6 ideas
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §1) | |
| A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to. |
| 8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
| Full Idea: The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right. | |
| From: Fraser MacBride (Structuralism Reconsidered [2007], §3) | |
| A reaction: Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others. |
| 22455 | Many ethical theories neglect the power of regretting the ought not acted upon [Williams,B] |
| Full Idea: It is a fundamental criticism of many ethical theories that their accounts of moral conflict and its resolution do not do justice to the facts of regret...: basically because they eliminate from the scene the ought that is not acted upon. | |
| From: Bernard Williams (Ethical consistency [1965], p.175), quoted by Philippa Foot - Moral Realism and Moral Dilemma p.39 | |
| A reaction: [p.175 in Problems of the Self] Williams seems to have initiated this idea. It doesn't matter much for Kantians and Utilitarians (any more than a wrong answer in maths), but it matters if character is the focus. The virtuous have regrets. |
| 22453 | Moral conflicts have a different feeling and structure from belief conflicts [Williams,B, by Foot] |
| Full Idea: Williams insisted that the feelings we have in situations of moral conflict show that the 'structure' of moral judgements is unlike that of assertions expressing beliefs. | |
| From: report of Bernard Williams (Ethical consistency [1965]) by Philippa Foot - Moral Realism and Moral Dilemma p.36 | |
| A reaction: Foot presents this as a key reason for the non-cognitivist view of ethics, and her paper attacks it. I don't usually react to moral disagreement with the same vigour I have when I think a belief is untrue. It may just be uncertainty, though. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |