Combining Texts

All the ideas for 'Action, Intention and Reason', 'The Nature of Existence vol.2' and 'Which Logic is the Right Logic?'

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27 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]
7. Existence / B. Change in Existence / 1. Nature of Change
15200 How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
14761 Change is not just having two different qualities at different points in some series [McTaggart]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
20064 Actions are not mere effects of reasons, but are under their control [Audi,R]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
2608 For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
22936 A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin]
4231 Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
8591 There could be no time if nothing changed [McTaggart]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
22935 The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin]
7802 A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
4230 A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
15199 The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]