Combining Texts
Ideas for
'Logical Pluralism', 'On boundary numbers and domains of sets' and 'Travels in Four Dimensions'
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10 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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13246
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Relevant logic does not abandon classical logic [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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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 / 4. Axioms for Sets / a. Axioms for sets
17832
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Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13028
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Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
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