Combining Philosophers
Ideas for Paul Ricoeur, Keith Hossack and Volker Halbach
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11 ideas
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
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In Strong Kleene logic a disjunction just needs one disjunct to be true [Halbach]
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In Weak Kleene logic there are 'gaps', neither true nor false if one component lacks a truth value [Halbach]
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
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To prove the consistency of set theory, we must go beyond set theory [Halbach]
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Every attempt at formal rigour uses some set theory [Halbach]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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The Axiom of Choice is a non-logical principle of set-theory [Hossack]
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The Axiom of Choice guarantees a one-one correspondence from sets to ordinals [Hossack]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
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Predicativism says only predicated sets exist [Hossack]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
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Maybe we reduce sets to ordinals, rather than the other way round [Hossack]
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4. Formal Logic / G. Formal Mereology / 3. Axioms of Mereology
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Extensional mereology needs two definitions and two axioms [Hossack]
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