Combining Texts

All the ideas for 'fragments/reports', 'A Specimen of Discoveries' and 'First-Order Logic'

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12 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
5035 The two basics of reasoning are contradiction and sufficient reason [Leibniz]
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]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
5038 Assume that mind and body follow their own laws, but God has harmonised them [Leibniz]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
5037 God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz]