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 
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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