Combining Texts

All the ideas for 'fragments/reports', 'Which Logic is the Right Logic?' and 'The Sovereignty of Good'

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32 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
22338 An unexamined life can be virtuous [Murdoch]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
22337 Philosophy must keep returning to the beginning [Murdoch]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
23563 Philosophy moves continually between elaborate theories and the obvious facts [Murdoch]
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]
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
22341 Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
22347 Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch]
22. Metaethics / B. Value / 2. Values / g. Love
22339 Love is a central concept in morals [Murdoch]
22348 Ordinary human love is good evidence of transcendent goodness [Murdoch]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
22343 If I attend properly I will have no choices [Murdoch]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
22349 Art trains us in the love of virtue [Murdoch]
22340 It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
22350 Only trivial virtues can be possessed on their own [Murdoch]
22346 Moral reflection and experience gradually reveals unity in the moral world [Murdoch]
23. Ethics / F. Existentialism / 7. Existential Action
22342 Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch]
22351 Only a philosopher might think choices create values [Murdoch]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
22345 Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch]