display all the ideas for this combination of texts
3 ideas
| 15049 | Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett] |
| Full Idea: The anti-realist view undercuts the ground for accepting bivalence. ...Acceptance of bivalence should not be taken as a sufficient condition for realism. ..They accept the weaker principle that unambiguous statements are determinately true or not true. | |
| From: Michael Dummett (Realism and Anti-Realism [1992], p.467) | |
| A reaction: [cited by Kit Fine, when discussing anti-realism] I take it be quite an important component of realism that there might be facts which will never be expressed, or are even beyond our capacity to grasp or express them |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |