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Ideas for 'Logicism Revisited', 'Recent Debates on the A Priori' and 'Topics'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
Unit is the starting point of number [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism seems to exclude all creative, growing mathematics [Musgrave]
Formalism is a bulwark of logical positivism [Musgrave]