Combining Texts

All the ideas for 'Philosophy of Mathematics', 'On the Syllogism IV' and 'Second Philosophy'

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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 / A. Overview of Logic / 7. Second-Order Logic
10594 Henkin semantics is more plausible for plural logic than for second-order logic [Maddy]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
17744 De Morgan started the study of relations and their properties [De Morgan, by Walicki]
13501 De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD]
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]