Combining Philosophers
Ideas for Bernard Williams, ystein Linnebo and Marcus Rossberg
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9 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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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
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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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
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14085
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'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
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14084
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Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
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14086
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'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
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14087
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'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
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14089
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Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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14083
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Structuralism is right about algebra, but wrong about sets [Linnebo]
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14090
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In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
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