Combining Texts

All the ideas for 'Which Logic is the Right Logic?', 'The Semantic Tradition from Kant to Carnap' and 'Deflationary Metaontology of Thomasson'

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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]
18270 Choice suggests that intensions are not needed to ensure classes [Coffa]
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]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
14082 No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J]
9. Objects / F. Identity among Objects / 6. Identity between Objects
14081 Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
18263 The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
18272 Platonism defines the a priori in a way that makes it unknowable [Coffa]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
18266 Mathematics generalises by using variables [Coffa]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
18279 Relativity is as absolutist about space-time as Newton was about space [Coffa]