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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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. |
| 20618 | Persons must be conscious, reasoning, motivated, communicative, self-aware [Warren, by Tuckness/Wolf] |
| Full Idea: Suggested characteristics of personhood: consciousness (esp. of pain); reasoning and problem solving; self-motivated activity; varied communication on many topics; self-concepts and self-awareness. | |
| From: report of Mary Anne Warren (On the Moral and Legal State of Abortion [1973], p.55) by Tuckness,A/Wolf,C - This is Political Philosophy 8 'Standing' | |
| A reaction: [a 'famous' article] A number of non-human animals come very close to passing these tests. I suspect the complex communication is only in there to disqualify them from getting the full certificate. (But she wrote on animal rights). |
| 18265 | We don't judge by combining subject and concept; we get a concept by splitting up a judgement [Frege] |
| Full Idea: Instead of putting a judgement together out of an individual as subject and an already previously formed concept as predicate, we do the opposite and arrive at a concept by splitting up the content of possible judgement. | |
| From: Gottlob Frege (Boole calculus and the Concept script [1881], p.17) | |
| A reaction: This is behind holistic views of sentences, and hence of whole languages, and behind Quine's rejection of 'properties' inferred from the predicates in judgements. |