Combining Philosophers
Ideas for Arcesilaus, Jeremiah and Stewart Shapiro
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13 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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4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
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10206
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Modal operators are usually treated as quantifiers [Shapiro]
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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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10208
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Axiom of Choice: some function has a value for every set in a given set [Shapiro]
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10252
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The Axiom of Choice seems to license an infinite amount of choosing [Shapiro]
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10301
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The axiom of choice is controversial, but it could be replaced [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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13640
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Russell's paradox shows that there are classes which are not iterative sets [Shapiro]
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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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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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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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10207
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Anti-realists reject set theory [Shapiro]
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