Combining Texts

Ideas for 'On the Question of Absolute Undecidability', 'Letters to Hegel' and 'Causation and Laws of Nature'

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3 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
14607 T adds □p→p for reflexivity, and is ideal for modeling lawhood [Schaffer,J]
     Full Idea: System T is a normal modal system augmented with the reflexivity-generating axiom □p→p, and is, I think, the best modal logic for modeling lawhood.
     From: Jonathan Schaffer (Causation and Laws of Nature [2008], n46)
     A reaction: Schaffer shows in the article why transitivity would not be appropriate for lawhood.
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)