Bruno Marchal wrote:
> 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.
It doesn't. Anti-Platonists can do string theory.
String theorists aren't claiming anything exists
for purely mathematical reason; they are doing
physics, i.e. finding a mathematical
model for what is observed.
Physics makes explicitly existentially posits:
it says "suppose such-and-such a field
and particle exists", and then draws existential
conclusions, which can be tested empirically.
That is quite different from conjuring up existential conclusions
from non-existential premises.
> UD exists like PI exists, or like square root of two exists.
The questions is whether it exists like *I* exist.
If it doesn't, I cannot be generated by it!
> 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).
I very much doubt that the Platonism can be reduced to
a formal procedure without circularity.
> 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.
Matter can't be non-existent just because someone might one
day be able to run a UD programme
> 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.
It will not change the *truth*, no.
Matter can't be non-existent just because of
the abstract truth of the behaviour of the UD programme
> You can prove the existence of the UD in Robinson Arithmetic (cf the
> failed roadmap).
The mathematical existence. Leaving open the question
of how that relates to the kind of existence I have.
> You can make a non trivial part of the UDA reasoning
> in Peano Arithmetic.
Any mathematical argument, however sound, leaves
the existential question open. Mathematics
cannot prove what mathematical existence is.
Different mathematicians disagree about it,
and there debates ar caried outin the language of philosophy.
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