V7079 UNIVERSITY OF SUSSEX BA FIRST YEAR EXAMINATION 2019/20 August 2020 (A3) PARADOX AND ARGUMENT Essay (1000 words) In no more than 1000 words, explain and evaluate the epistemic solution to the Sorites Paradox Vagueness is ubiquitous in our everyday language. This can be illustrated by the Sorites Paradox: (SP) (1) 1,000,000 grains of sand is a heap. (2) If n grains of sand is a heap, then n-1 grains of sand is also a heap. (3) 999,999 grains of sand is a heap. Applying (2) repeatedly, we get problematic conclusions: (n) 1 grain of sand is a heap. (n+1) 0 grains of sand is a heap. Something has gone wrong here, but how? The possibilities are either that (a) the conclusion doesn't follow from the premises, or (b) not all premises are true. Immediately we can rule out (a), since the argument takes the very safe form of modus ponens . This leaves us with (b). 1 Now it looks like (SP)(2) is dubious: it does not seem to hold true for just any number n, since otherwise we would reach the aforementioned absurd conclusions. This suggests that a boundary, defining a heap, had to be drawn somewhere. But is it possible, and how? Epistemicists assert that there really is a sharp boundary as to what counts as a heap and what does not, only we do not have knowledge of where that is. In other words, instead of addressing the vagueness and the resulting indeterminacy, epistemicists make the problem one about our ignorance. They outright reject (SP)(2), suggesting: (SP) (~2) There is an n such that n grains of sand is a heap, but n-1 grains of sand is not. We just don't know where this n is. This is a rather bold solution as it does not come to us intuitively (it does away with the apparent vagueness) and requires an element of belief (that it is really the case but we don't and cannot know); it gives rise to some questions: how is the source of our supposed ignorance in borderline cases to be accounted for? Further, what is it that determines the supposed sharp boundaries? Modus ponens is an argument that takes the form: (1) if p, then q; (2) p; so (3) q. 1 Williamson gives the most authoritative epistemicist response. He explains by introducing the notion of margins for error within the framework of our inexact knowledge , asserting that in order 2 for our knowledge of something to hold, we must leave a margin for error (2001, pp. 226): we count as knowing something only if it obtains in all similar cases that fall within the corresponding margin 3 for error. For example, one counts as knowing that Bob, who is a borderline case of tall, is tall, only if this assertion would still hold were Bob shorter by an indistinguishably smaller amount 4 It should be noted that by Williamson's principle, if one's assertion could have been false in situations similar enough to be indistinguishable from the actual case concerned, then one could only be accidentally right at best, and this would not be considered knowledge. This applies neatly to the problem of vagueness, as I shall show: consider again the Sorites Paradox. Suppose the margin for error is 100, i.e. it is indistinguishable to us whether there are n grains of sand or n+100. So for us if n grains is a heap, n-1 grains is also a heap. Suppose also that there is a sharp boundary m, the fewest grains of sand required for a heap. Now if we assert that m grains of sand make a heap, we could have been wrong — since our assertion would no longer be true in a similar case, e.g. had there been m-1 grains. This means that we could only be wrong or accidentally right, thereby inevitably giving rise to our ignorance. Requiring a margin of error thus prevents one's estimate about a borderline case from counting as knowledge — for it is unknowably true or false. Williamson notes that inexactness is in our knowledge (2001, pp. 217), not in things inherently; similarly for vagueness — it is created by limitations in our knowledge, not by reality. It seems, then, the commitment of epistemicists to this ignorance is justified. But this gives rise to issues. What Williamson does here seems merely to be defining away our inscrutable ignorance by introducing a convenient concept — more problematically, the kind of ignorance he deals with is different from what we had expected an explanation for. If, as epistemicists assert, we are ignorant of sharp boundaries of vague predicates, we are indeed ignorant about requirements for things that fall within that boundary, not about things that fall within that boundary , which is what Williamson accounts for: e.g., he makes it a question of whether we'd know the difference had something been marginally shorter, but this is not the sort of ignorance we are concerned with. Further, what is it that determines sharp boundaries? Some (Keefe, 2003, pp. 79) see Williamson's other claim that meaning supervenes on use (2001, pp. 201-203) as a response: it is our use of terms that draws the boundary determining what the vague terms really mean. But we could easily make the objection that this is not how we use vague terms, e.g., as if one hundredth of a centimetre would make someone who is tall short by that mere difference. Keefe (2003, pp. 81) further argues a point about supervenience — for a claim that facts about x supervene on facts about y is not necessarily enough to show how facts about y determine what the facts about x are. This is important because it demonstrates exactly that the fact that use determines meaning will not answer how the sharp boundary to the extension of, e.g., "tall" or "short", are drawn at particular points and not at others. According to Williamson, we have inexact knowledge when our knowledge of something is an 2 estimate that could very well have been wrong in a similar case (so in a sense, we are right by accident), and is thus unreliable, e.g., estimating the number of people in a stadium. Williamson defines "similar cases" to be cases which would be similar enough to the actual case 3 for the difference to be indistinguishable to us; i.e., cases that fall into a range wherein the difference would be indistinguishable to us More intuitively, this is similar to saying that one must know that Bob would not be tall were he 4 marginally shorter The epistemicist solution then seems inadequate in accounting for what it so boldly asserts. But it is an interesting approach that does away with the conventional problems of higher-order vagueness which would be produced if the indeterminacy of vague terms were directly addressed, as well as preserves the law of the excluded middle , allowing one to apply classical logic unlike in 5 other conventional approaches. Bibliography Keefe, R. (2003) Theories of Vagueness . Cambridge: Cambridge University Press, pp. 62-84. Williamson, T. (2001) Vagueness . London: Taylor & Francis, pp. 185-247. The law of the excluded middle states that either a given proposition p, is true, or its negation, ~p, 5 is true, i.e. p v ~p.