Combining Texts

All the ideas for 'German Philosophy: a very short introduction', 'Artistic Value and Opportunistic Moralism' and 'Which Logic is the Right Logic?'

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24 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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
22049 Transcendental idealism aims to explain objectivity through subjectivity [Bowie]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
22055 The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie]
22054 German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie]
22056 Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
22693 The works we value most are in sympathy with our own moral views [John,E]
22694 We should understand what is morally important in a story, without having to endorse it [John,E]
22695 We value morality in art because that is what we care about - but it is a contingent fact [John,E]
22692 A work can be morally and artistically excellent, despite rejecting moral truth [John,E]