Combining Texts

All the ideas for 'Symposium', 'Grounding, Transitivity and Contrastivity' and 'First-Order Logic'

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14 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17304 As causation links across time, grounding links the world across levels [Schaffer,J]
17306 If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J]
14. Science / D. Explanation / 2. Types of Explanation / b. Contrastive explanations
17308 Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
5845 Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
26. Natural Theory / A. Speculations on Nature / 1. Nature
17305 I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J]
26. Natural Theory / C. Causation / 1. Causation
17307 Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J]