Combining Texts

All the ideas for 'The Strangest Man', 'Commentary on 'Physics'' 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 / 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]
9. Objects / E. Objects over Time / 6. Successive Things
16698 Days exist, and yet they seem to be made up of parts which don't exist [Burley]
16690 Unlike permanent things, successive things cannot exist all at once [Burley]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
21236 Instead of gravitational force, we now have a pervasive gravitational field [Farmelo]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21235 The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
21234 Experiments show that fundamental particles of one type are identical [Farmelo]