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Ideas of Michael D. Resnik, by Text

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

1997 Maths as a Science of Patterns
One.1 p.3 There are too many mathematical objects for them all to be mental or physical
One.1 p.9 Maths is pattern recognition and representation, and its truth and proofs are based on these
One.4 p.55 Euclid's geometry is synthetic, but Descartes produced an analytic version of it
One.5.1 p.84 Axioms are often affirmed simply because they produce results which have been accepted
Three.10.1 p.201 Mathematical constants and quantifiers only exist as locations within structures or patterns
Three.10.3 p.209 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest
Three.10.4 p.213 Structuralism must explain why a triangle is a whole, and not a random set of points
Three.10.5 p.218 Sets are positions in patterns
Three.12.9 p.271 Mathematical realism says that maths exists, is largely true, and is independent of proofs