Combining Texts
Ideas for
'Isagoge ('Introduction')', 'Foundations without Foundationalism' and 'On Interpretation'
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16 ideas
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
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13643
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Aristotelian logic is complete [Shapiro]
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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 / D. Modal Logic ML / 1. Modal Logic
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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 / a. Types of set
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13651
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A set is 'transitive' if contains every member of each of its members [Shapiro]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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13647
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Choice is essential for proving downward Löwenheim-Skolem [Shapiro]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
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13631
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Are sets part of logic, or part of mathematics? [Shapiro]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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13654
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It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro]
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13640
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Russell's paradox shows that there are classes which are not iterative sets [Shapiro]
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13666
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Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro]
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4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
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13653
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'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro]
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