Combining Philosophers

All the ideas for Anaxarchus, Wilfrid Hodges and Duncan Pritchard

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30 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
2. Reason / E. Argument / 1. Argument
19504 My modus ponens might be your modus tollens [Pritchard,D]
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 / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [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 / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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 / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [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]
10. Modality / B. Possibility / 9. Counterfactuals
19503 An improbable lottery win can occur in a nearby possible world [Pritchard,D]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
19505 Moore begs the question, or just offers another view, or uses 'know' wrongly [Pritchard,D, by PG]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19499 We can have evidence for seeing a zebra, but no evidence for what is entailed by that [Pritchard,D]
19500 Favouring: an entailment will give better support for the first belief than reason to deny the second [Pritchard,D]
19502 Maybe knowledge just needs relevant discriminations among contrasting cases [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19498 Epistemic internalism usually says justification must be accessible by reflection [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
19506 Externalism is better than internalism in dealing with radical scepticism [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / c. Disjunctivism
19496 Disjunctivism says perceptual justification must be both factual and known by the agent [Pritchard,D]
19497 Metaphysical disjunctivism says normal perceptions and hallucinations are different experiences [Pritchard,D]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
19495 Epistemic externalism struggles to capture the idea of epistemic responsibility [Pritchard,D]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
19501 We assess error against background knowledge, but that is just what radical scepticism challenges [Pritchard,D]
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
19507 Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D]