Combining Texts
Ideas for
'Logical Pluralism', 'Dispositional Modality' and 'Believing the Axioms I'
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19 ideas
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
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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
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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
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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
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13011
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New axioms are being sought, to determine the size of the continuum [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
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13013
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The Axiom of Extensionality seems to be analytic [Maddy]
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13014
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Extensional sets are clearer, simpler, unique and expressive [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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13021
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The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
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13022
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Infinite sets are essential for giving an account of the real numbers [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
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13023
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The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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13024
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Efforts to prove the Axiom of Choice have failed [Maddy]
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13025
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Modern views say the Choice set exists, even if it can't be constructed [Maddy]
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13026
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A large array of theorems depend on the Axiom of Choice [Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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13019
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The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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13018
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Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
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