Combining Texts

All the ideas for '27: Book of Daniel', 'First-Order Logic' and 'Platonistic Theories of Universals'

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13 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
8964 Entities can be multiplied either by excessive categories, or excessive entities within a category [Hoffman/Rosenkrantz]
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]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
8962 'There are shapes which are never exemplified' is the toughest example for nominalists [Hoffman/Rosenkrantz]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
8961 Nominalists are motivated by Ockham's Razor and a distrust of unobservables [Hoffman/Rosenkrantz]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
8963 Four theories of possible worlds: conceptualist, combinatorial, abstract, or concrete [Hoffman/Rosenkrantz]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
7482 Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson]