`At 09:19 AM 6/30/2004, Bruno Marchal wrote:`

Also, you said that your are not platonist. Could you tell me how you understand

the proposition that the number seventeen is prime. (I want just be sure I understand

your own philosophical hypothesis).

A quick aside: It might be better not to even use the term "platonist" in these discussions, because it means at least two different things. It can be used to refer to Plato's "essentialism" - the idea that there's a world of Forms in which exists (for instance) the Ideal Horse, and all physical horses represent imperfect copies of this Horse. This is certainly a more elaborate belief than "mathematical realism" (or "arithmetical realism", or "computational realism"). One can be a mathematical realist without being an essentialist. I am. So some people would call me a Platonist, and some wouldn't, but that's just a disagreement about a definition. I prefer just to use the term "mathematical realism" or "essentialism", depending on what I'm talking about.

A quick aside: It might be better not to even use the term "platonist" in these discussions, because it means at least two different things. It can be used to refer to Plato's "essentialism" - the idea that there's a world of Forms in which exists (for instance) the Ideal Horse, and all physical horses represent imperfect copies of this Horse. This is certainly a more elaborate belief than "mathematical realism" (or "arithmetical realism", or "computational realism"). One can be a mathematical realist without being an essentialist. I am. So some people would call me a Platonist, and some wouldn't, but that's just a disagreement about a definition. I prefer just to use the term "mathematical realism" or "essentialism", depending on what I'm talking about.

-- Kory