Kory Heath wrote:

Thanks for the clarification. In this short discussion I've seen at least three conflicting ways that people use the term "Platonism":

1. Platonism == Mathematical Realism.
2. Platonism == The belief in Ideal Horses, which "real" horses only approximate.
3. Platonism == Non-constructivism.

Roger Penrose uses the word "mathematical Platonism" to describe his philosophy of math, which is clearer in that it obviously does not require believing in such a beast as the "Ideal Horse". As for the non-constructivism definition, is it possible to be a non-constructivist but not a mathematical realist? If not then these aren't really separate definitions.


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