Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, Alan Musgrave and Leon Horsten
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12 ideas
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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15326
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Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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15341
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Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten]
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5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
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10061
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The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
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10065
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Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
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15328
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A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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15349
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It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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10049
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Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
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10050
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A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
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15366
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Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
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10884
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A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
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15353
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The first incompleteness theorem means that consistency does not entail soundness [Horsten]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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15355
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Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten]
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