7 ideas
21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
Full Idea: Metaphysics is the most general attempt to make sense of things. | |
From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro) | |
A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too. |
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! |
21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality. | |
From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507) |
20795 | Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus] |
Full Idea: Dogmatists say something can be its own criterion. The straight is the standard of itself, and a set of scales establishes the equality of other things and of itself, and light seems to reveal not just other things but also itself. | |
From: Sextus Empiricus (Against the Mathematicians [c.180], 442) | |
A reaction: Each of these may be a bit dubious, but deserves careful discussion. |
20794 | How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus] |
Full Idea: The dogmatists ask how the sceptic can show there is no criterion. If without a criterion, he is untrustworthy; with a criterion he is turned upside down. He says there is no criterion, but accepts a criterion to establish this. | |
From: Sextus Empiricus (Against the Mathematicians [c.180], 440) | |
A reaction: This is also the classic difficulty for foundationalist views of knowledge. Is the foundation justified, or not? |