display all the ideas for this combination of philosophers
8 ideas
| 3302 | Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA] |
| Full Idea: Quine has showed us how set theory - now recognised to be positively awash in Platonistic metaphysics - can and should be prevented from infecting logic proper. | |
| From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Intro |
| 9879 | NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett] |
| Full Idea: Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions. | |
| From: report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded. |
| 10211 | Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro] |
| Full Idea: Quine suggests that V = L be accepted in set theory because it makes for a cleaner theory, even though most set theorists are skeptical of V = L. | |
| From: report of Willard Quine (works [1961]) by Stewart Shapiro - Philosophy of Mathematics Ch.1 | |
| A reaction: Shapiro cites it as a case of a philosopher trying to make recommendations to mathematicians. Maddy supports Quine. |
| 21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
| Full Idea: Quine charges that the axiom of Reducibility both undoes the effect of the ramification, and commits the theory to a platonist view of propositional functions (which is a theory of sets, once use/mention confusions are cleared up). | |
| From: report of Willard Quine (Set Theory and its Logic [1963], p.249-58) by Bernard Linsky - Russell's Metaphysical Logic 6.1 |
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
| From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |
| 21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |
| Full Idea: Each proposed revision of set theory is unnatural, because the natural scheme is the unrestricted one that the antinomies discredit. | |
| From: Willard Quine (The Ways of Paradox [1961], p.16) | |
| A reaction: You can either takes this free-far-all version of set theory, and gradually restrain it for each specific problem, or start from scratch and build up in safe steps. The latter is (I think) the 'iterated' approach. |
| 21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
| Full Idea: In the case of Russell's antinomy, the tacit and trusted pattern of reasoning that is found wanting is this: for any condition you can formulate, there is a class whose members are the things meeting the condition. | |
| From: Willard Quine (The Ways of Paradox [1961], p.11) | |
| A reaction: This is why Russell's Paradox is so important for set theory, which in turn makes it important for the foundations of mathematics. |
| 3336 | Two things can never entail three things [Quine, by Benardete,JA] |
| Full Idea: Two things can never entail three things. | |
| From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.17 |