Ideas from 'Frege on Apriority (with ps)' by Tyler Burge [2000], by Theme Structure

[found in 'Truth, Thought, Reason (on Frege)' by Burge,Tyler [OUP 2001,0-19-927854-7]].

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6. Mathematics / A. Nature of Mathematics / 2. Geometry
The equivalent algebra model of geometry loses some essential spatial meaning
                        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
Peano arithmetic requires grasping 0 as a primitive number
                        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.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
Is apriority predicated mainly of truths and proofs, or of human cognition?
                        Full Idea: Whereas Leibniz and Frege predicate apriority primarily of truths (or more fundamentally, proofs of truths), Kant predicates apriority primarily of cognition and the employment of representations.
                        From: Tyler Burge (Frege on Apriority (with ps) [2000], 1)