Combining Texts

All the ideas for 'Which Logic is the Right Logic?', 'Intro to 'Philosophy of Logic'' and 'Epistemology Externalized'

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25 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
9456 Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10775 The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9457 The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette]
10766 Logic is either for demonstration, or for characterizing structures [Tharp]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10767 Elementary logic is complete, but cannot capture mathematics [Tharp]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10769 Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10762 In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10776 The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
10774 There are at least five unorthodox quantifiers that could be used [Tharp]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
9458 Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette]
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
9461 Intensionalists say meaning is determined by the possession of properties [Jacquette]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10777 Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
10773 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
5. Theory of Logic / K. Features of Logics / 3. Soundness
10765 Soundness would seem to be an essential requirement of a proof procedure [Tharp]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10763 Completeness and compactness together give axiomatizability [Tharp]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10770 If completeness fails there is no algorithm to list the valid formulas [Tharp]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10771 Compactness is important for major theories which have infinitely many axioms [Tharp]
10772 Compactness blocks infinite expansion, and admits non-standard models [Tharp]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10764 A complete logic has an effective enumeration of the valid formulas [Tharp]
10768 Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
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 / C. Assigning Meanings / 7. Extensional Semantics
9460 Extensionalist semantics forbids reference to nonexistent objects [Jacquette]
9459 Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette]
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]