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Ideas of Michael D. Resnik, by Text
[American, fl. 1997, At the University of North Carolina, Chapel Hill.]
1997
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Maths as a Science of Patterns
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One.1
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p.3
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6295
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There are too many mathematical objects for them all to be mental or physical
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One.1
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p.9
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6296
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Maths is pattern recognition and representation, and its truth and proofs are based on these
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One.5.1
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p.84
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6299
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Axioms are often affirmed simply because they produce results which have been accepted
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Three.10.1
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p.201
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6300
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Mathematical constants and quantifiers only exist as locations within structures or patterns
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Three.10.3
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p.209
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6301
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Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest
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Three.10.4
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p.213
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6302
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Structuralism must explain why a triangle is a whole, and not a random set of points
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Three.10.5
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p.218
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6303
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Sets are positions in patterns
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Three.12.9
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p.271
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6304
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Mathematical realism says that maths exists, is largely true, and is independent of proofs
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