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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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. |
490 | Everything happens by reason and necessity [Leucippus] |
Full Idea: Nothing happens at random; everything happens out of reason and by necessity. | |
From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where? |
7319 | If we give up synonymy, we have to give up significance, meaning and sense [Grice/Strawson] |
Full Idea: If we are to give up the notion of sentence-synonymy as senseless, we must give up the notion of sentence-significance (of a sentence having meaning) as senseless too. But then perhaps we might as well give up the notion of sense. | |
From: P Grice / P Strawson (In Defense of a Dogma [1956]), quoted by Alexander Miller - Philosophy of Language 4.2 | |
A reaction: This is very prescient. Nearly all American philosophers seem to embrace Quine's view of analyticity (the philosophical equivalent of Americans putting a man on the moon?), but have they digested the implications (which Quine later largely admits)? |