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Ideas for '', 'Identity and Existence in Logic' and 'Frege on Apriority (with ps)'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

16901	The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
	Full Idea: Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost.
	From: Tyler Burge (Frege on Apriority (with ps) [2000], 4)
	A reaction: I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic.

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

16902	Peano arithmetic requires grasping 0 as a primitive number [Burge]
	Full Idea: In the Peano axiomatisation, arithmetic seems primitively to involve the thought that 0 is a number.
	From: Tyler Burge (Frege on Apriority (with ps) [2000], 5)
	A reaction: Burge is pointing this out as a problem for Frege, for whom only the logic is primitive.