display all the ideas for this combination of texts
2 ideas
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
Full Idea: We can give an exhaustive account of the identity of the empty set and its singleton without mentioning infinite sets, and it might be possible to defend the view that one natural number depends on its predecessor but not vice versa. | |
From: Øystein Linnebo (Structuralism and the Notion of Dependence [2008], V) | |
A reaction: Linnebo uses this as one argument against mathematical structuralism, where the small seems to depend on the large. The view of sets rests on the iterative conception, where each level is derived from a lower level. He dismisses structuralism of sets. |
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 |