice that we can judge of things by means of alleged knowledge previously acquired -though this is precisely what has first to be called in question -we should only fancy we saw everywhere what we had already known, because the expressions have a similar sound. But everything would appear utterly metamorphosed, senseless, and unintelligible, because we should have as a foundation our own thoughts, made by long habit a second nature, instead of the author's." (Kant, Prolegomena, p.10)

The point I am trying to make is that any radically new science must be given some breathing room. Radical ideas, deeply radical conceptions must advance on broad fronts, across multiple thinkers perhaps for centuries before they become fully adequate. The problem of the mind, (a “Newtonian physics” of the brain), I believe, is as far from us today as was the Newtonian physical world then from the Ptolemean and Aristotelian one Copernicus inherited. The crucial difficulty today is that there is not even the shadow of a conception of how a solution to the mind-brain problem might exist or even what it might be like! I know this sounds harsh, but I think it is the literal truth.

On the subject of my own conceptions, I stand with Kepler:

“Now, since the dawn eight months ago, and since a few days ago, when the full sun illuminated my wonderful speculations, nothing holds me back. I yield freely to the sacred frenzy; I dare frankly to confess that I have stolen the golden vessels of the Egyptians to build a tabernacle for my God far from the bounds of Egypt. If you pardon me, I shall rejoice; if you reproach me, I shall endure. The die is cast, and I am writing the book –to be read either now or by posterity, it matters not. It can wait a century for a reader, as God himself has waited six thousand years for a witness.” (Boorstin quoting Kepler in “The Discoverers”, Random House.)

I wish to present what I think is a valid beginning. Like Copernican cosmology, it does not yet have a “calculus”. Its justification for consideration, like his, is found in the radical simplification of the problem it provides. This is not to say that it will not generate a specific calculus ever however. Science does not guide itself solely by "Occam's Razor". It is closer to the process of creating a great symphony. Occam's razor is just the tip of the conceptual iceberg. My solution will require a “Galileo”, a “Kepler”, and a “Newton” -and they will be the true and everlasting heroes of our species. Each will have to combine art and science because each will have to generate new conceptions! There are shadows of such new beginnings now. Contemporary biologists, (e.g. Maturana, Edelman, Freeman...), are questioning the “Aristotelian” suppositions of their predecessors. Attempts at a “Galilean relativity” have been, (and are being), proposed, (Kant, Cassirer).

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No matter how we approach it, the most difficult part of the mind-brain problem is consciousness itself. But how do we start? How can we start? I think we must explain consciousness -that is to say that I think we absolutely must explain consciousness and not explain it away! But at the same time we must retain the perspective of materialism -also absolutely. These are the two basic prerequisites of realism and the ground we must stand upon. It is imperative that we must retain both of them. But how can we retain them both? How can we have our cake and eat it too? This is the essence of the mind-body problem. Barring the discovery of the "consciousness particle", (which I think will never happen), I think I have evolved the first viable answer compatible with science.

Long ago, I saw a connection with a long resolved, purely mathematical problem which seemed to show great promise for this problem of the brain as well. It was the purely mathematical and logical conception of "implicit definition" first conceived by the eminent mathematician David Hilbert over a century ago. (Hilbert is widely regarded as the most significant mathematician of the 20th century). "Implicit definition" defined what "objects" as objects are for mathematics, just as I propose that it also defines what objects are for the brain itself. It suggested a new possibility of self-knowledge, opened the first possibility of a "Cartesian theater", (Dennett) and it removed the need for a "homunculus" altogether. It also opened a genuine pathway to "knowing" for a biological organism. (Whatever could that mean for a mechanism?), All this and without the price that strict materialists demand of the problems. Implicit definition (as such) has fallen into disfavor today however and is viewed as a flawed conception. Mathematical "structuralism", a respected philosophy of current mathematics, seems to furnish and validate the same answer however. Mathematics is much richer conceptually than our current physical notions acknowledge -and it still remains our lodestone into the future.

