Combining Texts
Ideas for
'Unconscious Cerebral Initiative', 'First-Order Logic' and 'Problems of Philosophy'
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10 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282
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Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
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5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
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Demonstration always relies on the rule that anything implied by a truth is true [Russell]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
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Proper names are really descriptions, and can be replaced by a description in a person's mind [Russell]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
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The phrase 'a so-and-so' is an 'ambiguous' description'; 'the so-and-so' (singular) is a 'definite' description [Russell]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
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10285
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I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
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10284
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There are three different standard presentations of semantics [Hodges,W]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
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10288
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Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
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