Combining Philosophers
Ideas for David Fair, Michael Dummett and Rahulabhadra
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13 ideas
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
19053
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Logic would be more natural if negation only referred to predicates [Dummett]
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4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
19060
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Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett]
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4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
16951
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It was realised that possible worlds covered all modal logics, if they had a structure [Dummett]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
16952
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If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
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16953
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Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
16960
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If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett]
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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
16958
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In S4 the actual world has a special place [Dummett]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18073
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Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
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18832
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Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
10537
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The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193
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ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
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9194
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The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10542
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To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]
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