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'Unconscious Cerebral Initiative', 'First-Order Logic' and 'On What There Is'
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11 ideas
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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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 / E. Structures of Logic / 4. Variables in Logic
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1618
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We study bound variables not to know reality, but to know what reality language asserts [Quine]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
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8455
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Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein]
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8456
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Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein]
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5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
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1611
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Names can be converted to descriptions, and Russell showed how to eliminate those [Quine]
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5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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10283
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A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [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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10285
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I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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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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10289
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Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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10287
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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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