5 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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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. |
14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
Full Idea: Many decent candidates could the referent of this 'cup', differing over whether outlying particles are parts. No further sortal I could invoke will be selective enough to rule out all but one referent for it. | |
From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1 n8) | |
A reaction: I never had much faith in sortals for establishing individual identity, so this point comes as no surprise. The implication is strongly realist - that the cup has an identity which is permanently beyond our capacity to specify it. |
14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
Full Idea: There can be determinately true identity claims despite indeterminate reference of the terms flanking the identity sign; these will be identity claims true under all admissible interpretations of the flanking terms. | |
From: Jonathan Schaffer (Deflationary Metaontology of Thomasson [2009], 3.1) | |
A reaction: In informal contexts there might be problems with the notion of what is 'admissible'. Is 'my least favourite physical object' admissible? |
1863 | If the soul achieves well-being in another life, it doesn't follow that I do [Aquinas] |
Full Idea: Even if soul achieves well-being in another life, that doesn't mean I do or any other human being does. | |
From: Thomas Aquinas (Super Epistolam Pauli Apostoli [1272]) |