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.

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.

Jesse