Now Playing: REPOSTED
Topic: GENERAL LOGIC
Yablo's paradox rides again: a reply to Ketland
By Otavio Bueno & Mark Colyvan
Yablo ' s paradox is generated by the following (infinite) list of sentences (called Yablo's list):(S1) For all k> 1, Sk is not true.
(S2) For all k> 2, Sk is not true.
(S3) For all k> 3, Sk is not true.
(Sn) For all k>n, Sk is not true.
A little reflection reveals that this list is paradoxical. The source and nature of the paradox has been the focus of a fascinating debate. The crucial issue, of course, is whether Yablo's paradox involves circularity. Stephen Yablo (1993), Roy Sorensen (1998), and Bueno and Colyvan (2003b) have argued that the Yablo list generates a liar-like paradox without circularity. In the other camp are Graham Priest (1997) and JC Beall (2001), who argue that the paradox involves a fixed-point construction and therefore is circular. In Bueno and Colyvan (2003a), we respond by showing that there is a way of deriving a contradiction from the Yablo list without invoking any fixed-point construction and so, it would seem, the paradox does not essentially involve circularity.
In a recent paper, Jeffrey Ketland (2004) argues that our response is incorrect, and claims that the derivation presented in our paper is invalid.