Ideas of Michael D. Resnik, by Theme

[American, fl. 1997, At the University of North Carolina, Chapel Hill.]

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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs
6. Mathematics / A. Nature of Mathematics / 5. Geometry
Euclid's geometry is synthetic, but Descartes produced an analytic version of it
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns
Sets are positions in patterns
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / d. Platonist structuralism
Maths is pattern recognition and representation, and its truth and proofs are based on these
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest
Structuralism must explain why a triangle is a whole, and not a random set of points
There are too many mathematical objects for them all to be mental or physical