Combining Texts
Ideas for
'The Philosophy of Philosophy', 'Must We Believe in Set Theory?' and 'Modal Logics and Philosophy'
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14 ideas
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
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7786
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Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle]
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7798
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There are three axiom schemas for propositional logic [Girle]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
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7799
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Proposition logic has definitions for its three operators: or, and, and identical [Girle]
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4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
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7797
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Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
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7794
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There are seven modalities in S4, each with its negation [Girle]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
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7793
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◊p → □◊p is the hallmark of S5 [Girle]
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7795
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S5 has just six modalities, and all strings can be reduced to those [Girle]
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4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
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7787
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Possible worlds logics use true-in-a-world rather than true [Girle]
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7788
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Modal logic has four basic modal negation equivalences [Girle]
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7796
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Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
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10482
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The logic of ZF is classical first-order predicate logic with identity [Boolos]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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10492
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A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
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10485
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Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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10484
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The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
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