Combining Texts

All the ideas for 'Through the Looking Glass', 'The Sublime and the Good' and 'First-Order Logic'

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14 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]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
21. Aesthetics / B. Nature of Art / 1. Defining Art
22709 We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
22715 Great art proves the absurdity of art for art's sake [Murdoch]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
22714 Because art is love, it improves us morally [Murdoch]
22712 Art and morals are essentially the same, and are both identical with love [Murdoch]
22. Metaethics / B. Value / 2. Values / g. Love
22713 Love is realising something other than oneself is real [Murdoch]