The Sorites is Not Successful

There are three facts supporting the falsity of the sorites. The first is that the argument sounds “funny” or “suspicious” to the untrained ear, and there is a fairly good track-record of errors being uncovered in “funny”-sounding would-be paradoxes. The second is that one feels no compulsion to believe the contradic- tory conclusion of the argument, which suggests that the argument does not, after all, conform to the rules governing vague language. The third is that there is simply no independent evidence that vague language is incoherent. Let us consider each in detail.

Circumstantial evidence in favor of our lumping the sorites with Zeno’s para- dox lies in how similar are our common-sense reactions to the two arguments. It takes a sophisticated intellect to believe the sorites, and this distinguishes it from the liar paradox while drawing it closer to Zeno’s arguments. Just as no normal person has ever believed the sorites argument to show that our everyday vague concepts are incoherent3_{, no one has earnestly believed Zeno’s paradoxes} to show that our concepts of space and time are incoherent 4_{. To the average} person, living in Alexandria as in New York, Zeno’s paradox and the sorites sound “wrong”; they appear “funny.” As with simpler false paradoxes, such as the paradox of the preface or the paradox of the surprise quiz, the average per- son detects that there is something “queer” about Zeno’s reasoning, though he cannot quite put it into words or articulate a refutation. Indeed, when told the accepted refutation, his head may very well spin, but nevertheless, his implicit knowledge of the operation of his concepts is sufficient for him to recognize that such reasonings as appear in these arguments are illicit.

Now, compare these false paradoxes to the liar paradox or to Russell’s anti- nomy. No one finds anything wrong with the argument that the liar’s sentence must be both true and false if it is either, or with the argument that the Russell set must be both a member of itself and not a member of itself. A general distaste for admitting the existence of paradox, then, cannot be what is respon- sible for the widespread skepticism concerning the sorites. One suspects that, like Zeno’s paradox, the paradox of the preface, and the paradox of the surprise quiz, our reluctance to accept the sorites — our feeling that there is something “wrong” with it — is due to our detecting something genuinely hazy within the reasoning, something which our semantic theory of vague predicates simply has yet to draw out into the light of day.

Of course, it could also be that the sorites argument sounds “funny” merely because its way of reasoning with vague predicates, though legitimate, is unfa- miliar. We don’t naturally employ such arguments in our daily life, and so the sorites strikes us as a novelty. There is, however, a more direct line of evidence that the sorites fails. Recall that the sorites beginning this section intends to show that the rules governing the predicate “tall” commit a speaker to two

3_{“Normal” here means, approximately, not a linguist or philosopher, and certainly not}

Michael Dummett or Peter Unger; see, for example, Unger 1979.

4_{Except for maybe Zeno, of course. But, Diogenes himself replied that “it is solved by}

contradictory statements. For the argument to succeed, it must construct from these rules a deduction that a five foot man is both tall and not tall. But, no speaker accepts the constructed deduction that a person five feet in height is tall. No one feels in the least that they must apply the adjective “tall” to Michael Jackson simply because there is a sorites series linking him to Michael Jordan. Indeed, despite the existence of that series, speakers feel compelled to describe Michael Jackson as “not tall” and to disagree with anyone who believes otherwise. However, if the meaning of “tall” sanctioned the deduction used in the sorites argument, people should recognize it as providing them reason for asserting that Michael Jackson is tall. That they don’t demonstrates it doesn’t. Thus, the dirty fact that average speakers are never led by the sorites into the assertion that Michael Jackson is tall reveals that the argument does not truly conform to the principles governing vague predicates, contrary to its aims. Again, the sorites can be contrasted with the liar paradox. Everyone agrees with the reasoning behind the liar paradox; everyone agrees that it shows there to be equal reason for labeling the liar’s sentence ‘true’ and for labeling it ‘false’. Thus, the liar paradox, by creating a situation in which people honestly perceive themselves as committed to two contradicting propositions, succeeds in its aims, while the sorites, by not creating such a situation, fails.

Both of these points are compactly and acutely summarized in Wright 1987. “This brings us to the third, and, I think, a decisive objection to (the view that the sorites genuinely creates a paradox – SC). I do not see how we can rest content with the idea that certain implicitly known semantic rules are incoherent whennobody’sreaction, on being pre- sented with the purported demonstration of the inconsistency, i.e., the paradox – even if they can find no fault with it – is to lose confi- dence in the unique propriety of the response – e.g. “That’s orange” – which the demonstration seems to confound. Think of your re- action when, having received as explanation of the notion of class only the usual informal patter plus the axioms of naive set theory, you first confronted Russell’s paradox. If, which is unlikely, you held any intuitive conviction about whether Russell’s class was a member of itself, you will have been forced to recognize an exact parity in the opposing case; and the effect should have been to cause you to realize that there is just no view to take on the matter before some refinement of the notion of class has been made. But that is exactly

not our response to the sorties paradox for “red”. Our conviction of the correctness of the non-inferential ingredient in the contradiction is lefttotally undisturbed. So far from bringing us to recognize that, pending some refinement in the meaning of “red”, there is just no such thing as justifiably describing something as “red” or not, our conviction is that no one ought to be disturbed by the paradox – and this conviction is not based on certainty that we shall be able to disclose some simple fallacy. If the rules for the use of “red” really do sanction the paradox, why do we have absolutely no sense of dis-

turbance, no sense that areal casehas been made for the inferential ingredient at all? . . . A different account is called for.” (Wright 1987) Finally, as was already mentioned, the success of the sorites argument would imply that an activity which can largely be described via consistent sets of rules is nevertheless governed by rules which are inconsistent. It would be an incred- ible feat for our use of vague language to have the coherency it is observed to have, were the principles underlying it to have none. After all, the only situ- ations in which this supposed incoherency is claimed to reveal itself are those in which sorites series are exhibited. Why doesn’t the inconsistency become apparent anywhere else? Recall, too, that not even these situations reveal a genuine inconsistency of use, since speakers never accept the contradictory con- clusion of the sorites argument. At best, the sorites reveals a situation in which it is impossible to justify one’s consistent behavior, not in which one behaves inconsistently. So, aside from the fact that no one has yet convincingly refuted the sorites argument, there is no evidence to support the claim that vague lan- guage is governed by an inconsistent logic, and so the task of explaining how, despite its overwhelming appearance of consistency, the logic of vague predicates is inconsistent, looks uniquely unpromising.