Le 07-oct.-06, à 16:48, 1Z a écrit :

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> That is obviously wrong. Formalists are not Platonists,
> structuralists are not Platonists, Empiricists are not
> Platonists.
After Godel, even formalists are platonist about numbers. 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.
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.
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. That
would provide much more help for settling the possible interpretation
problems.
Bruno
http://iridia.ulb.ac.be/~marchal/
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