Combining Texts

All the ideas for 'Philosophy of Mathematics', 'On the Concept of Number' and 'Epistemic Justification'

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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 / 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]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
22293 Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19679 'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
19678 Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig]