Combining Texts

All the ideas for 'The Limits of Communitarianism', 'First-Order Logic' and 'Moral Realism and Moral Dilemma'

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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]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
22456 Maybe virtues conflict with each other, if some virtue needs a vice for its achievement [Foot]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
22265 I can't defend the view that the majority values of a community are thereby right [Sandel]
25. Social Practice / A. Freedoms / 3. Free speech
22268 If persons define themselves by a group membership, insults to that group are a real harm [Sandel]
22267 In the liberal view an insult to my group doesn't hurt me, since I'm defined by choices not groups [Sandel]
25. Social Practice / E. Policies / 2. Religion in Society
22266 The case for religious liberty depends on the religion contributing to a morally good life [Sandel]