Combining Texts
Ideas for
'Laches', 'The Tarskian Turn' and 'Principia Mathematica'
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11 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 / B. Logical Consequence / 7. Strict Implication
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8204
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Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
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9359
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Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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21707
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Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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10036
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In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
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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 / 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 / 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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