Combining Texts

All the ideas for 'fragments/reports', 'Introduction to the Philosophy of History' and 'Which Logic is the Right Logic?'

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26 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
20109 Hegel inserted society and history between the God-world, man-nature, man-being binary pairs [Hegel, by Safranski]
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]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
23274 World history has no room for happiness [Hegel]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
23275 The state of nature is one of untamed brutality [Hegel]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
23276 The soul of the people is an organisation of its members which produces an essential unity [Hegel]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
23272 The human race matters, and individuals have little importance [Hegel]
24. Political Theory / D. Ideologies / 14. Nationalism
23273 In a good state the goal of the citizens and of the whole state are united [Hegel]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
23271 The goal of the world is Spirit's consciousness and enactment of freedom [Hegel]
25. Social Practice / E. Policies / 5. Education / d. Study of history
23270 We should all agree that there is reason in history [Hegel]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]