Combining Texts

All the ideas for 'Philosophical Essay on Probability', 'On a supposed right to lie' and 'First-Order Logic'

expand these ideas     |    start again     |     specify just one area for these texts

12 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]
13. Knowledge Criteria / C. External Justification / 7. Testimony
7458 The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
3441 If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
22442 If lies were ever acceptable, with would undermine all duties based on contract [Kant]
23. Ethics / D. Deontological Ethics / 2. Duty
22441 The law will protect you if you tell a truth which results in murder [Kant]