Combining Philosophers
Ideas for B Hale / C Wright, Plato and Alasdair MacIntyre
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11 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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9863
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We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
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9864
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In pure numbers, all ones are equal, with no internal parts [Plato]
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8727
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Geometry is not an activity, but the study of unchanging knowledge [Plato]
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10216
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We master arithmetic by knowing all the numbers in our soul [Plato]
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16150
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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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9861
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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 / a. Early logicism
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8788
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Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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10622
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The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
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8783
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Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
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12225
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Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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12224
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Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
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