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. |
| 6262 | We lack some sense or other, and hence objects may have hidden features [Montaigne] |
| Full Idea: We may all lack some sense or other; because of that defect, most of the features of objects may be concealed from us. | |
| From: Michel de Montaigne (Apology for Raymond Sebond [1580], p.0666) | |
| A reaction: This strikes me as simple, straightforward common sense, and right. I cannot make sense of the claim that reality really is just the way it appears. We do not have a built-in neutrino detector, for example. |