Bruno Marchal wrote:

On 22 Jan 2010, at 20:52, Brent Meeker wrote: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/* as usedin "physical worldview" (I think in parentheses _by both of us_).Nothing (materially) PRIMITIVE, it is an 'explanation' of poorlyunderstood and received observations at the various levels of theevolving human mindset (~actual enriching epistemic cognitiveinventory and the pertinent (at that level) application ofrelational 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 that arithmeticis not only almost all unknown but is, ex hypothesi, unknowable.What I said is related to the failure of logicism. Some people thoughtthat we could derive the existence of natural numbers from logic orvery weak theory. But this can be shown impossible. So any theory inwhich we have terms denoting the natural numbers contains arithmeticas a sub-theory. Anyone wanting the natural numbers in its reality,like a wave physicist who would desire interferences processes, willhave to explicitly or implicitly assumes arithmetic.Now, having postulated the natural numbers with addition andmultiplication, they organized themselves, independently of ourwhishes, in a way which escapes *any* attempt of *complete*unification. They defeat all our theories, in a sense. Once wepostulate them, they get a life of their own. To understand them, wehave literally no choice, in general, than to observe them and inferlaws.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 of arithmetic.On the contrary. It shows that arithmetical reality kicks back. We mayalso know greater and greater portion of it. We may discover newinteresting properties, and we progress indeed since a long time. FromDiophantus to Matiyasevitch, to mention a beautiful line.Are you alluding to fictionalism? Do you defend the idea that "3 isprime" is a false proposition?

No, I just don't think it's truth implies the existence of "3".

I have no real clue of what that could seriously mean.Of course I would never expect that someone who doesn't believe that 3is prime can say anything about the consequence of DIGITAL mechanism.Such a move cut the uda (and the auda) at their roots, and everythingbecomes infinitely mysterious. Frankly I would not ask him to computemy 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 run outof numbers to count with?You can do that. But assuming you are not fictionalist, if you saythat the infinity of natural numbers is a fiction, you are lead, ITSM,to ultrafinitism.

`What's the difference between finitism and ultrafinitism? Doesn't`

`postulating the integers plus ZF also commit you to existence of the`

`whole hierarchy of infinite cardinals?`

With fictionalism, I think that you can say "yes" to the doctor, andreject the reversal consequences. This leads to a matter problem, amind problem, and the usual mind/matter problem. I would take this asa 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 tosubstitute the brain for a computer, and this with a reasonableunderstanding of what a computer is (and this asks for a minimalamount of arithmetical realism) then the laws of physics arenecessarily a consequence of the (usual, recursive) definition ofaddition and multiplication. Indeed it is the global couplingconsciousness/realities which emerges from + and * (and classicallogic). (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 perceptualcounting" already assumes (postulates) arithmetic. And with digitalmechanism you can explain why universal number can use natural numbersas "model of their perceptual counting".You should not confuse the numbers as thought by the philosophicalhumans (what are they? does they exists?) with the numbers as used bymathematicians, physicists or neurophysiologists, like in "thisflatworm has a brain constituted by 2 * 39 neurons" or "all positiveintegers can be written as the sum of *four* integers squares.(Then the number takes another dimension once you say "yes" to thedoctor, because in that case, relatively to the (quantum) environment,you say "yes", not for a "model", but because you bet the doctor willput in your skull the actual thing "you", yet through "other matter",and all what counts is that he put the right number, relatively to thecurrent environment. That other dimension is somehow the object of allour discussions).May be I can ask you a question, which I asked to Peter Jones, andwhich is this. Do you see that NON-COMP + arithmetical realism entailsthe existence of a realm full of zombies?

No, I don't see that.

Yet, like in the empty wave of the Bohmians, those zombie acts andtalk like you and me, have thought processes, and asks themselvesabout mechanism, consciousness, realities, and what constitute theirenvironment (matter), and all this in a genuine way, as defined by thelogics of (correct/consistent) (relative) self-references. WithNON-COMP, I would be tended toward fictionalism myself, because Iwould wish those zombies could not exist.

Such zombies seem like an incoherent concept to me.

In a sense, there *exist* local zombies, because from their own firstperson points of view, they belong to the projection of the set of allcomputations. Their first person indeterminacy bears on the wholecomputational space, and what is observable in any stable way can onlybelong to the border of that space.

How do you define the border of computational space?

This is really just a consequence of the impossibility to be aware ofthe UD delays, or of where "we" are in (Sigma_1)-reality, orcomp-reality. The comp supervenience thesis is hard to explain withoutdigging in the details, but consciousness, our consciousness, isrelated to a big infinite cloud of intricate number relations. The"identity thesis" is partially justified only in a very relative andlocal way. It is a bit like the appearance of a collapse in the QMwithout collapse.

`I don't find the multiple-worlds interpretation of QM very convincing`

`either. In conventional QM it implies that a single radioactive atom`

`causes a continuous splitting of the world. I suspect that real numbers`

`should not be taken seriously.`

Brent

Bruno http://iridia.ulb.ac.be/~marchal/

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