In my book, I stated this perspective of implicit definition as my second hypothesis, (though first conceived) -as the basis for a solution to the problems of "mind" per se. For the sake of a linear and comprehensible presentation, however, I was forced to begin with a strictly materialist, physicalist description of brain function as I thought it would be required by my readers to take my central theme seriously. Let me state a caveat at the outset: the first two chapters of this book constitute a constructive reductio ad absurdum of the ordinary scientific view of the mind-brain relationship. Like the usual reductio arguments, they assume that which we will ultimately refute. Do not let them deter you if you are coming from a different perspective. …And yet they present what I believe are superior answers to the specific problems they address –i.e. the scientific perspective of the brain and the scientific perspective of the mind. The work will not be for nothing, however, as those conclusions are embodied in the perspective we will finally reach, albeit relativistically.

My biological perspective is itself also absolutely legitimate however. It furnishes the perspective required by my second and central assertion furthermore. Each of these perspectives logically requires the other, and their combined weight forces us into my third hypothesis which I advance as an actual solution to the mind-brain problem. The answer to the mind-brain problem lies in the expansion of epistemology beyond the mutual boundaries of materialism and dualism. This is a surprising, but, I believe, an absolutely necessary conclusion consistent with an intrinsic, (though relativized), Darwinian perspective. It is supported by the conclusions of Immanuel Kant and Ernst Cassirer, Gerald Edelman, Walter J. Freeman. It is also supported by the blatantly obvious confusion in the current dialogue.

As my first (physicalist/materialist) thesis, I proposed that mind is solely, (and only), the biological coordinator of primitive, profoundly complex, and blind metacellular process -pure and simple! It is an optimized purely organizational scheme embodied in a "tactile" graphic user interface, (GUI). Our "objects" are organizational objects only, metaphors of behavioral process! This is a legitimate and pure biological perspective, though radical, and is absolutely consistent with a Darwinian perspective. But this aspect of my hypothesis is not good enough for the whole of the problem, is it?

My second (mental) thesis of implicit definition resolves the problem from the other end. It resolves the perplexities of mind from the standpoint of implicit logic. Utilizing Hilbert's conception in a mechanistic context, our mental objects are purely logical objects, implicitly defined by the structure of the brain. As such, (following Hilbert), we are actually allowed to know them. All the aspects of the "mental" perspective are legitimate here to include the "Cartesian theatre"! (There is no requirement of a homunculus, however!) But these are not representative objects! It is in the conception of "representation" that the problem arises. Representative objects are not the right sort of objects to fit within mathematics qua mathematics. Rather, our objects are logical objects implicit in the evolutionary logical calculus of the brain, and that, echoing Darwin, is concerned solely with an optimized operationality.

What I call "the concordance" argues that both of these hypotheses are compatible and synergistic. For modern science must consider logic itself as an evolutionary phenomenon and not as a gift from God. Logic therefore becomes “bio-logic”! My first and second hypotheses are therefore compatible and synergistic. My book: "Virtual Reality: Consciousness Really Explained" moves on then to give a whole answer. There are other, equally necessary and equally valid perspectives, in their sum absolutely crucial to the problem as well. The specific problem of consciousness is the hardest problem and the one that ties it all together.

Contrary to the way it might appear, this problem is important for all of us -it is not just philosophy. I bring a message of hope -hope for real minds, real values, real meaning -and, ultimately, for a real decency in this strange tortured animal called "man". I think this problem embodies the real "Rosetta Stone", urgently necessary to our continued survival as a race. It will take real work, however to get there -I seek collaborators with courage enough to gamble with radical ideas.

But whatever made you think that a solution to the mind-brain problem would be simple? If it were so, you would not be reading this at all -it would be a finished problem. The principle of parsimony is applicable only given the prior equivalence of explanatory power and that is precisely the problem in the current dialogue. The standard proposed solutions just don't work -as the continuing broad and variegated opinions on even the basic statement of the problem clearly demonstrate.

RESPONSE:

If you have constructive comments or suggestions- or questions, please email me at jiglowitz@rcsis.com . (Please indicate in the header that yours is a response to the Web Page or it will probably be deleted, unread as "spam" .) I am interested in creating a realistic and scientifically productive dialogue on the real issues of this problem leading to better theoretical models of the brain and the mind. I especially court biologists and mathematicians. Philosophy, as philosophy , is not my purpose.

Jerry Iglowitz
October 20, 1998

Last Update: Sep 7, 2007

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