Combining Philosophers
Ideas for Homer, Plato and Frank P. Ramsey
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9 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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We master arithmetic by knowing all the numbers in our soul [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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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 / 6. Logicism / b. Type theory
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The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
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