Combining Philosophers

All the ideas for Luitzen E.J. Brouwer, George Santayana and Duncan Pritchard

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26 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
8000 He who is ignorant of the history of philosophy is doomed to repeat it [Santayana, by MacIntyre]
2. Reason / E. Argument / 1. Argument
19504 My modus ponens might be your modus tollens [Pritchard,D]
4. Formal Logic / E. Nonclassical Logics / 7. Paraconsistency
12452 Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18247 Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
12451 Scientific laws largely rest on the results of counting and measuring [Brouwer]
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
12454 Intuitionists only accept denumerable sets [Brouwer]
12453 Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer]
8728 Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18521 The criterion of existence is the possibility of action [Santayana]
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]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
19507 Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10117 Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23060 The good is not relative, but is rooted in facts about human needs [Santayana]