Le 17-août-06, à 17:30, 1Z a écrit :

> The argument has to assume the necessary existence of the UD.
> (If it is possible that the UD doesn't exist, it is possible
> that physics is emerging from semething else)
> It is difficult to see what would entail that  except Platonism.

I agree, but I put Arithmetical Realism (an extremely weak form of 
"platonism") inside the definition of comp (which is ambiguous 
without).  Comp = "yes doctor" + Church Thesis + AR. You can call it 
"classical computationalism".

Now, you could as well criticize String Theory for assuming the 
necessary existence of PI.
UD exists like PI exists, or like square root of two exists.

In the interview, "platonism" is translated into the (p or not p) 
axiom, with p restricted to a class of verifiable arithmetical 
propositions. (the so called Sigma1, one).

Logically I need no more than the idea that if you run a program, and 
if no asteroïd, big crunch or other contingent events like that occur, 
then the program will stop, or not stop. Arithmetical Realism is the 
acceptance that in case that damned asteroid kills me, this will not 
change the fact that the program will stop, or will not stop.

You can prove the existence of the UD in Robinson Arithmetic (cf the 
failed roadmap). You can make a non trivial part of the UDA reasoning 
in Peano Arithmetic.

Bruno

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


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