4 ideas
19433 | The universe is infinitely varied, so the Buridan's Ass dilemma could never happen [Leibniz] |
Full Idea: The Buridan's Ass case of perfect equilibrium is chimerical. ...The universe has no centre and its parts are infinitely varied; thus it will never happen that all will be perfectly equal and will strike equally from one side or the other. | |
From: Gottfried Leibniz (Letters to Coste [1707], 1707) | |
A reaction: Can the great Leibniz have missed the point? Surely all that matters is that the ass cannot distinguish the two options - not that they actually are identical in every detail? If the ass is short-sighted, that should be easy to set up. |
10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
Full Idea: Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth. | |
From: Blaise Pascal (works [1660]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: [Quoted in Auden and Kronenberger's Book of Aphorisms] Presumably we would now say that contradiction is a purely formal, syntactic notion, and not a semantic one. If you hit a contradiction, something has certainly gone wrong. |
18203 | Avoid non-predicative classifications and definitions [Poincaré] |
Full Idea: Never consider any objects but those capable of being defined in a finite number of word ...Avoid non-predicative classifications and definitions. | |
From: Henri Poincaré (The Logic of Infinity [1909], p.63), quoted by Penelope Maddy - Naturalism in Mathematics II.4 |
19434 | There may be a world where dogs smell their game at a thousand leagues [Leibniz] |
Full Idea: There will perhaps be a world in which dogs will have sufficiently good noses to scent their game at a thousand leagues. | |
From: Gottfried Leibniz (Letters to Coste [1707], 1707) | |
A reaction: Wonderful. This should immediately replace Lewis's much repeated example of a world containing a talking donkey. We should always honour the first person to suggest an idea. That is one of the motivations for this collection of ideas. |