Combining Texts
Ideas for
'Three Varieties of Knowledge', 'On Interpretation' and 'Introduction to Mathematical Philosophy'
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21 ideas
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
22272
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Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle]
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9405
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Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle]
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4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
14453
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The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell]
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4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9728
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Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn]
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9729
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Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
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9730
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Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
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9731
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Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
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9732
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Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
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9733
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Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
14427
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We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
14428
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Members define a unique class, whereas defining characteristics are numerous [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
14440
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We may assume that there are infinite collections, as there is no logical reason against them [Russell]
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14447
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Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
14443
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The British parliament has one representative selected from each constituency [Russell]
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14445
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Choice shows that if any two cardinals are not equal, one must be the greater [Russell]
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14444
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Choice is equivalent to the proposition that every class is well-ordered [Russell]
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14446
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We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
14459
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Reducibility: a family of functions is equivalent to a single type of function [Russell]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
14461
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Propositions about classes can be reduced to propositions about their defining functions [Russell]
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4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8469
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Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
8745
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Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
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