Combining Philosophers
Ideas for Herodotus, Volker Halbach and John Mayberry
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18 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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17786
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The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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17788
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First-order logic only has its main theorems because it is so weak [Mayberry]
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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 / A. Overview of Logic / 7. Second-Order Logic
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17791
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Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
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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 / G. Quantification / 2. Domain of Quantification
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17787
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Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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17790
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No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]
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5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
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17779
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'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]
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17778
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Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]
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17780
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'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]
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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 / K. Features of Logics / 6. Compactness
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17789
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No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
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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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