Bruno Marchal wrote:
> Le 21-août-06, à 18:55, David Nyman a écrit :
>
> >
> >> I don't think Bruno and Stathis are arguing that numbers are
> >> neceesarily
> >> the only things that exist (although a standard Platonist might argue
> >> that
> >> that they are the only things that exist necessarily..)
> >
> > But aren't they claiming that numbers are the only things necessary
> > (together with the operations required for CT+YD, whatever they might
> > be) to account for *our* existence? If not, what else is required?
>
>
>
> Since the failure of logicism, by Godel's theorem, we can argue that
> numbers does not necessarily exist. Numbers does not come from logic
> alone. If you want them,

to exist

> you have to do a ontological commitment.

..and if you want to play with them as a formal
system, you don't.

> To
> believe, like all mathematicians, in the structure (N,+,*,0,1) is
> enough for that (actually to believe in (N,+,*,0,1) is too much, but I
> don't want to enter in the technical details before it is really
> necessary).
> 
> Bruno
> 
> 
> 
> 
> 
> 
> http://iridia.ulb.ac.be/~marchal/


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