Combining Texts

All the ideas for 'What Price Bivalence?', 'Knowledge and the Philosophy of Number' and 'Logical Consequence'

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18 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
18755 Validity is explained as truth in all models, because that relies on the logical terms [McGee]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
19043 Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18751 Natural language includes connectives like 'because' which are not truth-functional [McGee]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
18761 Second-order variables need to range over more than collections of first-order objects [McGee]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18753 An ontologically secure semantics for predicate calculus relies on sets [McGee]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18754 Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
5. Theory of Logic / K. Features of Logics / 3. Soundness
18757 Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18760 The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
19042 Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine]
19. Language / F. Communication / 2. Assertion
18762 A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee]