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3 ideas
18350 | Truth-maker theorists should probably reject the converse Barcan formula [Rami] |
Full Idea: There are good reasons for the truth-maker theorist to reject the converse Barcan formula. | |
From: Adolph Rami (Introduction: Truth and Truth-Making [2009], note 16) | |
A reaction: In the text (p.15) Rami cites the inference from 'necessarily everything exists' to 'everything exists necessarily'. [See Williamson 1999] |
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) |