Combining Texts

All the ideas for 'Conditionals', 'Against the Ethicists (one book)' and 'Which Logic is the Right Logic?'

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24 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
22752 Reasoning is impossible without a preconception [Sext.Empiricus]
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]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
13768 Validity can preserve certainty in mathematics, but conditionals about contingents are another matter [Edgington]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
13770 There are many different conditional mental states, and different conditional speech acts [Edgington]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
13764 Are conditionals truth-functional - do the truth values of A and B determine the truth value of 'If A, B'? [Edgington]
13765 'If A,B' must entail ¬(A & ¬B); otherwise we could have A true, B false, and If A,B true, invalidating modus ponens [Edgington]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
22754 Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
22755 Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
22756 If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus]