5 ideas
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
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. |