display all the ideas for this combination of texts
3 ideas
| 10928 | Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine] |
| Full Idea: Perhaps there is no objection to quantifying into modal contexts as long as the values of any variables thus quantified are limited to intensional objects, but they also lead to disturbing examples. | |
| From: Willard Quine (Reference and Modality [1953], §3) | |
| A reaction: [Quine goes on to give his examples] I take it that possibilities are features of actual reality, not merely objects of thought. The problem is that they are harder to know than actual objects. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |