Combining Philosophers
Ideas for Herodotus, Ren Descartes and ystein Linnebo
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17 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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2430
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I can learn the concepts of duration and number just from observing my own thoughts [Descartes]
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2252
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Surely maths is true even if I am dreaming? [Descartes]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
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13445
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Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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24036
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I can only see the proportion of two to three if there is a common measure - their unity [Descartes]
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24035
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Unity is something shared by many things, so in that respect they are equals [Descartes]
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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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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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21963
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It is possible that an omnipotent God might make one and two fail to equal three [Descartes]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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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
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23442
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Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
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