5 ideas
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
| From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
| From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
| A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |
| 22381 | Being a good father seems to depend on intentions, rather than actual abilities [Foot] |
| Full Idea: Being a good father, or daughter, or friend seems to depend on one's intentions, rather than on such things as cleverness and strength. | |
| From: Philippa Foot (Goodness and Choice [1961], p.138) | |
| A reaction: Not sure about that. In wartime a good father might need to be actually brave, and in times of hardship be actually economically successful. 'He meant well, but he was a hopeless father'? |
| 22380 | Some words, such as 'knife', have a meaning which involves its function [Foot] |
| Full Idea: The word 'knife' names an object in respect of its function. That is not to say (simply) that it names an object which has a function, but also that the function is involved in the meaning of the word. | |
| From: Philippa Foot (Goodness and Choice [1961], p.134) | |
| A reaction: It seems faintly possible that someone (a child, perhaps) could know the word and recognise the object, but not know what the object is for. Ditto with other things which have functional names. |