Combining Texts

All the ideas for 'A Résumé of Metaphysics', 'Seven Types of Atheism' and 'First-Order Logic'

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16 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]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
5049 Intelligent pleasure is the perception of beauty, order and perfection [Leibniz]
28. God / A. Divine Nature / 3. Divine Perfections
5048 Perfection is simply quantity of reality [Leibniz]
28. God / C. Attitudes to God / 5. Atheism
23061 Free atheism should start by questioning its faith in humanity [Gray]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
23057 Gnosticism has a supreme creator God, giving way to a possibly hostile Demiurge [Gray]
29. Religion / B. Monotheistic Religion / 2. Judaism
23056 Judaism only became monotheistic around 550 BCE [Gray]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
23055 Christians introduced the idea that a religion needs a creed [Gray]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
23058 Buddhism has no divinity or souls, and the aim is to lose the illusion of a self [Gray]
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]