Combining Texts

All the ideas for 'Croce and Collingwood', 'Could There Be Unicorns?' and 'Which Logic is the Right Logic?'

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29 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16951 It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
16953 Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
16952 If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
16960 If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
16958 In S4 the actual world has a special place [Dummett]
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
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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10773 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
10777 Skolem mistakenly inferred that Cantor's conceptions were illusory [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]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
16957 Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
16959 If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
20416 By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20417 Expression can be either necessary for art, or sufficient for art (or even both) [Kemp]
20419 We don't already know what to express, and then seek means of expressing it [Kemp]
20418 The horror expressed in some works of art could equallly be expressed by other means [Kemp]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
16956 To explain generosity in a person, you must understand a generous action [Dummett]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
16954 Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett]