Le 17-août-06, à 16:41, 1Z a écrit :
> Arithemtical Platonism is the belief that mathematical
> structures *exist* independently of you,
> not just that they are true independently of you.
What is the difference between ""the proposition "it exists a prime
number" is true independently of me", and the proposition "it exists a
prime number (independently of me)"?
I can see a nuance, and that is why I prefer to use the expression "
Arithmetical Realism (AR)" (and then I always define what I mean by
that) instead of "platonism" (which I prefer to reserve when Plato is
actually mentionned, like with the Theatetical definition of
knowledge).
Of course some people use some other term, and I just try not to bore
people with terminological remark. You can take AR negatively as the
statement : "arithmetical truth" is not a human construction or
convention. It is not even a lobian machine invention, because I need
numbers to define what is a digital machine. Perhaps you should focus
on the reasoning to see how the expression are used, instead on
focusing on terminological issues, if I may suggest.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Aug 17 2006 - 11:57:37 PDT