Combining Texts

All the ideas for 'Philosophy of Mathematics', 'works' and 'Syntactic Structure'

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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]
2. Reason / F. Fallacies / 8. Category Mistake / c. Category mistake as semantic
18009 Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor]
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 / F. Identity among Objects / 5. Self-Identity
3144 Everything is what it is, and not another thing [Butler]
19. Language / C. Assigning Meanings / 1. Syntax
18007 Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor]