Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Frege on Apriority (with ps)' and 'Identity over Time'

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10 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 / 2. Geometry
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
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]
9. Objects / E. Objects over Time / 1. Objects over Time
16025 If things change they become different - but then no one thing undergoes the change! [Gallois]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
16026 4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois]
9. Objects / F. Identity among Objects / 6. Identity between Objects
16027 If two things are equal, each side involves a necessity, so the equality is necessary [Gallois]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
16892 Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]