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. 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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