Sorites Paradox

2014190046 – DaYe Shin
Professor Colin Caret
World Philosophy (UIC1901-03)
October 31th 2014
Vagueness: The Sorites Paradox and Supervaluationism Vagueness is common and pervasive in our everyday use of language. Being bald, tall or red are all vague concepts which are used without being detected as such. Vagueness is caused by “borderline cases”, cases in which “we do not know what to say, despite having all the information that would normally fix the correct verdict” (Paradoxes, p.41). To illustrate, it is not stipulated as to which boundary a person should be lacking in hair in order to be described as “bald.” If people with varying numbers of hair were to line up, one could not possibly designate a person to be the criterion for differentiating
bolds from non-bolds. It is difficult to determine if the concept “boldness” is applicable to the person standing somewhere in the middle of the line. Posing negligible hindrance to daily communications, vagueness seems to be a trivial matter; however, to one’s surprise, it has triggered considerable philosophical and ethical issues. Whether abortion is an act of murder, for instance, is controversial because the concept of life-form is vague and indecisive. Lawmakers are prudent with their wordings so as to exclude vagueness in every way.
Thus, vagueness has been a popular subject among scholars upon which elaborate theories and ideas were developed. In this paper, subsequent to describing the Sorites paradox, a
typical example of vagueness, I will evaluate the “Supervaluational Theory” and argue that it is an interesting but incorrect solution to the paradox. “Sorites” is a Greek term for “heap,” and the sorites paradox represents all paradoxes of the kind similar to the aforementioned example of baldness. The border between heaps and non-heaps is indiscernible, so a heap of sand will always remain as a heap even if a single grain of sand is repeatedly removed from the heap. The logic behind is based on the “principle of tolerance”, which denotes that “if an n-grained collection can make a heap, then so can an n-1 grained collection” (Paradoxes, p.49). In other words, the difference of a single grain does not draw a clear distinction as to which extent the concept “heap” could be applied, leading to the counter-intuitive conclusion that all collections of grains of sand are heaps. Facing a paradox, one could either accept the conclusion, or try to find a fallacy in the structure of its argument (Paradoxes, p.47). Since the sorites paradox entails an undeniably wrong conclusion, the Supervaluational theory attempts to challenge one of its premises to solve the paradox.
The supervaluationism is derived from semantic theories which ascribe vagueness to the “incompleteness of meaning” (Paradoxes, p.42).
To clarify, vagueness occurs because the language fails to cover all the cases to which a concept might apply. Hence, supervaluationists assert that each and every case of a concept should be subjected to a series of “sharpening” or “precisification,” a function which fills in the undetermined gaps within the concept. Symbolizing a sharpening as S, if an object is definitely Y, based on actual use, it must satisfy S(Y). If it is definitely not Y, then it must not satisfy S(Y). S(Y) must decide for every case whether or not it satisfies the concept. According to the logic, a sentence is super-true if and only if it is true on every sharpening, and false vice versa. Borderline cases, however, could be decided differently on different sharpenings. In such cases, the sentence is “neither true nor false.” The statement that “a person with absolutely no hair is bald” is super-true, whereas a person with n hairs could be bald or not depending on whether a sharpening larger than the number n is applied. In this regard, the premise of the sorites paradox that “if n-grained collection of sand is a heap, then so is n-l grained collection” does not hold because it could be true on one sharpening but false on another. Intriguingly, supervaluationism rejects the principle of bivalence, the dichotomy between truth and falsity, allowing for the intermediate
cases. Nevertheless, supervaluationists claim that there is a border drawn somewhere on every sharpening at the same time by referring to line-drawing sorites reasoning. In this reasoning, a series of similar cases are paired up as such: X1⇔X2⇔…Xn⇔Xn+1. Among the pairs, there is some point in which Xk is Y but Xl is not Y, and this is where the precise border is supposed to lie. This leaves room for much confusion: supervaluationists advocate the existence of borders, indicating that a sentence should be either true or false, yet accept that it could be neither true nor false. They refute such a criticism by highlighting that a border does exist, but it is implausible to pinpoint the one definite border on which every sharpening forms a consensus. Such an explanation is confronted with another problem of “higher-order vagueness,” which is one of the most significant criticisms that undermine the supervaluational theory. Higher-order vagueness “presupposes that the notion of a sharpening is precise, yet it seems that the notion itself is vague” (Paradoxes, p.55). It points out that the sharpening is an open-ended process which could continue perpetually, bringing about the hierarchy of borderline cases; that is, there may be borderline cases of borderline cases. To elucidate, the borderline cases are already vague, but the vagueness is aggravated as it is unclear as to where the vagueness begins; being “vague” is vague. For example, orange could be a borderline case for red, but orange itself has a variety of shades that are borderline cases of being orange. In this case, infinite process of sharpening could take place, and by embracing numerous borders, supervaluationism runs the risk of denying the truth value of a concept. A sentence is super-true if and only if it is true on every sharpening, but one cannot ascertain whether all sharpenings possible have been applied or not. However, it is irrefutable that definite cases which are perfectly applicable to a concept exist, as is with the case of a completely hairless man being bold.
Overall, although supervaluationism is a thought-provoking theory that should not be set aside, it turns out to be inadequate in resolving the paradox. As demonstrated by the higher-order vagueness, it gives rise to more and more borderline cases, which are the very cause of vagueness and makes further delay in actual eradication of vagueness. Instead of directly responding to the paradox, supervaluationism creates further redundant intermediates between the true and false, ultimately reaching the conclusion that the sorites paradox is inevitable. I believe that the fundamental key to solving the sorites paradox lies in drawing a precise, unitary border, but supervaluationism evades the task of doing so. Therefore, the supervaluational theory is an insufficient way of responding to the sorites paradox.

Works cited
Sainsbury, R. M. Paradoxes. 3rd ed. Cambridge [Cambridgeshire: Cambridge UP, 1988. Print.]

Works consulted
Sorensen, Roy. Vagueness. The Stanford Encyclopedia of Philosophy (Winter 2013 Edition)
Sainsbury, Mark. Is There Higher-Order Vagueness?. Oxford University Press, 1991
Wright, Crispin. The Illusion of Higher-Order Vagueness. Oxford University Press, 2009.
Keefe, Rosanna. Vagueness: Supervaluationism. Philosophy Compass, 2008.