Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Beauty: a very short introduction'

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20 ideas

2. Reason / A. Nature of Reason / 7. Status of Reason
18543 Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton]
3. Truth / A. Truth Problems / 2. Defining Truth
18542 Defining truth presupposes that there can be a true definition [Scruton]
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]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
18546 The pleasure taken in beauty also aims at understanding and valuing [Scruton]
18550 Art gives us imaginary worlds which we can view impartially [Scruton]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
18544 Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton]
18553 Beauty shows us what we should want in order to achieve human fulfilment [Scruton]
18556 Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
18548 Natural beauty reassures us that the world is where we belong [Scruton]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
18551 Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18541 Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton]
25. Social Practice / F. Life Issues / 5. Sexual Morality
18554 Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton]