Combining Texts

All the ideas for 'fragments/reports', 'Ancient Philosophy: very short introduction' and 'First-Order Logic'

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14 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
12036 Xenophanes began the concern with knowledge [Annas]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
12046 Plato was the first philosopher who was concerned to systematize his ideas [Annas]
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]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
12037 Euripides's Medea is a key case of reason versus the passions [Annas]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
12040 Virtue is a kind of understanding of moral value [Annas]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]