Combining Texts
Ideas for
'Summa totius logicae', 'Precepts for Advancing Science and Arts' and 'Maths as a Science of Patterns'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
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Sets are positions in patterns [Resnik]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
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Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
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There are too many mathematical objects for them all to be mental or physical [Resnik]
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Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
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Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
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Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham]
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