Combining Texts

All the ideas for 'Reply to Richards', 'Dialectic of Enlightenment' and 'First-Order Logic'

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11 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
22140 The greatest philosophers are methodical; it is what makes them great [Grice]
1. Philosophy / H. Continental Philosophy / 5. Critical Theory
15663 Adorno and Horkheimer subjected the Enlightenment to 'critical theory' analysis [Adorno/Horkheimer, by Finlayson]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
20572 De Sade said it was impossible to rationally argue against murder [Adorno/Horkheimer]