The Ubiquitous Heat Kernel: AMS Special Session, the

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Yet appeal to second-order logic in the philosophy of mathematics is by no means uncontroversial. For example, in Book I of the Elements, the demonstration of Proposition 16 (``in any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles'') is a chain of syllogisms with Postulate 2, Common Notion 5, and Propositions 3, 4 and 15 (``if two straight lines cut one another, they make the vertical angles equal to one another'') occurring as premises.

Pages: 402

Publisher: American Mathematical Society (March 21, 2006)

ISBN: 0821836986

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