3 ideas
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] |
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 |
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 |