Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Introduction of 'Essence of Christianity''

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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
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]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
19451 When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
19450 Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
27. Natural Reality / G. Biology / 5. Species
19448 Consciousness is said to distinguish man from animals - consciousness of his own species [Feuerbach]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
19454 A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach]
28. God / C. Attitudes to God / 4. God Reflects Humanity
19452 The nature of God is an expression of human nature [Feuerbach]
28. God / C. Attitudes to God / 5. Atheism
19453 If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
19449 Religion is the consciousness of the infinite [Feuerbach]
19455 Today's atheism will tomorrow become a religion [Feuerbach]