Combining Texts

All the ideas for 'The Really Hard Problem', 'First-Order Logic' and 'Grundlagen (Foundations of Theory of Manifolds)'

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17 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
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 / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
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]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
21833 Research suggest that we overrate conscious experience [Flanagan]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
21834 Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
21837 Morality is normative because it identifies best practices among the normal practices [Flanagan]
22. Metaethics / B. Value / 2. Values / f. Altruism
21830 For Darwinians, altruism is either contracts or genetics [Flanagan]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
21835 We need Eudaimonics - the empirical study of how we should flourish [Flanagan]
24. Political Theory / D. Ideologies / 9. Communism
21831 Alienation is not finding what one wants, or being unable to achieve it [Flanagan]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
21832 Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan]