Combining Texts

All the ideas for 'works', 'First-Order Logic' and 'Possible Worlds'

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12 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
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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 / A. Nature of Existence / 2. Types of Existence
15789 Lewis's distinction of 'existing' from 'being actual' is Meinong's between 'existing' and 'subsisting' [Lycan on Lewis]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
15790 Lewis can't know possible worlds without first knowing what is possible or impossible [Lycan on Lewis]
15791 What are the ontological grounds for grouping possibilia into worlds? [Lycan on Lewis]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
20239 Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]