Combining Texts

All the ideas for 'works', 'Letters to Coste' and 'The Logic of Infinity'

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4 ideas

2. Reason / A. Nature of Reason / 9. Limits of Reason
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.
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
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.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
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.