Stathis Papaioannou wrote:
> 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
But the fact that a theorem is true relative to some axioms doesn't make it true
or existent. Some mathematicians I know regard it as a game. Is true that a
bishop can only move diagonally? It is relative to chess. Does chess exist?
It does in our heads. But without us it wouldn't.
Brent Meeker
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Received on Fri Aug 18 2006 - 13:25:05 PDT