Combining Texts

All the ideas for 'fragments/reports', 'Defeasibility Theory' and 'First-Order Logic'

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16 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]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
19718 Indefeasibility does not imply infallibility [Grundmann]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
19717 Can a defeater itself be defeated? [Grundmann]
19716 Simple reliabilism can't cope with defeaters of reliably produced beliefs [Grundmann]
19715 You can 'rebut' previous beliefs, 'undercut' the power of evidence, or 'reason-defeat' the truth [Grundmann]
19713 Defeasibility theory needs to exclude defeaters which are true but misleading [Grundmann]
19714 Knowledge requires that there are no facts which would defeat its justification [Grundmann]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
19719 'Moderate' foundationalism has basic justification which is defeasible [Grundmann]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
22511 Some reasonings are stronger than we are [Philolaus]