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3 ideas
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) |
10653 | Maybe set theory need not be well-founded [Varzi] |
Full Idea: There are some proposals for non-well-founded set theory (tolerating cases of self-membership and membership circularities). | |
From: Achille Varzi (Mereology [2003], 2.1) | |
A reaction: [He cites Aczel 1988, and Barwise and Moss 1996] |