On 22 Jan 2010, at 20:52, Brent Meeker wrote:

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Bruno Marchal wrote:Hi John, On 21 Jan 2010, at 22:19, John Mikes wrote:Dear Bruno,you took extra pain to describe (in your vocabulary) what I standfor (using MY vocabulary).-------------------------------------------------On Thu, Jan 21, 2010 at 2:17 PM, Bruno Marchal <marc...@ulb.ac.be <mailto:marc...@ulb.ac.be>> wrote:John, What makes you think that a brain is something material? I mean /primitively/ material. JM:I refer to 'matter' as a historically developed */figment/* asused in "physical worldview" (I think in parentheses _by both ofus_). Nothing (materially) PRIMITIVE, it is an 'explanation' ofpoorly understood and received observations at the various levelsof the evolving human mindset (~actual enriching epistemiccognitive inventory and the pertinent (at that level) applicationof relational changing (=function??).I think we agree on that.You know (I hope) that I pretend (at least) to have shown that *IF* we are machine, and thus if our (generalized) brain is a machine, (for example: we say "yes" to the doctor) *THEN* "we" are immaterial, and eventually matter itself emerges from the statistical interference of computations. The term computation is taken in its original mathematical (and unphysical, immaterial) sense (of Church, Turing, Post, ...) Remember that "comp" is the belief (axiom, theory, hypothesis, faith) that we can survive with an artificial digital (a priori primitively material for the aristotelian) brain. Then I show that if we believe furthemore that matter is primitive, like 99,999%of the Aristotelians, we get a contradiction. JM:"you have shown..." - your *_DESCRIPTION_ of comp* and I do notthrow out my belief to accept yours;"Mine" is just the usual one, make enough pecise to prove theoremsfrom it. But it is really just Descartes, update with the discoveryof the universal machine.first of all I carry a close, but different term for 'machine'because IMO numbers are not "god-made" primitives.I can prove that no theory can prove the existence of the naturalnumbers without postulating them (or equivalent things).They are the inventions in human speculation (cf: D. Bohm)Of course I differ here. It is the notion of "humans" which is aspeculation by the numbers/machines.Yet above you note that numbers can only be postulated. Isn't thisan example of misplacing the concrete? You point out thatarithmetic is not only almost all unknown but is, ex hypothesi,unknowable.

`What I said is related to the failure of logicism. Some people thought`

`that we could derive the existence of natural numbers from logic or`

`very weak theory. But this can be shown impossible. So any theory in`

`which we have terms denoting the natural numbers contains arithmetic`

`as a sub-theory. Anyone wanting the natural numbers in its reality,`

`like a wave physicist who would desire interferences processes, will`

`have to explicitly or implicitly assumes arithmetic.`

`Now, having postulated the natural numbers with addition and`

`multiplication, they organized themselves, independently of our`

`whishes, in a way which escapes *any* attempt of *complete*`

`unification. They defeat all our theories, in a sense. Once we`

`postulate them, they get a life of their own. To understand them, we`

`have literally no choice, in general, than to observe them and infer`

`laws.`

`We can prove that they have definite behaviors, but we can prove`

`(assuming mechanism) that we cannot predict them, in general.`

ISTM that can be read as a reductio against the reality ofarithmetic.

`On the contrary. It shows that arithmetical reality kicks back. We may`

`also know greater and greater portion of it. We may discover new`

`interesting properties, and we progress indeed since a long time. From`

`Diophantus to Matiyasevitch, to mention a beautiful line.`

`Are you alluding to fictionalism? Do you defend the idea that "3 is`

`prime" is a false proposition?`

I have no real clue of what that could seriously mean.

`Of course I would never expect that someone who doesn't believe that 3`

`is prime can say anything about the consequence of DIGITAL mechanism.`

`Such a move cut the uda (and the auda) at their roots, and everything`

`becomes infinitely mysterious. Frankly I would not ask him to compute`

`my taxes either.`

So why not suppose that the natural numbers are just a model ofperceptual counting; and their potential infinity is a convenientfiction whereby we avoid having to worry about where we might runout of numbers to count with?

`You can do that. But assuming you are not fictionalist, if you say`

`that the infinity of natural numbers is a fiction, you are lead, ITSM,`

`to ultrafinitism. With fictionalism, I think that you can say "yes" to`

`the doctor, and reject the reversal consequences. This leads to a`

`matter problem, a mind problem, and the usual mind/matter problem. I`

`would take this as a defect of fictionalism.`

`Brent, I am not saying that ultrafinitism and fictionalism are false.`

`I am just saying that IF you say yes to your doctor's proposal to`

`substitute the brain for a computer, and this with a reasonable`

`understanding of what a computer is (and this asks for a minimal`

`amount of arithmetical realism) then the laws of physics are`

`necessarily a consequence of the (usual, recursive) definition of`

`addition and multiplication. Indeed it is the global coupling`

`consciousness/realities which emerges from + and * (and classical`

`logic). (or from K and S and the combinators rules, + equality rules`

`(this is much less)).`

`A sentence like "naturals numbers are just a model of perceptual`

`counting" already assumes (postulates) arithmetic. And with digital`

`mechanism you can explain why universal number can use natural numbers`

`as "model of their perceptual counting".`

`You should not confuse the numbers as thought by the philosophical`

`humans (what are they? does they exists?) with the numbers as used by`

`mathematicians, physicists or neurophysiologists, like in "this`

`flatworm has a brain constituted by 2 * 39 neurons" or "all positive`

`integers can be written as the sum of *four* integers squares.`

`(Then the number takes another dimension once you say "yes" to the`

`doctor, because in that case, relatively to the (quantum) environment,`

`you say "yes", not for a "model", but because you bet the doctor will`

`put in your skull the actual thing "you", yet through "other matter",`

`and all what counts is that he put the right number, relatively to the`

`current environment. That other dimension is somehow the object of all`

`our discussions).`

`May be I can ask you a question, which I asked to Peter Jones, and`

`which is this. Do you see that NON-COMP + arithmetical realism entails`

`the existence of a realm full of zombies? Yet, like in the empty wave`

`of the Bohmians, those zombie acts and talk like you and me, have`

`thought processes, and asks themselves about mechanism, consciousness,`

`realities, and what constitute their environment (matter), and all`

`this in a genuine way, as defined by the logics of (correct/`

`consistent) (relative) self-references. With NON-COMP, I would be`

`tended toward fictionalism myself, because I would wish those zombies`

`could not exist.`

`In a sense, there *exist* local zombies, because from their own first`

`person points of view, they belong to the projection of the set of all`

`computations. Their first person indeterminacy bears on the whole`

`computational space, and what is observable in any stable way can only`

`belong to the border of that space. This is really just a consequence`

`of the impossibility to be aware of the UD delays, or of where "we"`

`are in (Sigma_1)-reality, or comp-reality. The comp supervenience`

`thesis is hard to explain without digging in the details, but`

`consciousness, our consciousness, is related to a big infinite cloud`

`of intricate number relations. The "identity thesis" is partially`

`justified only in a very relative and local way. It is a bit like the`

`appearance of a collapse in the QM without collapse.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.