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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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. |
| 5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |
| Full Idea: Critolaus reformulated Aristotelian theory by defining happiness as a 'fulfilment' (sumplêrôma) of psychic, physical, and external goods, where virtue vastly outweighs the rest. | |
| From: report of Critolaus (fragments/reports [c.170 BCE]) by Stephen A. White - Critolaus | |
| A reaction: The sounds more like an attempt at clarification than a real change of Peripatetic doctrine. Occasionally 'fulfilment' is offered as a translation for eudaimonia. Maybe we should just take up Critolaus' suggestion when we are discussing Aristotle. |
| 16709 | Some people return to scholastic mysterious qualities, disguising them as 'forces' [Leibniz] |
| Full Idea: It pleases others to return to occult qualities or scholastic faculties, but since these crude philosophers and physicians see that those terms are in bad repute they change their name, calling them 'forces'. | |
| From: Gottfried Leibniz (Against Barbaric physics [1716], A&G:313), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 19.7 | |
| A reaction: Deceptive, because Leibniz embraced forces in his revised Aristotelian essentialism. Leibniz placed forces within essences, and he is worried about forces as separate entities, unsupported by any substance. |