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Ideas for 'Metaphysics', 'Philosophy of Science' and 'Which Logic is the Right Logic?'

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32 ideas

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 / D. Assumptions for Logic / 1. Bivalence
22154 For Aristotle bivalence is a feature of reality [Aristotle, by Boulter]
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]
5. Theory of Logic / L. Paradox / 2. Aporiai
11264 Aporia 3: Does one science investigate all being, or does each kind of being have a science? [Aristotle, by Politis]
11258 We must start with our puzzles, and progress by solving them, as they reveal the real difficulty [Aristotle]
11265 Aporia 4: Does metaphysics just investigate pure being, or also the characteristics of being? [Aristotle, by Politis]
11262 Aporia 1: is there one science of explanation, or many? [Aristotle, by Politis]
11263 Aporia 2: Does one science investigate both ultimate and basic principles of being? [Aristotle, by Politis]
11266 Aporia 5: Do other things exist besides what is perceptible by the senses? [Aristotle, by Politis]
11270 Aporia 9: Is there one principle, or one kind of principle? [Aristotle, by Politis]
11267 Aporia 6: Are the basic principles of a thing the kinds to which it belongs, or its components? [Aristotle, by Politis]
11268 Aporia 7: Is a thing's kind the most general one, or the most specific one? [Aristotle, by Politis]
11269 Aporia 8: Are there general kinds, or merely particulars? [Aristotle, by Politis]
11271 Aporia 10: Do perishables and imperishables have the same principle? [Aristotle, by Politis]
11272 Aporia 11: Are primary being and unity distinct, or only in the things that are? [Aristotle, by Politis]
11273 Aporia 12: Do mathematical entities exist independently, or only in objects? [Aristotle, by Politis]
11274 Aporia 13: Are there kinds, as well as particulars and mathematical entities? [Aristotle, by Politis]
11276 Aporia 15: Are the causes of things universals or particulars? [Aristotle, by Politis]
11275 Aporia 14: Are ultimate causes of things potentialities, or must they be actual? [Aristotle, by Politis]