On 01 Sep 2009, at 18:46, Flammarion wrote:

> On 1 Sep, 17:29, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> By comp, mainly by Church thesis only, you (in the third person  
>> sense)
>> are implemented in the mathematical UD. OK?
> The mathemaitcal UD doesn't exist.

Do you agree that it exists in the mathematical sense? And that all  
the description of all possible machines going through your current  
comp states at all your substitution levels, which exist by digital  
mechanism, are generated
in that mathematical structure?

Here "generated" has been defined using first order logic language  
together with the symbole 0, s, +, * and parentheses. It is the level  
0 if you want. With comp *any* universal system can be used, the  
problem is to justifies the "inning quantum computations". With Church  
thesis I can use elementary arithmetic to implement the computations,  
notably the universal dovetailer, which really correspond to the  
finite and infinite proofs of the Sigma_1 sentences (the true and the  
false). Then you *can* interpret formally all the richer machines'  
talk simulated by that UD. Their are richer because they are   
"believing" (and thus using this in their reasoning process) the  
induction axioms, like Peano Arithmetic. That gives the epistemology,  
the physical qualia, the physical quanta, the universal knower, the  
universal doubter, and the "one" which is just arithmetical truth. It  
does not yet gives the measure, but it gives the logic pertaining on  
that measure.

Do you know modal logic? Are you aware of Solovay double completeness  
G/G* theorem on the logic of self-reference?

I have a question, also, how can you be formalist, and make an  
ontological commitment?  How can you believe in a notion of  
"ontological existence"? What does that mean for a formalist? Can you  
give me a formal definition of "ontological existence"?

I confess to you, also, that I am not sure that Church thesis, can  
make sense for a formalist. Funnily, CT is a chance for the formalisms  
and the machines, but the price (the chance?) is the impossibility to  
describe completely and formally the truth on formalism and mechanism.  
It is a chance for the machine, it preserves them against closed  
formalism or reductionism.
This makes us more ignorant (assuming comp, which is just a more  
precise version than usual CTM, if you want a nuance).

I must say that I begin to ask myself if it is sane for me to continue  
to discuss with someone who goes through the loop:

seven does not exist physically
seven does not exist ontologically
seven does not exist at all
seven does not exist
seven does not exist physically

You are free to restrict my use of existence as the use of the  
existential quantifier introduction rules of first order logic. If I  
prove to you "prime(s(s(s(0)))", I can deduce "Exprime(x)", in  
english: there is a prime number, or prime numbers exist. Physical  
existence is reduced to such formal existence, but the quantifier  
rules changes for respecting the observable modalities. Themselves can  
be motivated through your implication in the UDA thought experiences,  
or can be given by a literal arithmetical interpretation of  
Theaetetus' theories of knowledge.



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