4 ideas
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
| From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
| A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| Full Idea: God made the integers, all the rest is the work of man. | |
| From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
| A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
| 14494 | Epiphenomenalism is like a pointless nobleman, kept for show, but soon to be abolished [Alexander,S] |
| Full Idea: Epiphenomenalism supposes something to exist in nature which has nothing to do, no purpose to serve, a species of noblesse which depends on the work of its inferiors, but is kept for show and might as well, and undoubtedly would in time be abolished. | |
| From: Samuel Alexander (Space, Time and Deity (2 vols) [1927], 2:8), quoted by Jaegwon Kim - Nonreductivist troubles with ment.causation IV | |
| A reaction: Wonderful! Kim quotes this, and labels the implicit slogan (to be real is to have causal powers) 'Alexander's Dictum'. All the examples given of epiphenomena are only causally inert within a defined system, but they act causally outside the system. |
| 7825 | The politics of Leibniz was the reunification of Christianity [Stewart,M] |
| Full Idea: The politics of Leibniz may be summed up in one word: theocracy. The specific agenda motivating much of his work was to reunite the Protestant and Catholic churches | |
| From: Matthew Stewart (The Courtier and the Heretic [2007], Ch. 5) | |
| A reaction: This would be a typical project for a rationalist philosopher, who thinks that good reasoning will gradually converge on the one truth. |