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.
Gist of Idea
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism
Source
Peter Koellner (On the Question of Absolute Undecidability [2006], Intro)
Book Reference
-: 'Philosophia Mathematica' [-], p.2