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Ideas for 'On the Question of Absolute Undecidability', 'Humean metaphysics vs metaphysics of Powers' and 'Remarks on axiomatised set theory'

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3 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

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)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879	Axiomatising set theory makes it all relative [Skolem]
	Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation.
	From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296)