Yablo's Paradox and omega-Paradoxes

BARRIO, EDUARDO ALEJANDRO

Logic and Philosophy of Logic: Recent Trends in Latin America and Spain

Collage Pu

Año: 2017; p. 21 - 40

In this paper, I analyze the paradox of Yablo: a semantic antinomy that involves an infinite sequence of sentences each of them claims that all linguistic items occurring later in the series are not truth. At least on a superficial level, the paradox does not seem to implicate any circularity. And this would mean that the set of sentences of Yablo shows that circularity is not a necessary condition to paradoxes. I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a correct representation of that paradox in first-order arithmetic, there are some technical results that give rise to doubts about this approach. In particular, one of the aims of this work is to show that the formalization of this paradox in first order arithmetic is omega-inconsistent, even though the set of this sentences is consistent and has a (non-standard) model. Then, the plan is to draw the philosophical consequences of this result. Further, I am going to take into account Priest?s point according to which this representation is also circular according to the same standard that the Liar sentence. All these reasons justify the necessity to look for alternative formalizations to the paradox. So, another proposal of this paper is also to consider different versions of Yablo?s paradox that do not use first order arithmetic. Then, I will show some problems connected with such formulations. I will argue that there are reasonable doubts to adopt any of these formalizations as modeling the set of sentences of Yablo.