Combining Texts

All the ideas for 'Reference and Contingency', 'First-Order Logic' and 'Les quaestiones de anima (lectures on the soul)'

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11 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]
10. Modality / B. Possibility / 5. Contingency
14895 'Superficial' contingency: false in some world; 'Deep' contingency: no obvious verification [Evans, by Macià/Garcia-Carpentiro]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11881 Rigid designators can be meaningful even if empty [Evans, by Mackie,P]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
16618 Intellectual and moral states, and even the soul itself, depend on prime matter for their existence [Blasius, by Pasnau]