Combining Texts

All the ideas for 'The Guide of the Perplexed', 'First-Order Logic' and 'A Rsum of Metaphysics'

expand these ideas     |    start again     |     specify just one area for these texts

13 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 / 2. Divine Nature
20696 We can approach knowledge of God by negative attributes [Maimonides]
28. God / A. Divine Nature / 3. Divine Perfections
5048 Perfection is simply quantity of reality [Leibniz]
28. God / C. Attitudes to God / 4. God Reflects Humanity
19085 Thinking of God as resembling humans results from a bad translation of Genesis 1:26 [Maimonides]
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]