I’m quite tempted by the view that it is indeterminate that might be one of those fundamental, brute bits of machinery that goes into constructing the world. Imagine, for example, you’re tempted by the thought that in a strong sense the future is “open”, or “unfixed”. Now, maybe one could parlay that into something epistemic (lack of knowledge of what the future is to be), or semantic (indecision over which of the existing branching futures is “the future”) or maybe mere non-existence of the future would capture some of this unfixity thought. But I doubt it. (For discussion of what the openness of the future looks like from this perspective, see Ross and Elizabeth’s forthcoming Phil Studies piece).
The open future is far from the only case you might consider—I go through a range of possible arenas in which one might be friendly to a distinctively metaphysical kind of indeterminacy in this paper—and I think treating “indeterminacy” as a perfectly natural bit of kit is an attractive way to develop that. And, if you’re interested in some further elaboration and defence of this primitivist conception see this piece by Elizabeth and myself—and see also Dave Barnett’s rather different take on a similar idea in a forthcoming piece in AJP (watch out for the terminological clashes–Barnett wants to contrast his view with that of “indeterminists”. I think this is just a different way of deploying the terminology.)
I think everyone should pay more attention to primitivism. It’s a kind of “null” response to the request for an account of indeterminacy—and it’s always interesting to see why the null response is unavailable. I think we’ll learn a lot about what the compulsory questions the a theory of indeterminacy must answer, from seeing what goes wrong when the theory of indeterminacy is as minimal as you can get.
But here I want to try to formulate a certain kind of objection to primitivism about indeterminacy. Something like this has been floating around in the literature—and in conversations!—for a while (Williamson and Field, in particular, are obvious sources for it). I also think the objection if properly formulated would get at something important that lies behind the reaction of people who claim *just not to understand* what a metaphysical conception of indeterminacy would be. (If people know of references where this kind of idea is dealt with explicitly, then I’d be really glad to know about them).
The starting assumption is: saying “it’s an indeterminate case” is a legitimate answer to the query “is that thing red?”. Contrast the following. If someone asks “is that thing red?” and I say: it’s contingent whether it’s red”, then I haven’t made a legitimate conversational move. The information I’ve given is simply irrelevant to it’s actual redness.
So it’s a datum that indeterminacy-answers are in some way relevant to redness (or whatever) questions. And it’s not just that “it is indeterminate whether it is red” has “it is red” buried within it – so does the contingency “answer”, but it is patently irrelevant.
So what sort of relevance does it have? Here’s a brief survey of some answers:
(1) Epistemicist. “It’s indeterminate whether p” has the sort of relevance that answering “I don’t know whether p” has. Obviously it’s not directly relevant to the question of whether p, but at least expresses the inability to give a definitive answer.
(2) Rejectionist (like truth-value gap-ers, inc. certain supervaluationists, and LEM-deniers like Field, intuitionists). Answering “it’s indeterminate” communicates information which, if accepted, should lead you to reject both p, and not-p. So it’s clearly relevant, since it tells the inquirer what their attitudes to p itself should be.
(3) Degree theorist (whether degree-supervaluationist like Lewis, Edgington, or degree-functional person like Smith, Machina, etc). Answering “it’s indeterminate” communicates something like the information that p is half-true. And, at least on suitable elaborations of degree theory, we’ll then now how to shape our credences in p itself: we should have credence 0.5 in p if we have credence 1 that p is half true.
(4) Clarification request. (maybe some contextualists?) “it’s indeterminate that p” conveys that somehow the question is ill-posed, or inappropriate. It’s a way of responding whereby we refuse to answer the question as posed, but invite a reformulation. So we’re asking the person who asked “is it red?” to refine their question to something like “is it scarlet?” or “is it reddish?” or “is it at least not blue?” or “does it have wavelength less than such-and-such?”.
(For a while, I think, it was assumed that every series account of indeterminacy would say that if p was indeterminate, one couldn’t know p (think of parallel discussion of “minimal” conceptions of vagueness—see Patrick Greenough’s Mind paper). If that was right then (1) would be available to everybody. But I don’t think that that’s at all obvious — and in particular, I don’t think it’s obvious the primitivist would endorse it, and if they did, what grounds they would have for saying so).
There are two readings of the challenge we should pull apart. One is purely descriptive. What kind of relevance does indeterminacy have, on the primitivist view? The second is justificatory: why does it have that relevance? Both are relevant here, but the first is the most important. Consider the parallel case of chance. There we know what, descriptively, we want the relevance of “there’s a 20% chance that p” to be: someone learning this information should, ceteris paribus, fix their credence in p to 0.2. And there’s a real question about whether a metaphysical primitive account of chance can justify that story (that’s Lewis’s objection to a putative primitivist treatment of chance facts).
The justification challenge is important, and how exactly to formulate a reasonable challenge here will be a controversial matter. E.g. maybe route (4), above, might appeal to the primitivist. Fine—but why is that response the thing that indeterminacy-information should prompt? I can see the outlines of a story if e.g. we were contextualists. But I don’t see what the primitivist should say.
But the more pressing concern right now is that for the primitivist about indeterminacy, we don’t as yet have a helpful answer to the descriptive question. So we’re not even yet in a position to start engaging with the justificatory project. This is what I see as the source of some dissatisfaction with primitivism – the sense that as an account it somehow leaves something unimportant explained. Until the theorist has told me something more I’m at a loss about what to do with the information that p is indeterminate
Furthermore, at least in certain applications, one’s options on the descriptive question are constrained. Suppose, for example, that you want to say that the future is indeterminate. But you want to allow that one can rationally have different credences for different future events. So I can be 50/50 on whether the sea battle is going to happen tomorrow, and almost certain I’m not about to quantum tunnel through the floor. Clearly, then, nothing like (2) or (3) is going on, where one can read off strong constraints on strength of belief in p from the information that p is indeterminate. (1) doesn’t look like a terribly good model either—especially if you think we can sometimes have knowledge of future facts.
So if you think that the future is primitively unfixed, indeterminate, etc—and friends of mine do—I think (a) you owe a response to the descriptive challenge; (b) then we can start asking about possible justifications for what you say; (c) your choices for (a) are very constrained.
I want to finish up by addressing one response to the kind of questions I’ve been pressing. I ask: what is the relevance of answering “it’s indeterminate” to first-order questions? How should I alter my beliefs in receipt of the information, what does it tell me about the world or the epistemic state of my informant?
You might be tempted to say that your informant communicates, minimally, that it’s at best indeterminate whether she knows that p. Or you might try claiming that in such circumstances it’s indeterminate whether you *should* believe p (i.e. there’s no fact of the matter as to how you should shape your credences on the question of whether p). Arguably, you can derive these from the determinate truth of certain principles (determinacy, truth as the norm of belief, etc) plus a bit of logic. Now, that sort of thing sounds like progress at first glance – even if it doesn’t lay down a recipe for shaping my beliefs, it does sound like it says something relevant to the question of what to do with the information. But I’m not sure about that it really helps. After all, we could say exactly parallel things with the “contingency answer” to the redness question with which we began. Saying “it’s contingent that p” does entail that it’s contingent at best whether one knows that p, and contingent at best whether one should believe p. But that obviously doesn’t help vindicate contingency-answers to questions of whether p. So it seems that the kind of indeterminacy-involving elaborations just given, while they may be *true*, don’t really say all that much.
J Robert G Williams 