Combining Texts

All the ideas for 'fragments/reports', 'Method and Results' and 'First-Order Logic'

expand these ideas     |    start again     |     specify just one area for these texts

11 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
23367 Even pointing a finger should only be done for a reason [Epictetus]
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]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
3157 T.H.Huxley gave the earliest clear statement of epiphenomenalism [Huxley, by Rey]
3154 Brain causes mind, but it doesn't seem that mind causes actions [Huxley]