Combining Philosophers
Ideas for Melvin Fitting, George Boolos and Oliver,A/Smiley,T
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17 ideas
4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
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15375
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If terms change their designations in different states, they are functions from states to objects [Fitting]
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15376
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Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
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4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
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15378
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Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting]
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4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
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15379
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Justication logics make explicit the reasons for mathematical truth in proofs [Fitting]
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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 / 3. Types of Set / b. Empty (Null) Set
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14239
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The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
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14240
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The empty set is something, not nothing! [Oliver/Smiley]
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14241
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We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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14242
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Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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14243
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The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
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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 / 4. Axioms for Sets / h. Axiom of Replacement VII
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18192
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Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
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7785
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The use of plurals doesn't commit us to sets; there do not exist individuals and collections [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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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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13547
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Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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10699
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Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
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