It is so much a part of “thinking philosophically” to be impressed with the special character of mathematical truth that it is hard to shake off the grip of the Platonic Principle. If, however, we think of “rational certainty” as a matter of victory in argument rather than of relation to an object known, we shall look toward our interlocutors rather than to our faculties for the explanation of the phenomenon. If we think of our certainty about the Pythagorean Theorem as our confidence, based on experience with arguments on such matters, that nobody will find an objection to the premises from
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