Combining Philosophers
Ideas for Helen Cartwright, Volker Halbach and Richard Posner
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10 ideas
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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16333
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The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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15652
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We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
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5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
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15651
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Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
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16310
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A theory is some formulae and all of their consequences [Halbach]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
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10670
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A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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16342
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You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach]
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16341
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Normally we only endorse a theory if we believe it to be sound [Halbach]
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16344
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Soundness must involve truth; the soundness of PA certainly needs it [Halbach]
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5. Theory of Logic / L. Paradox / 1. Paradox
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16347
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Many new paradoxes may await us when we study interactions between frameworks [Halbach]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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16336
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The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach]
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