Combining Texts

Ideas for 'The Logical Syntax of Language', 'Schopenhauer' and 'Introduction to the Philosophy of Mathematics'

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5 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

13342

Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]

5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention

13251

Each person is free to build their own logic, just by specifying a syntax [Carnap]

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 / 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]