Combining Philosophers
Ideas for Alfred Tarski, Peter Auriol and Plato
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8 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
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In pure numbers, all ones are equal, with no internal parts [Plato]
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Geometry is not an activity, but the study of unchanging knowledge [Plato]
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One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
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We master arithmetic by knowing all the numbers in our soul [Plato]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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The sun was made for light, so we could learn numbers from astronomical movement [Plato]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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The same thing is both one and an unlimited number at the same time [Plato]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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Tarski's theory of truth shifted the approach away from syntax, to set theory and semantics [Feferman/Feferman on Tarski]
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