Combining Texts
Ideas for
'After Finitude', 'Introducing the Philosophy of Mathematics' and 'The Art of the Infinite'
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12 ideas
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
8713
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In classical/realist logic the connectives are defined by truth-tables [Friend]
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4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
8708
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Double negation elimination is not valid in intuitionist logic [Friend]
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4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
8694
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Free logic was developed for fictional or non-existent objects [Friend]
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4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
19663
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We can allow contradictions in thought, but not inconsistency [Meillassoux]
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19664
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Paraconsistent logics are to prevent computers crashing when data conflicts [Meillassoux]
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19665
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Paraconsistent logic is about statements, not about contradictions in reality [Meillassoux]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
8665
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A 'proper subset' of A contains only members of A, but not all of them [Friend]
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8672
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A 'powerset' is all the subsets of a set [Friend]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
8677
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Set theory makes a minimum ontological claim, that the empty set exists [Friend]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
8666
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Infinite sets correspond one-to-one with a subset [Friend]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8682
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Major set theories differ in their axioms, and also over the additional axioms of choice and infinity [Friend]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
15717
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Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
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