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Ideas for 'Structures and Structuralism in Phil of Maths', 'Philosophies of Mathematics' and 'Logicism Revisited'

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12 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
10111 Asserting Excluded Middle is a hallmark of realism about the natural world [George/Velleman]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10175 Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10129 A 'model' is a meaning-assignment which makes all the axioms true [George/Velleman]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10105 Differences between isomorphic structures seem unimportant [George/Velleman]
5. Theory of Logic / K. Features of Logics / 2. Consistency
10119 Consistency is a purely syntactic property, unlike the semantic property of soundness [George/Velleman]
10126 A 'consistent' theory cannot contain both a sentence and its negation [George/Velleman]
5. Theory of Logic / K. Features of Logics / 3. Soundness
10120 Soundness is a semantic property, unlike the purely syntactic property of consistency [George/Velleman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10127 A 'complete' theory contains either any sentence or its negation [George/Velleman]