Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Explanatory Coherence'

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15 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]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
17064 1: Coherence is a symmetrical relation between two propositions [Thagard, by Smart]
17065 2: An explanation must wholly cohere internally, and with the new fact [Thagard, by Smart]
17066 3: If an analogous pair explain another analogous pair, then they all cohere [Thagard, by Smart]
17067 4: For coherence, observation reports have a degree of intrinsic acceptability [Thagard, by Smart]
17068 5: Contradictory propositions incohere [Thagard, by Smart]
17069 6: A proposition's acceptability depends on its coherence with a system [Thagard, by Smart]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]