The Journal of Philosophy Indeterminacy and Incomplete Definitions* * for Helpful Comments and Discussion, I Am Indebted To

Intuitively, a question is indeterminate just in case it is unsettled, not merely epistemically, but metaphysically. We ordinarily ascribe indeterminacy by saying that there is no fact of the matter. Some say, for instance, that there is no fact of the matter how many mountains exist. The topographical facts appear to settle that there are some mountains, but not how many. While it can seem obvious that certain questions are indeterminate, it is remarkably easy, expanding on arguments by Paul Horwich and Timothy Williamson, to reduce an arbitrary ascription of indeterminacy to absurdity. Suppose, for reductio, that it is indeterminate— that is, metaphysically unsettled—whether Harry is bald. Because it is metaphysically unsettled whether Harry is bald only if it is not metaphysically settled that Harry is bald and not metaphysically settled that Harry is not bald, it is not metaphysically settled that Harry is bald and not metaphysically settled that Harry is not bald. Because it is true that Harry is bald only if it is metaphysically settled that he is bald, and because it is true that Harry is not bald only if it is metaphysically settled that he is not bald, it is not true that Harry is bald and not true that Harry is not bald. Because Harry is bald only if it is true that he is bald, and because Harry is not bald only if it is true that he is not bald, Harry is not bald and Harry is not not bald. This is a contradiction. Hence, our supposition is false. Moreover, because the question of whether Harry is bald was chosen arbitrarily, the argument generalizes: indeterminacy is impossible.