Combining Philosophers
Ideas for Archimedes, Robert C. Stalnaker and Michal Walicki
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9 ideas
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
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17749
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Post proved the consistency of propositional logic in 1921 [Walicki]
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17765
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Propositional language can only relate statements as the same or as different [Walicki]
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4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
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17764
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Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
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16468
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Non-S5 can talk of contingent or necessary necessities [Stalnaker]
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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
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18823
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To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Stalnaker, by Rumfitt]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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17752
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The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
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17753
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The empty set avoids having to take special precautions in case members vanish [Walicki]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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16449
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In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker]
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4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
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17759
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Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
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