Combining Texts
Ideas for
'Metaphysics', 'works' and 'Philosophy of Mathematics'
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8 ideas
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
562
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Axioms are the underlying principles of everything, and who but the philosopher can assess their truth? [Aristotle]
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573
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The axioms of mathematics are part of philosophy [Aristotle]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18122
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Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
18114
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There is no single agreed structure for set theory [Bostock]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
18107
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A 'proper class' cannot be a member of anything [Bostock]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18115
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We could add axioms to make sets either as small or as large as possible [Bostock]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
18139
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The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
18105
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Replacement enforces a 'limitation of size' test for the existence of sets [Bostock]
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