Combining Philosophers
Ideas for Archimedes, Hilary Putnam and Chistoph Scheibler
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7 ideas
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18953
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Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
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4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18949
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The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
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4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
18952
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'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
18958
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In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
9944
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We understand some statements about all sets [Putnam]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13655
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The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]
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9915
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V = L just says all sets are constructible [Putnam]
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