A Minimal Characterization of Indeterminacy
Taylor (David E.)
Source: Philosophers' Imprint, Vol. 18, No. 5, March 2018, pp. 1-25
Paper - Abstract

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Author's Introduction1

  1. From time to time we find ourselves confronted with a question which, though perfectly intelligible on its face, admits of no determinate answer. For example: You and I are discussing the finer points of the 2012 presidential election. We both agree that, had Romney won, Obama would have conceded graciously, and that if Obama had conceded, Biden would have been by his side. But now you wonder: if Romney had won, would Biden have been standing to the left or to the right of Obama during his concession? No answer is forthcoming. It’s not just that we cannot know where exactly Biden would have been standing in this counterfactual scenario, but rather that there is, in some basic sense, no relevant fact to be known.
  2. To acknowledge such cases is to recognize that, for certain matters p, it is simply indeterminate — there is no fact of the matter — whether p. With respect to our example, it is indeterminate whether Biden would have been standing to the left or to the right of Obama, had Romney won.
  3. Examples of indeterminacy abound. Some we run up against in the course of ordinary conversation or experience. Is her shirt red or orange? At what exact point did we leave Iowa and enter Minnesota? Would Biden have stood to the left or to the right? Others are more theoretical and contentious. Does ‘gavagai’ translate as ‘rabbit’ or as ‘undetached rabbit part’? Is A the same person as B or as C? Do these two objects compose to make a third?
  4. The phenomenon of indeterminacy has received considerable attention in the past few decades. This attention has tended to focus on the following two questions:
    1. First, what is the logic of indeterminacy? Specifically, what revisions to classical logic and semantics (if any) are required to accommodate indeterminate sentences in our language?
    2. Second, what is the nature or source of indeterminacy? Specifically, is indeterminacy a semantic or a metaphysical phenomenon? Is it a product of how we represent the world, or an objective feature of the world itself?
  5. These are both good questions, and they deserve good answers. But it won’t be my goal to weigh in on either of them here. Instead my purpose in this paper is to introduce, motivate and go some way toward answering a new, third question about indeterminacy. This question concerns neither the logic nor the metaphysics of indeterminacy (at least not directly), but rather has to do with what we might call a minimal characterization of indeterminacy.
  6. A minimal characterization, to a first approximation, is a set of necessary and sufficient conditions that captures all and only the genuine cases of indeterminacy and which is neutral between the different substantive views regarding the underlying nature and logic of indeterminacy. It’s the sort of thing that, ideally, you and I, no matter our differences in opinion regarding the nature and logic of indeterminacy, could both agree applies in exactly the cases that we think exhibit the phenomenon whose nature and logic is at issue. Hence the question with which I’m concerned: How might we give a proper minimal characterization of indeterminacy?
  7. To my mind, there has been practically no attention paid to this question in the literature on indeterminacy. That’s a shame. I think a minimal characterization, properly formulated, could have great theoretical value for debates about indeterminacy. It’s something we should be just as concerned with as we are with thinking about the nature and logic of indeterminacy. Or so I hope to show in this paper. My plan will be as follows:
    1. In the next section I’ll say a bit more about what I mean by a minimal characterization (henceforth, “MC”).
    2. In §3 I’ll then outline a number of different ways in which I think providing such an MC has theoretical value.
    3. In §§4 and 5 I will establish some desiderata for a satisfactory MC, and use these to motivate a general strategy for formulating an MC.
    4. With these tools in hand, I will, in §6, look at some initially plausible proposals of MCs and argue that each is unsatisfactory, failing to meet one or another of our established desiderata.
    5. Finally, in §§7–9 I will sketch the beginnings of my own MC and respond to some objections.


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