On 04 Sep 2009, at 19:21, Flammarion wrote:

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> ... Bruno has been arguign that numbers
> exist because there are true mathematical statements asserting their
> existence. The counterargument is that "existence" in mathematical
> statements is merely metaphorical. That is what is being argued
> backwards
I have never said that numbers exists because there are true
mathematical statements asserting their existence.
I am just saying that in the comp theory, I have to assume that such
truth are not dependent of me, or of anything else. It is necessary to
even just enunciate Church thesis. A weakening of Church thesis is 'a
universal machine exists". In the usual mathematical sense, like with
the theorem asserting that 'prime numbers exists.
I just make explicit that elementary true arithmetical statements are
part of the theory. You are free to interpret them in a formlaistic
way, or in some realist way, or metaphorically. The reasoning does not
depend on the intepretation, except that locally you bet you can 'save
your relative state' in a digital backup, for UDA. And you don't need
really that for the 'interview' of the universal machine.
All theories in physics uses at least that arithmetical fragment. But
fermions and bosons becomes metaphor, with comp. May be very fertile
one. Like galaxies and brains.
Scientist does not commit themselves ontologically. They postulate
basic entities and relations in theories which are always
hypothetical. I am just honest making explicit my use of the non
constructive excluded middle in the arithmetical realm.
You get stuck at step zero by a bullet you are ntroducing yourself, I
'm afraid.
Bruno
http://iridia.ulb.ac.be/~marchal/
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