more on this theme | more from this thinker
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.
Gist of Idea
'Reflection principles' say the whole truth about sets can't be captured
Source
Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1)
Book Ref
-: 'Philosophia Mathematica' [-], p.13
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |