display all the ideas for this combination of philosophers
14 ideas
| 21696 | Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine] |
| Full Idea: 'Nominalism' is distinct from 'extensionalism'. The main point of the latter doctrine is rejection of properties or attributes in favour of classes. But class are universals equally with attributes, and nominalism in the defined sense rejects both. | |
| From: Willard Quine (Lecture on Nominalism [1946], §3) | |
| A reaction: Hence Quine soon settled on labelling himself as an 'extensionalist', leaving proper nominalism to Nelson Goodman. It is commonly observed that science massively refers to attributes, so they can't just be eliminated. |
| 17738 | Quine blurs the difference between knowledge of arithmetic and of physics [Jenkins on Quine] |
| Full Idea: Quine cannot deal with the intuition that there is a difference in kind between our knowledge of arithmetic and our knowledge of physics. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Carrie Jenkins - Grounding Concepts 7.5 | |
| A reaction: The endorses this criticism, which she says is widespread. I'm not convinced that there is a clear notion of 'difference in kind' here. Jenkins gets arithmetic from concepts and physics from the world. Is that a sharp distinction? |
| 9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
| Full Idea: Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects. | |
| From: Willard Quine (Word and Object [1960], §55) | |
| A reaction: Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually). |
| 18198 | Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine] |
| Full Idea: The mathematics wanted for use in empirical sciences is for me on a par with the rest of science. Transfinite ramifications are on the same footing as simplifications, but anything further is on a par rather with uninterpreted systems, | |
| From: Willard Quine (Review of Parsons (1983) [1984], p.788), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
| A reaction: The word 'uninterpreted' is the interesting one. Would mathematicians object if the philosophers graciously allowed them to continue with their transfinite work, as long as they signed something to say it was uninterpreted? |
| 8993 | If mathematics follows from definitions, then it is conventional, and part of logic [Quine] |
| Full Idea: To claim that mathematical truths are conventional in the sense of following logically from definitions is the claim that mathematics is a part of logic. | |
| From: Willard Quine (Truth by Convention [1935], p.79) | |
| A reaction: Quine is about to attack logic as convention, so he is endorsing the logicist programme (despite his awareness of Gödel), but resisting the full Wittgenstein conventionalist picture. |
| 21557 | Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey] |
| Full Idea: Quine (1941) said that Russell had confused use and mention, and thus thought he had reduced classes to linguistic entities, while in fact he reduced them only to Platonic properties. | |
| From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133 | |
| A reaction: This is cited as the 'orthodox critical interpretation' of Russell and Whitehead. Confusion of use and mention was a favourite charge of Quine's. |
| 1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
| Full Idea: The logicism of Frege, Russell, Whitehead, Church and Carnap condones the use of bound variables or reference to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately. | |
| From: Willard Quine (On What There Is [1948], p.14) |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| Full Idea: We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic. |
| 1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
| Full Idea: Mathematics reduces only to set theory, and not to logic proper… but set theory cannot claim the same firmness and obviousness as logic. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.69-70) |
| 1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
| Full Idea: The formalism of Hilbert keeps classical maths as a play of insignificant notations. Agreement is found among the rules which, unlike the notations, are quite significant and intelligible. | |
| From: Willard Quine (On What There Is [1948], p.15) |
| 1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
| Full Idea: The intuitionism of Poincaré, Brouwer, Weyl and others holds that classes are invented, and accepts reference to abstract entities only if they are constructed from pre-specified ingredients. | |
| From: Willard Quine (On What There Is [1948], p.14) |
| 8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
| Full Idea: Quine feels that the intuitionist's ontology of abstract objects is too slight to serve the needs of classical mathematics. | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: Quine, who devoted his life to the application of Ockham's Razor, decided that sets were an essential part of the ontological baggage (which made him, according to Orenstein, a 'reluctant Platonist'). Dummett defends intuitionism. |
| 8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
| Full Idea: Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: (See Idea 8454 for the categories of numbers). This is a problem for Dummett. |
| 1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
| Full Idea: Conceptualism holds that there are universals but they are mind-made. | |
| From: Willard Quine (On What There Is [1948], p.14) |