3 ideas
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
| From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
| A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
| 13128 | 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins] |
| Full Idea: 'Ultimate sortals' are said to be non-subordinated, disjoint from one another, and uniquely paired with each object. Because of this, the ultimate sortal cannot be a satisfactory explication of the notion of an ontological category. | |
| From: comment on David Wiggins (Identity and Spatio-Temporal Continuity [1971], p.75) by Jan Westerhoff - Ontological Categories §26 | |
| A reaction: My strong intuitions are that Wiggins is plain wrong, and Westerhoff gives the most promising reasons for my intuition. The simplest point is that objects can obviously belong to more than one category. |
| 10805 | A sentence should be recarved to reveal its content or implication relations [Yablo] |
| Full Idea: A sentence invites recarving iff it will then do better justice to the internal structure of its content and/or its implication relations. | |
| From: Stephen Yablo (Carving Content at the Joints [2002], §11) | |
| A reaction: This invites human intervention in a logical process (by choosing which recarvings to do, instead of allowing all equivalences to generate them). He seems to think we should abstract in order to reveal logical form. |