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! |
| 8353 | Freedom involves acting according to an idea [Anscombe] |
| Full Idea: Freedom at least involves the power of acting according to an idea. | |
| From: G.E.M. Anscombe (Causality and Determinism [1971], §2) | |
| A reaction: Since 'you' presumably have to sit above the idea and pass a judgement on it, then the same principle should apply to acting on a desire, which presumably 'you' could reject because it just wasn't attractive enough. |
| 8352 | To believe in determinism, one must believe in a system which determines events [Anscombe] |
| Full Idea: 'The ball's path is determined' must mean 'there is only one possible path for the ball (assuming no air currents)', but what ground could one have for believing this, if one does not believe in some system for which it is a consequence? | |
| From: G.E.M. Anscombe (Causality and Determinism [1971], §2) | |
| A reaction: This seems right, but it doesn't follow that one has to know the full details of the system. The system might just be the best explanation, or even a matter of vague faith. It might, though, be just that you can't imagine any other outcome. |
| 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. |
| 8351 | With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe] |
| Full Idea: It is much easier to trace effects back to causes with certainty than to predict effects from causes. If I have one contact with someone with a disease and I get it, we suppose I got it from him, but a doctor cannot predict a disease from one contact. | |
| From: G.E.M. Anscombe (Causality and Determinism [1971], §1) | |
| A reaction: An interesting, and obviously correct, observation. Her point is that we get more certainty of causes from observing a singular effect than we get certainty of effects from regularities or laws. |
| 4777 | The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe] |
| Full Idea: The word "cause" can be added to a language in which are already represented many causal concepts; a small selection: scrape, push, wet, carry, eat, burn, knock over, keep off, squash, make, hurt. | |
| From: G.E.M. Anscombe (Causality and Determinism [1971], p.93) | |
| A reaction: An interesting point, perhaps reinforcing the Humean idea of causation as a 'natural belief', or the Kantian view of it as a category of thought. Or maybe causation is built into language because it is a feature of reality… |
| 10363 | Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J] |
| Full Idea: Anscombe has inspired the view that causation is an intensional relation, and takes it to be relative to the descriptions of the primary relata. | |
| From: report of G.E.M. Anscombe (Causality and Determinism [1971], 1) by Jonathan Schaffer - The Metaphysics of Causation 1 | |
| A reaction: It seems too linguistic to say that there is nothing more to it. It seems relevant in human examples, but if a landslide crushes a tree, what difference does the description make? 'It was just a few rocks and some miserable little tree'. No excuse! |
| 8350 | Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe] |
| Full Idea: Since Mill it has been fairly common to explain causation one way or another in terms of 'necessary' and 'sufficient' conditions. | |
| From: G.E.M. Anscombe (Causality and Determinism [1971], §1) | |
| A reaction: Interesting to see what Hume implies about these criteria. Anscombe is going to propose that causal events are fairly self-evident and self-explanatory, and don't need analyses of conditions. Another approach is regularities and laws. |