Posted by: Alexandre Borovik | April 10, 2010

Fred Richman’s “Confessions of a formalist, Platonist intuitionist”

Started to read Fred Richman’s “Confessions of a formalist, Platonist intuitionist“,  and stopped at the very first line:

All algebraists are formalists—it comes with the territory.

No, they are not. Or , in any case, not all of them.

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Responses

  1. He seems to mean it light-heartedly. A little later he writes,

    We are all Platonists, aren’t we? In the trenches, I mean—when the chips are down. Yes, Virginia, there really are circles, triangles, numbers, continuous functions, and all the rest. Well, maybe not free ultrafilters. Is it important to believe in the existence of free ultrafilters? Surely that’s not required of a Platonist. I can more easily imagine it as a test of sanity: “He believes in free ultrafilters, but he seems harmless.”


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