Circularity and Paradox in Cook's proposal

PAILOS, FEDERICO MATÍAS

Oxford

Encuentro; Third New College Logic Meeting; 2012

New College, Oxford University

The main thesis of this work is as follows: there are versions of Yablo´s paradox that, if Cook is right about the non-circular character of his version of it, are truly paradoxical and genuinely non-circular, and Cook´s version of Yablo´s paradox is one of them. Here I will not evaluate the "circular" or "non-circular" side of Cook´s proposal. In fact, I think that he is right about it, and that his version of Yablo´s list is non-circular. But is it paradoxical? In order to be so, the principles that lead to (i) the derivation of a contradiction, or (ii) the impossibility to give a stable assignment of truth values to the relevant set of sentences, must be acceptable. I will explore two ways to argue that they are not. I will conclude that these attempts lead to a very narrow conception of a theory of truth, or to deny that a paradigmatic case of paradox, such as the "Old-Fashioned Liar," is truly paradoxical.