Combining Texts

All the ideas for 'The Sign of Four', 'First-Order Logic' and 'Letters to Johann Bernoulli'

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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
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
13174 A piece of flint contains something resembling perceptions and appetites [Leibniz]
13175 Entelechies are analogous to souls, as other minds are analogous to our own minds [Leibniz]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
13172 What we cannot imagine may still exist [Leibniz]
14. Science / C. Induction / 1. Induction
22200 If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
22. Metaethics / B. Value / 2. Values / e. Death
13173 Death is just the contraction of an animal [Leibniz]