There is No Paradox of Logical Validity

A number of arguments, including (Whittle 2004), (Field 2008), (Shapiro 2012), and (Beall & Murzi 2012), have been put forward for the claim that logical validity is plagued by a paradox (or paradoxes) similar to the more well-known paradoxes that afflict notions such as truth, knowledge, or set. These claims are incorrect. As I will show here, there is no paradox of logical validity. In addition, I will demonstrate that a recent argument (Ketland 2012) against the existence of a paradox of logical validity, although promoting the right conclusion, nevertheless provides a partially mistaken picture of what goes wrong in the arguments for the existence of such a paradox. Further, and perhaps most importantly, this analysis of the purported paradox of logical validity brings with it important lessons regarding the kinds of inferences that can be taken to be logically valid (versus, e.g., merely truth-preserving). There is general agreement amongst those who have put forward one or another version of the paradox that the stakes are high. Of course, almost no one in this group agrees on exactly what these high stakes are: Whittle argues that the paradox shows that a dialethiest, such as (Priest 2002), will need to appeal to a Tarski-like hierarchy of logical validity predicates; Field uses the paradox to (among other things) suggest that validity does not preserve truth; and Shapiro and Beall & Murzi argue (independently) that the paradox forces us to give up the structural rule of contraction.1 Thus, the conclusions drawn from the purported paradox of validity are varied, and in the latter case, at least, the paradox is not the only evidence marshalled for the conclusion in question. Thus, I will not attempt to examine any of these further claims directly. Instead, I will be content to show that there is no paradox of logical validity. As a result, whatever other arguments one might have, this supposed paradox provides no additional support for the views just listed.