Combining Philosophers
Ideas for Stilpo, Vann McGee and John Mayberry
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15 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
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
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 / 7. Second-Order Logic
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 / B. Logical Consequence / 1. Logical Consequence
18755
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Validity is explained as truth in all models, because that relies on the logical terms [McGee]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18751
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Natural language includes connectives like 'because' which are not truth-functional [McGee]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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 / G. Quantification / 5. Second-Order Quantification
18761
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Second-order variables need to range over more than collections of first-order objects [McGee]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18753
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An ontologically secure semantics for predicate calculus relies on sets [McGee]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
18754
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Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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
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
18757
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Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
17789
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No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
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