Combining Texts
Ideas for
'fragments/reports', 'The Theory of Logical Types' and 'Model Theory'
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10 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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10478
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Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
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10477
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|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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6023
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Every proposition is either true or false [Chrysippus, by Cicero]
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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
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21566
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'Propositional functions' are ambiguous until the variable is given a value [Russell]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
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10474
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|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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10473
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Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
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10475
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A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
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10481
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Models in model theory are structures, not sets of descriptions [Hodges,W]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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21567
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'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
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