Combining Texts

All the ideas for 'fragments/reports', 'fragments/reports' and 'Which Logic is the Right Logic?'

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27 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
5988 Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
1496 The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle]
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]
5. Theory of Logic / L. Paradox / 1. Paradox
6007 If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
6008 Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
7. Existence / A. Nature of Existence / 1. Nature of Existence
14874 Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
1495 Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius]
405 The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander]
13222 The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander]
404 Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
1746 The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius]