Combining Texts
Ideas for
'In Defense of Absolute Essentialism', 'Thinking About Logic' and 'A Subject with No Object'
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18 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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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
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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
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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
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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
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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 / E. Structures of Logic / 6. Relations in Logic
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9926
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A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
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10973
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A theory is logically closed, which means infinite premisses [Read]
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5. Theory of Logic / G. Quantification / 1. Quantification
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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
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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
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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
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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
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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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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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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 / 5. Paradoxes in Set Theory / a. Set theory paradoxes
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9932
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The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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11014
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Self-reference paradoxes seem to arise only when falsity is involved [Read]
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