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
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.
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