Combining Texts

All the ideas for 'fragments/reports', 'fragments/reports' and 'Which Logic is the Right Logic?'

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26 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
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]
7. Existence / D. Theories of Reality / 4. Anti-realism
5953 For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
3023 Even the foolish may have some virtues [Aristippus young, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
3026 Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
3024 Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius]
23. Ethics / A. Egoism / 1. Ethical Egoism
3025 For a Cyrenaic no one is of equal importance to himself [Aristippus young, by Diog. Laertius]
23. Ethics / A. Egoism / 3. Cyrenaic School
3019 No one pleasure is different from or more pleasant than another [Aristippus young, by Diog. Laertius]
3021 The Cyrenaics asserted that corporeal pleasures were superior to mental ones [Aristippus young, by Diog. Laertius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
541 Virtue comes more from habit than character [Critias]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
3027 Cyrenaics say wise men are self-sufficient, needing no friends [Aristippus young, by Diog. Laertius]
28. God / C. Attitudes to God / 5. Atheism
542 Fear of the gods was invented to discourage secret sin [Critias]