8 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! |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |
| 3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
| Full Idea: A highly rational, efficient and unmitigated application of the idea of equality of opportunity, while abandoning the idea of equality of respect as vague and nostalgic, would lead to a quite inhuman society. | |
| From: Bernard Williams (The Idea of Equality [1962], §3) |
| 3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
| Full Idea: Equality seems to require that each person is owed an effort at identification; they should not be seen as a surface to which a label can be applied, but one should try to see the world (including the label) from their point of view. | |
| From: Bernard Williams (The Idea of Equality [1962], §2) |
| 3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
| Full Idea: Supporters of equality have asserted that people are alike in certain things they could do or achieve, as well as in the things that they need and could suffer. | |
| From: Bernard Williams (The Idea of Equality [1962], §2) |
| 3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
| Full Idea: It is a mark of extreme exploitation or degradation that those who suffer it do NOT see themselves differently from the way they are seen by the exploiters. | |
| From: Bernard Williams (The Idea of Equality [1962], §2) |