Combining Texts

All the ideas for 'Contextualist Solutions to Scepticism', 'Which Logic is the Right Logic?' and 'Scientific Thought'

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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]
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 / E. Objects over Time / 4. Four-Dimensionalism
14759 A thing is simply a long event, linked by qualities, and spatio-temporal unity [Broad]
11842 If short-lived happenings like car crashes are 'events', why not long-lived events like Dover Cliffs? [Broad]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
19508 Contextualism needs a semantics for knowledge sentences that are partly indexical [Schiffer,S]
19509 The indexical aspect of contextual knowledge might be hidden, or it might be in what 'know' means [Schiffer,S]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
8160 The present and past exist, but the future does not [Broad, by Dummett]
14609 We could say present and past exist, but not future, so that each event adds to the total history [Broad]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
22933 We imagine the present as a spotlight, moving across events from past to future [Broad]