Combining Philosophers
Ideas for Herodotus, John Heil and Palle Yourgrau
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7 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17818
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How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
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17822
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Nothing is 'intrinsically' numbered [Yourgrau]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
18518
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Infinite numbers are qualitatively different - they are not just very large numbers [Heil]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17817
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Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
17815
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We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
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17821
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You can ask all sorts of numerical questions about any one given set [Yourgrau]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
18500
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How could structures be mathematical truthmakers? Maths is just true, without truthmakers [Heil]
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