Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Ian Rumfitt and Kathrin Koslicki
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11 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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18842
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Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
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17435
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Objects do not naturally form countable units [Koslicki]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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17433
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We can still count squares, even if they overlap [Koslicki]
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17462
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A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
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17439
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There is no deep reason why we count carrots but not asparagus [Koslicki]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
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17434
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We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
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18834
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Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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18846
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Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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17312
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It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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17461
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Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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14505
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Some questions concern mathematical entities, rather than whole structures [Koslicki]
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