Combining Philosophers
Ideas for Melvin Fitting, Carrie Jenkins and Volker Halbach
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11 ideas
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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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 / A. Overview of Logic / 8. Logic of Mathematics
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Classical logic is deliberately extensional, in order to model mathematics [Fitting]
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5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
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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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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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A theory is some formulae and all of their consequences [Halbach]
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5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
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λ-abstraction disambiguates the scope of modal operators [Fitting]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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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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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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The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach]
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