Combining Texts

All the ideas for 'Universal Prescriptivism', 'Two treatises' and 'Which Logic is the Right Logic?'

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28 ideas

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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16597 Quantity is the capacity to be divided [Digby]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
2705 How can intuitionists distinguish universal convictions from local cultural ones? [Hare]
2712 You can't use intuitions to decide which intuitions you should cultivate [Hare]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
2706 Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
2708 An 'ought' statement implies universal application [Hare]
2704 If morality is just a natural or intuitive description, that leads to relativism [Hare]
2703 Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare]
2707 If there can be contradictory prescriptions, then reasoning must be involved [Hare]
2709 Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare]
2711 Prescriptivism implies a commitment, but descriptivism doesn't [Hare]
23. Ethics / D. Deontological Ethics / 3. Universalisability
2710 Moral judgements must invoke some sort of principle [Hare]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
16731 Colours arise from the rarity, density and mixture of matter [Digby]