Combining Texts
Ideas for
'Logical Pluralism', 'Set Theory and Its Philosophy' and 'Causality: Reductionism versus Realism'
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14 ideas
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
13249
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(∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall]
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4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
13243
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Excluded middle must be true for some situation, not for all situations [Beall/Restall]
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13242
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It's 'relevantly' valid if all those situations make it true [Beall/Restall]
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13245
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Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall]
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13246
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Relevant logic does not abandon classical logic [Beall/Restall]
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13254
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A doesn't imply A - that would be circular [Beall/Restall]
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13255
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Relevant logic may reject transitivity [Beall/Restall]
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
13250
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Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713
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Usually the only reason given for accepting the empty set is convenience [Potter]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044
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Infinity: There is at least one limit level [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708
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Nowadays we derive our conception of collections from the dependence between them [Potter]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
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4. Formal Logic / G. Formal Mereology / 1. Mereology
10707
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Mereology elides the distinction between the cards in a pack and the suits [Potter]
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