Combining Texts

All the ideas for 'A Résumé of Metaphysics', 'First-Order Logic' and 'Events'

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18 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
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]
7. Existence / B. Change in Existence / 4. Events / a. Nature of events
15566 Events are classes, and so there is a mereology of their parts [Lewis]
15567 Some events involve no change; they must, because causal histories involve unchanges [Lewis]
15561 The events that suit semantics may not be the events that suit causation [Lewis]
15565 Events have inbuilt essences, as necessary conditions for their occurrence [Lewis]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
15564 An event is a property of a unique space-time region [Lewis]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
15563 Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
5049 Intelligent pleasure is the perception of beauty, order and perfection [Leibniz]
26. Natural Theory / C. Causation / 1. Causation
15562 Causation is a general relation derived from instances of causal dependence [Lewis]
28. God / A. Divine Nature / 3. Divine Perfections
5048 Perfection is simply quantity of reality [Leibniz]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
5050 Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz]