Combining Texts

All the ideas for 'Does Moral Subjectivism Rest on a Mistake?', 'First-Order Logic' and '17: Epistle to Titus'

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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
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]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
9464 One of their own prophets said that Cretans are always liars [Anon (Titus)]
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]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
22485 Non-cognitivists give the conditions of use of moral sentences as facts about the speaker [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
22486 The mistake is to think good grounds aren't enough for moral judgement, which also needs feelings [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22487 Moral arguments are grounded in human facts [Foot]