A Wittgensteinian Solution to the Sorites

Abstract

I develop a solution to the Sorites Paradox, according to which a concatenation of valid arguments need not itself be valid. I specify which chains of valid arguments are those that do not preserve validity: those that pass the vague boundary between cases where the relevant concept applies and cases where that concept does not apply. I also develop various criticisms of this solution, and show why they fail; basically, they all involve a petitio at some stage. I criticize the conviction that if every short argument in a long concatenated argument is valid, so is the long argument: it is, I argue, the result of an unjustified generalization from the case of arguments that do not employ vague concepts (as in mathematics) to arguments that do employ them. My approach is Wittgensteinian in its ‘leaving everything as it is’, in its claiming that the ‘beginning’ has been searched too far back (see paper’s epigraph), and in its claim that the paradox was generated by a misapplication of a partial picture of the behaviour of arguments. I conclude my paper by comparing and contrasting my approach to the few precedents found in the vagueness literature, and by answering a few additional objections that were raised there.