Combining Texts

All the ideas for 'A Dictionary of Political Thought', 'On the Reality of Accidents' and 'Which Logic is the Right Logic?'

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25 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]
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
19382 Abstracta are abbreviated ways of talking; there are just substances, and truths about them [Leibniz]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
7590 Consequentialism emphasises value rather than obligation in morality [Scruton]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
7589 Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
7595 The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton]
24. Political Theory / D. Ideologies / 3. Conservatism
7588 Allegiance is fundamental to the conservative view of society [Scruton]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
7594 Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
7593 Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
7592 For positivists law is a matter of form, for naturalists it is a matter of content [Scruton]
25. Social Practice / F. Life Issues / 3. Abortion
7587 The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton]