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Ideas for '', 'Explanation and Reference' and 'Introduction to the Philosophy of Mathematics'

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7 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

11211

If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]

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

17924

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

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11212

The sense of a connective comes from primitively obvious rules of inference [Rumfitt]

11210

Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]

5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names

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Using proper names properly doesn't involve necessary and sufficient conditions [Putnam]

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

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

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

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