Brent Meeker writes (quoting Peter Jones and SP):
> >>Arithemtical Platonism is the belief that mathematical
> >>structures *exist* independently of you,
> >>not just that they are true independently of you.
> >
> >
> > What's the difference?
> >
> > Stathis Papaioannou
>
> You could regard the theorems of arithmetic as just being relative to Peano's
> axioms: "1+1=2 assuming Peano" Somewhat as Bruno presents his theorems as
> relative to the "axiom" of COMP.
>
> Brent Meeker
Even if you say that, there is still a sense in which arithmetic is independent of the
real world. The same can be said of Euclidian geometry: it follows from Euclid's axioms
*despite* the fact that real space is not Euclidian. The fact that real space is not
Euclidian means that Euclidian geometry does not describe the real world, not that
it is false or non-existent.
Stathis Papaioannou
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Received on Fri Aug 18 2006 - 07:30:37 PDT