A Reply to Beall and Colyvan

TLDR: In this article, a paraconsistent approach to the Sorites paradox is proposed, based on the assumption that the paradoxes of self-reference are best dealt with by a paraconistent approach.

Abstract: Beall and Colyvan (2001) extend the debate over paraconsistent approaches to the Sorites Paradox, offering additional argument for and additional argument against pursuing such an approach. Additional argument for a paraconsistent approach comes from considerations of simplicity which stress, amongst other things, uniformity of approach. This, coupled with the assumption that the paradoxes of self-reference are best dealt with by a paraconsistent approach, gives weight to the thought that, all other things being equal, one should pursue paraconsistent solutions to Sorites paradoxes as well. However, as Beall and Colyvan themselves note (see their footnote 5), all other things may not be equal. One does not need to look far to find independent arguments for paracompleteness -presupposition failure, reference failure, future contingents, etc. If any such argument is found compelling then similar considerations to those adduced by Beall and Colyvan will push in the opposite direction to paraconsistency, namely towards paracompleteness. On this plausible view paraconsistent logics are simply not able to 'do it all' and so the question re-arises as to whether a paraconsistent approach to the Sorites is superior. (Interestingly, if the Sorites Paradox could be shown to be 'of a kind' with the paradoxes of self-reference, then a more specific uniformity argument could be mounted in favour of a paraconsistent approach to paradoxes 'of this kind'.) In the end, considerations of uniformity may simply amount to an argument in favour of an even weaker paralogical approach-that is, one that is both paraconsistent and paracomplete.1