Combining Philosophers

All the ideas for Archimedes, Leopold Kronecker and Andy Douglas

unexpand these ideas     |    start again     |     specify just one area for these philosophers

4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
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.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
15. Nature of Minds / B. Features of Minds / 3. Privacy
5210 We could know what a lion thinks by mapping both its brain patterns and its experiences [Douglas,A]
     Full Idea: In principle, it seems possible to monitor both the brain activity and the external experiences of a lion cub from birth, and by extensive mapping of one against the other to work out fairly accurately what a lion is thinking.
     From: Andy Douglas (talk [2003])
     A reaction: This has limitations (e.g. we could monitor the external events, but not the way the lion experiences them), but it seems to me to offer a real theoretical possibility of breaching the mental privacy of an inarticulate creature.