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Showing posts from August, 2011

Yablo's paradox: Bueno & Colyvan vs. Ketland

I am looking at the debate between Jeff Ketland on one hand and Bueno & Colyvan on the other, pertaining to the consistency of Yablo sentences. (See HERE for a wider list of references compiled by Jeff. While I think B&C have a few brilliant remarks, I also think their arguments are sometimes unsatisfactory, and I want to comment on these points. This is all rather sketchy, and presumably half-baked.
1. The provability of the existence of the Yablo sequence.
B&C complain: "it's not clear...how we know that the Yablo list exists. Priest's argument seems to presuppose the existence of the list, in order to establish that to derive a contradiction from the latter, a fixed-point construction is required." (Analysis 63, 156).For me, it seems like a very unusal approach to the diagonal lemma (DL). DL is an existence claim: it says that given a certain formula, another formula satisfying a certain equivalence exists. My impression is that DL is used by Priest to pr…