Combining Philosophers
Ideas for B Hale / C Wright, Thomas M. Crisp and Stephen Read
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24 ideas
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
14187
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If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read]
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5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10986
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Not all validity is captured in first-order logic [Read]
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5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
10972
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The non-emptiness of the domain is characteristic of classical logic [Read]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
11024
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Semantics must precede proof in higher-order logics, since they are incomplete [Read]
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5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10985
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We should exclude second-order logic, precisely because it captures arithmetic [Read]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
14188
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Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read]
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14182
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If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read]
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14183
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Maybe arguments are only valid when suppressed premises are all stated - but why? [Read]
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10970
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A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
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10984
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Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
14184
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In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
14186
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Logical connectives contain no information, but just record combination relations between facts [Read]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
10973
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A theory is logically closed, which means infinite premisses [Read]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
12230
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Singular terms refer if they make certain atomic statements true [Hale/Wright]
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5. Theory of Logic / G. Quantification / 1. Quantification
11007
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Quantifiers are second-order predicates [Read]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10978
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In second-order logic the higher-order variables range over all the properties of the objects [Read]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10971
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A logical truth is the conclusion of a valid inference with no premisses [Read]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10988
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Any first-order theory of sets is inadequate [Read]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
10974
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Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read]
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10975
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Compactness does not deny that an inference can have infinitely many premisses [Read]
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10977
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Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read]
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10976
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Compactness makes consequence manageable, but restricts expressive power [Read]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
11014
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Self-reference paradoxes seem to arise only when falsity is involved [Read]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
10631
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If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
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