Ideas from 'Maths as a Science of Patterns' by Michael D. Resnik [1997], by Theme Structure

[found in 'Mathematics as a Science of Patterns' by Resnik,Michael D. [OUP 1999,0-19-825014-2]].

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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL

6299	Axioms are often affirmed simply because they produce results which have been accepted

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

6304	Mathematical realism says that maths exists, is largely true, and is independent of proofs

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

6300	Mathematical constants and quantifiers only exist as locations within structures or patterns

6303	Sets are positions in patterns

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism

6295	There are too many mathematical objects for them all to be mental or physical

6296	Maths is pattern recognition and representation, and its truth and proofs are based on these

6301	Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest

6302	Structuralism must explain why a triangle is a whole, and not a random set of points