Combining Texts
Ideas for
'Thinking About Mathematics', 'Abstract Objects' and 'Model Theory'
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11 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 / D. Assumptions for Logic / 2. Excluded Middle
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8729
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Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
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10316
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We should decide whether singular terms are genuine by their usage [Hale]
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10312
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Often the same singular term does not ensure reliable inference [Hale]
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10313
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Plenty of clear examples have singular terms with no ontological commitment [Hale]
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10322
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If singular terms can't be language-neutral, then we face a relativity about their objects [Hale]
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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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