Combining Texts

All the ideas for 'Semantics, Conceptual Role', 'Paradox without Self-Reference' and 'Model Theory'

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10 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
9138 An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
18033 The meaning of a representation is its role in thought, perception or decisions [Block]