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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

6295

There are too many mathematical objects for them all to be mental or physical

One.1

p.9

6296

Maths is pattern recognition and representation, and its truth and proofs are based on these

One.5.1

p.84

6299

Axioms are often affirmed simply because they produce results which have been accepted

Three.10.1

p.201

6300

Mathematical constants and quantifiers only exist as locations within structures or patterns

Three.10.3

p.209

6301

Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest

Three.10.4

p.213

6302

Structuralism must explain why a triangle is a whole, and not a random set of points

Three.10.5

p.218

6303

Sets are positions in patterns

Three.12.9

p.271

6304

Mathematical realism says that maths exists, is largely true, and is independent of proofs
