Combining Texts

All the ideas for 'fragments/reports', 'What is Good?' and 'First-Order Logic'

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15 ideas

1. Philosophy / C. History of Philosophy / 3. Earlier European Philosophy / c. Later medieval philosophy
Lucretius was rediscovered in 1417 [Grayling]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
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
A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
There are three different standard presentations of semantics [Hodges,W]
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
Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
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
A 'set' is a mathematically well-behaved class [Hodges,W]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
In an honour code shame is the supreme punishment, and revenge is a duty [Grayling]
25. Social Practice / F. Life Issues / 4. Suicide
If suicide is lawful, but assisting suicide is unlawful, powerless people are denied their rights [Grayling]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion gives answers, comforts, creates social order, and panders to superstition [Grayling]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
To make an afterlife appealing, this life has to be denigrated [Grayling]
In Greek mythology only heroes can go to heaven [Grayling]