Combining Texts

All the ideas for 'fragments/reports', 'The Nature of Existence vol.2' and 'First-Order Logic'

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20 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]
7. Existence / B. Change in Existence / 1. Nature of Change
15200 How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
14761 Change is not just having two different qualities at different points in some series [McTaggart]
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]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
2608 For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
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]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
22936 A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin]
4231 Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
8591 There could be no time if nothing changed [McTaggart]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
22935 The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin]
7802 A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
4230 A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
15199 The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]