Combining Texts

All the ideas for 'Philosophical Grammar', 'Modern Moral Philosophy' and 'First-Order Logic'

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13 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 / A. Nature of Mathematics / 1. Mathematics
18281 In mathematics everything is algorithm and nothing is meaning [Wittgenstein]
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]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
6606 Consider: "Imagine this butterfly exactly as it is, but ugly instead of beautiful" [Wittgenstein]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
8070 It would be better to point to failings of character, than to moral wrongness of actions [Anscombe]
23. Ethics / D. Deontological Ethics / 1. Deontology
8065 'Ought' and 'right' are survivals from earlier ethics, and should be jettisoned [Anscombe]
8069 Between Aristotle and us, a Judaeo-Christian legal conception of ethics was developed [Anscombe]