Combining Texts

All the ideas for 'Euthyphro', 'First-Order Logic' and 'Phil of Mathematics and Natural Science'

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12 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]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
335 Do the gods also hold different opinions about what is right and honourable? [Plato]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
10246 The limit of science is isomorphism of theories, with essences a matter of indifference [Weyl]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
337 It seems that the gods love things because they are pious, rather than making them pious by loving them [Plato]
336 Is what is pious loved by the gods because it is pious, or is it pious because they love it? (the 'Euthyphro Question') [Plato]