Combining Texts

All the ideas for 'Philosophy of Mathematics', 'New Foundations for Mathematical Logic' and 'Warrant and Proper Function'

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6 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9879 NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett]
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]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6356 Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz]