Combining Texts

All the ideas for 'Taking Rights Seriously', 'Fear and Trembling' 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
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]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23104 Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes]
25. Social Practice / B. Equalities / 1. Grounds of equality
23257 We can treat people as equals, or actually treat them equally [Dworkin, by Grayling]
18621 Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka]
28. God / A. Divine Nature / 6. Divine Morality / a. Divine morality
16006 Either Abraham rises higher than universal ethics, or he is a mere murderer [Kierkegaard]
28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality
7577 Abraham was willing to suspend ethics, for a higher idea [Kierkegaard]