Combining Texts

All the ideas for 'Logical Consequence', 'Epistemology Externalized' and 'The Art of the Infinite'

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17 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
15717 Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
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 / 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 / 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 / 3. Nature of Numbers / b. Types of number
15712 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
15711 The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
15714 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
15715 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18760 The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
18. Thought / C. Content / 6. Broad Content
8872 It is widely supposed that externalism cannot be reconciled with first-person authority [Davidson]
8874 It is hard to interpret a speaker's actions if we take a broad view of the content [Davidson]
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]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
8873 The cause of a usage determines meaning, but why is the microstructure of water relevant? [Davidson]