Combining Texts

All the ideas for 'The Statesman', 'First-Order Logic' and 'Works of Love'

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18 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
16123 Whenever you perceive a community of things, you should also hunt out differences in the group [Plato]
2. Reason / D. Definition / 2. Aims of Definition
16125 To reveal a nature, divide down, and strip away what it has in common with other things [Plato]
16124 No one wants to define 'weaving' just for the sake of weaving [Plato]
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]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
5961 The soul gets its goodness from god, and its evil from previous existence. [Plato]
19. Language / F. Communication / 1. Rhetoric
283 The question of whether or not to persuade comes before the science of persuasion [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
282 Non-physical beauty can only be shown clearly by speech [Plato]
22. Metaethics / B. Value / 2. Values / g. Love
15998 Perfect love is not in spite of imperfections; the imperfections must be loved as well [Kierkegaard]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
281 The arts produce good and beautiful things by preserving the mean [Plato]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
22559 Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle]
28. God / A. Divine Nature / 2. Divine Nature
279 Only divine things can always stay the same, and bodies are not like that [Plato]