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Ideas for 'fragments/reports', 'W.V. Quine' and 'Introduction to the Philosophy of Mathematics'

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7 ideas

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

8078	Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

6023	Every proposition is either true or false [Chrysippus, by Cicero]

17924

Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]

5. Theory of Logic / G. Quantification / 1. Quantification

8452	Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

8475	The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17929

Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]

5. Theory of Logic / K. Features of Logics / 1. Axiomatisation

17930

Axioms are 'categorical' if all of their models are isomorphic [Colyvan]