Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Frank Close and Hilary Putnam

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7 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic

18953

Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic

18949

The universal syllogism is now expressed as the transitivity of subclasses [Putnam]

4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC

18952

'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set

18958

In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets

9944	We understand some statements about all sets [Putnam]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L

13655

The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro]

9915	V = L just says all sets are constructible [Putnam]