Combining Texts

All the ideas for 'Issues of Pragmaticism', 'First-Order Logic' and 'Of the original contract'

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16 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]
19. Language / A. Nature of Meaning / 1. Meaning
19087 The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce]
20. Action / C. Motives for Action / 5. Action Dilemmas / a. Dilemmas
21103 Moral questions can only be decided by common opinion [Hume]
24. Political Theory / A. Basis of a State / 3. Natural Values / b. Natural equality
21099 People must have agreed to authority, because they are naturally equal, prior to education [Hume]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
21100 The idea that society rests on consent or promises undermines obedience [Hume]
20495 We no more give 'tacit assent' to the state than a passenger carried on board a ship while asleep [Hume]
21101 The people would be amazed to learn that government arises from their consent [Hume]
25. Social Practice / A. Freedoms / 7. Freedom to leave
6703 Poor people lack the knowledge or wealth to move to a different state [Hume]
25. Social Practice / C. Rights / 4. Property rights
21102 We all know that the history of property is founded on injustices [Hume]