Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Mathematical Explanation' and 'Ancient Thought in Modern Physics'

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8 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 / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
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 / D. Essence of Objects / 3. Individual Essences
13230 Particular essence is often captured by generality [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
13229 Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
6552 You can only explain the qualities of large objects using entities which lack those qualities [Heisenberg]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
13231 Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]