Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Political Philosophy: all that matters'

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14 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]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
20582 World government needs a shared global identity [Oksala]
24. Political Theory / A. Basis of a State / 4. Original Position / b. Veil of ignorance
20568 The principles Rawls arrives at do not just conform to benevolence, but also result from choices [Oksala]
24. Political Theory / D. Ideologies / 2. Anarchism
20578 Anarchists prefer local and communal government [Oksala]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
20574 Utilitarianism neglects responsibility, duties and rights [Oksala]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]