Combining Philosophers

All the ideas for Micklethwait,J/Wooldridge,A, Philodemus and Leslie H. Tharp

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23 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]
20100 Classical liberalism seeks freedom of opinion, of private life, of expression, and of property [Micklethwait/Wooldridge]
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]
14. Science / C. Induction / 3. Limits of Induction
6027 From the fact that some men die, we cannot infer that they all do [Philodemus]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
22241 Don't fear god or worry about death; the good is easily got and the terrible easily cured [Philodemus]
24. Political Theory / D. Ideologies / 8. Socialism
20097 The welfare state aims at freedom from want, and equality of opportunity [Micklethwait/Wooldridge]
24. Political Theory / D. Ideologies / 9. Communism
20099 For communists history is driven by the proletariat [Micklethwait/Wooldridge]
24. Political Theory / D. Ideologies / 11. Capitalism
20098 Fans of economic freedom claim that capitalism is self-correcting [Micklethwait/Wooldridge]
25. Social Practice / C. Rights / 4. Property rights
20096 Roman law entrenched property rights [Micklethwait/Wooldridge]