Combining Texts

All the ideas for 'Purifications (frags)', 'The Analysis of Mind' 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]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
6417 In 1921 Russell abandoned sense-data, and the gap between sensation and object [Russell, by Grayling]
6474 Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
6476 We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data [Russell]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
2792 It is possible the world came into existence five minutes ago, complete with false memories [Russell]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
22326 Knowledge needs more than a sensitive response; the response must also be appropriate [Russell]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
6475 In perception, the self is just a logical fiction demanded by grammar [Russell]