On 09 Aug 2011, at 21:13, meekerdb wrote:



What more evidence would you need to believe mathematical objects exist?

I haven't seen any evidence yet. Mathematical objects are inventions of our minds dependent on language.

Are you not confusing human mathematical theories and the arithmetical reality, which does not depend on any language? The part of the brain treating numbers is quite different than the part handling the words. The twin prime conjecture seems to me independent of any language used to describe it.


They made be said to exist in Platonia or in some other way, but I think it is a confusion to suppose they exist in the sense of physical objects.


You are right, numbers certainly do not exist in the same sense as an electron or a chair or table.

Brent, I did reply to your remarks on the UDA, so I am not sure what I have to conclude? Are you thinking that we are infinite physical object? Computationalism has to be false to put sense of your reply. This is implicit in many remark that you did recently.

If we are machine, the "physical universe" is a mathematical sum on infinities of digital computations (in the sense of Church Turing Post: nothing physical there). So an electron is a much higher level cognitive object than a number.

Note that I do agree with you, and I insist, that physical existence and mathematical existence (if that means something) are *quite* different things. With comp mathematical existence is just arithmetical existence. It is Ex ... P(x) ...., with x in N. And physical existence is a high level inside construct, with inside cporresponding to the abstract sum operator given by modalities like BDp (the quantization of p) with a new box B given by Bp & Dp (with the old Beweisbar B of Gödel, and D = ~B~). So physical existence will be described by a modal expression of the form BD(Ex ... BD P(x) ...), which is quite different from Ex ... P(x) ...

If we are machine you have to add some magic in both mind and matter to save the mind-brain identity. OK?

If you are not OK with this, let me ask you again two questions which I do not remember clear answers for.

Let us say that a physical universe is *robust* if it executes a universal dovetailer. Let us call "physical ultrafinitism" the doctrine that there is a *primitive* and *non robust* physical universe.

Do you agree that UDA1-7 shows that either physical ultrafinitism is true or physics is a branch of theoretical computer science.

If you agree with this, and still believe that comp is true (I can survive with a digital brain/body/environment), it means that you disagree with the UDA step 8 (which eliminates the physical ultrafinitism move).

The only point in the step 8 (movie graph argument, MGA) which I think should be made more clear is that computationalism entails the 323- principle.

I recall for others what is the 323-principle:

323-principle: We assume comp. and the physical supervenience thesis (sup-phys). Suppose that a computer processes a particular computation C on which a particular experience E supervenes on (by sup-phys). We are told that during C, the computer does never use the register 323. The 323-principle asserts that consciousness will still supervene on C', which is the computation done by the same computer, in exactly the same condition than before except that the register 323 has been withdrawn.

If you agree that comp + sup-phys entails the 323 principle, step 8 of UDA becomes straightforward, and it is hard for me to believe than you still accept comp, and yet believe in some primary notion of physical existence. But your reply to Jason witnesses that you seem to believe in such a notion, so probably you believe that comp does not entail the 323-principle. This seems to me an attribution of a non Turing emulable role for the register 323 in the computation C. It leads also to attributing a physical role to something having no relevant, with respect to the computation C, physical activity at all. I don't see how I could still say "yes" to the digitalist doctor in virtue of having in my skull a machine doing the same computation as my brain at the correct substitution level.

This should also be taken into account in some post by Stathis, which I find not always enough clear, especially when he mentions the *behavior* of an entity. Does it means "all possible behaviors", or "one counterfactually correct behavior" or "particular behavior related to a particular computation"? Some human behavior (like sleeping-dreaming") can easily be emulated by machines which are so elementary that it makes no sense to attribute or associate any form of consciousness to them, at least in virtue of comp. I do agree with his conclusion in his conversation with Craig though, but they seems sometimes to rely on an identity thesis between particular work of a machine and possible consciousness.

Sorry for the probable hard work, but this is the crux of matter (elimination) :)

Bruno





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



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