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'fragments/reports', 'Philosophy of Mathematics' and 'The Boundary Stones of Thought'
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7 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
18842
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Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
18834
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Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
18846
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Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
23446
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You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
23448
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Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
23441
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Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
23442
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Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
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