Combining Texts

All the ideas for 'fragments/reports', 'Reference and Modality' and 'First-Order Logic'

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19 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10928 Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
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 / F. Referring in Logic / 1. Naming / b. Names as descriptive
10925 Failure of substitutivity shows that a personal name is not purely referential [Quine]
5. Theory of Logic / G. Quantification / 1. Quantification
10926 Quantifying into referentially opaque contexts often produces nonsense [Quine]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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]
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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]
9. Objects / D. Essence of Objects / 15. Against Essentialism
10930 Quantification into modal contexts requires objects to have an essence [Quine]
10. Modality / A. Necessity / 4. De re / De dicto modality
14645 To be necessarily greater than 7 is not a trait of 7, but depends on how 7 is referred to [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
9201 Whether 9 is necessarily greater than 7 depends on how '9' is described [Quine, by Fine,K]
10927 Necessity only applies to objects if they are distinctively specified [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
9203 We can't quantify in modal contexts, because the modality depends on descriptions, not objects [Quine, by Fine,K]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
10931 We can't say 'necessarily if x is in water then x dissolves' if we can't quantify modally [Quine]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]