Combining Texts

All the ideas for 'Philosophical Essay on Probability', 'Philosophy of Natural Science' and 'Philosophy of Mathematics'

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7 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
13. Knowledge Criteria / C. External Justification / 7. Testimony
The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
Scientific explanation aims at a unifying account of underlying structures and processes [Hempel]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]