Combining Texts

All the ideas for 'reports', 'Concepts and Counting' and 'Philosophy of Mathematics'

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7 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17462 A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17461 Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
10. Modality / A. Necessity / 8. Transcendental Necessity
3016 Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]