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.
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/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
