Combining Texts

All the ideas for 'talk', 'works' and 'The Inference to the Best Explanation'

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4 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
15941 For intuitionists excluded middle is an outdated historical convention [Brouwer]
     Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth.
     From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
     A reaction: [Brouwer 1952:510-11]
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]
     Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
     From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
     A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]
     Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature.
     From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8
14. Science / D. Explanation / 3. Best Explanation / a. Best explanation
17060 Best Explanation is the core notion of epistemology [Harman, by Smart]
     Full Idea: Gilbert Harman introduced the term 'inference to the best explanation', and argued that it is the core notion of epistemology.
     From: report of Gilbert Harman (The Inference to the Best Explanation [1974]) by J.J.C. Smart - Explanation - Opening Address p. 01
     A reaction: Hard to assess that, but it sounds right. I'm a fan of coherence theories of justification, and also coherence theories of explanation, and there is a neat package there somewhere.