10 ideas
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 24008 | Reference to a person's emotions is often essential to understanding their actions [Williams,B] |
| Full Idea: The reference to a man's emotions has a significance for our understanding of his moral sincerity, not as a substitute for or addition to how he acts, but as, on occasion, underlying our understanding of how he acts. | |
| From: Bernard Williams (Morality and the emotions [1965], p.223) | |
| A reaction: Williams aims to rescue emotion from the emotivists, and replace it at the centre of traditional modes of moral judgement. I suppose we could assess one rogue robot as behaving 'badly' in a community of robots. |
| 24009 | Moral education must involve learning about various types of feeling towards things [Williams,B] |
| Full Idea: If moral education does not revolve around what to fear, to be angry about, to despise, and where to draw the line between kindness and a stupid sentimentality - I do not know what it is. (Though there are principles, of truth-telling and justice). | |
| From: Bernard Williams (Morality and the emotions [1965], p.225) | |
| A reaction: He cites Aristotle as the obvious source of this correct idea. The examples of principle both require us to place a high value on truth and justice, and not just follow rules in the style of arithmetic. |
| 24007 | Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B] |
| Full Idea: Emotivism held that there were two purposes of moral judgements: to express the emotions of the speaker, and to influence the emotions of his hearers. | |
| From: Bernard Williams (Morality and the emotions [1965], p.209) | |
| A reaction: I take Ayer to be typical of the first project, and Hare of the second. The theory is much more plausible when the second aim is added. Would we ever utter a moral opinion if we didn't hope to influence someone? |
| 24010 | An admirable human being should have certain kinds of emotional responses [Williams,B] |
| Full Idea: One's conception of an admirable human being implies that he should be disposed to certain kinds of emotional response, and not to others. | |
| From: Bernard Williams (Morality and the emotions [1965], p.225) | |
| A reaction: So are the good emotions an indicator of being a good person, or is that what their goodness consists of? The goodness must be cashed out in actions, and presumably good emotions both promise good actions, and motivate them. |
| 24012 | Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B] |
| Full Idea: There is a certain moral woodenness or even insolence in Kant's blank regard for consistency. It smacks of Keynes's Principle of Unfairness - that if you can't do a good turn to everybody, you shouldn't do it to anybody. | |
| From: Bernard Williams (Morality and the emotions [1965], p.226) | |
| A reaction: He says it also turns each of us into a Supreme Legislator, which deifies man. It is clearly not the case that morality consists entirely of rules and principles, but Williams recognises their role, in truth-telling for example. |
| 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. |