Combining Texts

All the ideas for 'fragments/reports', 'The Foundations of Mathematics' and 'The Nature of Possibility'

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
18844 You would cripple mathematics if you denied Excluded Middle [Hilbert]
     Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists.
     From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4
     A reaction: [p.476 in Van Heijenoort]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
11003 The best version of reductionist actualism around is Armstrong's combinatorial account [Armstrong, by Read]
     Full Idea: Armstrong's combinatorial theory of possibility is perhaps the most sophisticated and best worked out reductionist version of actualism to date.
     From: report of David M. Armstrong (The Nature of Possibility [1986]) by Stephen Read - Thinking About Logic Ch.4
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