Bruno Marchal wrote:
> Le 07-oct.-06, à 16:48, 1Z a écrit :
>
> > That is obviously wrong. Formalists are not Platonists,
> > structuralists are not Platonists, Empiricists are not
> > Platonists.
>
>
> After Godel, even formalists are platonist about numbers.

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Of course not.
> If they say
> that they are formalist it means they are not platonist about things
> extending numbers like sets. Or it means they does not follows the
> mathematical news.
That is not how they describe themselves.
> Formalism at the level of numbers has been shown senseless. This is
> already clear in Dedekind, but provable in all details by using
> theorems by Skolem or Godel.
I think you are getting the Hilbertian programme, of mechanising
mathematics, confuse with formalism, which is a claim
about the meaning of mathematical propositions. Formalists
believe that mathematical propositions in general take
their meanings from systems of rules and defintions
in general . The discovery that particular systems have particular
limitations
does not destroy that claim.
> A strict formalist about natural numbers cannot even interpret the
> modus ponens rule and explains what formalism is.
> It is false to pretend (like we can heard sometimes) that Godel
> incompleteness has kill the formalist doctrine in mathematics, but it
> is correct to say that godel's incompleteness has kill the formalist
> doctrine in arithmetics.
>
> But I agree with David's yesterday post, you should should less quibble
> about terminology and try to understand the reasoning instead.
No-one can understand anyhting withiut clear definitions.
> That
> would provide much more help for settling the possible interpretation
> problems.
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
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