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 
I don’t think I understand the problem. Maybe it’s just because I can’t quite yet see how learning that p is indeterminate is different from learning any other proposition.
I was envisaging that, even when there are indeterminacies, you can still talk about complete ‘states’ telling me everything there is to know about how things are, including what things are indeterminate (or perhaps it’s better that we don’t use complete states at all, but situations, including incomplete situations to model indeterminacy.) So the information content of ‘it’s indeterminate whether p’ is just the set of states that say p is indeterminate (i.e. the set of situations that neither support p or its negation.) It’s informative because it tells me what the actual situation is like (it’s one of those states that’s indeterminate about p.) Similarly I’d imagine that you could put a probability measure over the maximal states – that this dice will land 6 isn’t decided in the actual situation, but we could find my credence by looking at the proportion of the maximal situations that extend the actual situation in which the dice lands 6. The talk of states and information content doesn’t seem to presuppose that indeterminacy isn’t some kind of primitive. This was my naïve thought: because things look so similar to ordinary cases of learning and assigning credences to propositions, why should it be different here?
Hi Andrew, thanks for this!
Yup, I guess I’d hope that we could treat “it’s indeterminate whether p” as any other proposition when it comes to updating (though it might well be that certain special features of indeterminacy call for various generalizations). But of course, that doesn’t tell us what happens when we do this updating. That’s illustrated by a couple of the more familiar options. Updating by epistemicism indefinite-that-p eliminates worlds where people know the truth-value of p. But that’s compatible with one’s credence in p remaining unchanged (e.g. the prior credence in it might be 0.5, and the same for the posterior credence). Updating by Fieldian-indeterminate-that-p will, on the other hand, reduce one’s credence in p and one’s credence in ~p to zero. (Obviously you can’t do that with a classical probability measure—that’s why we might need to generalize standard settings a bit).
If both those options are compatible with the updating story, I want to press the question for the primitivist: do you think either of these things will happen? Or something else? With continency, negation or other sentential operators, we’ve got a story. It’s not clear to me what the primitivist story should be.
Whaddya think? Have I missed your point?
(I guess I should think through whether the story that Elizabeth and I give about modality and (primitive) indeterminacy already gives us a line on these matters—the conjoined modal/indetermate semantics we favour has some delicate elements in it, so it’s not immediately obvious to me what would happen.)
Interesting. If I’ve got this straight, the worry is that it’s unclear what rational relevance being told that it’s indeterminate that p should have, when what we start off interested in is whether p. Without such a story, primitive determinacy/indeterminacy looks like an idle cog – just calling a contrast determinacy/indeterminacy doesn’t by itself give a grip on what it does. And then it is doubtful whether this contrast can do the work it’s meant to, for example in explaining our intuition that the future is unsettled. This all looks pretty convincing to me.
Ah, thanks for that! I think I get it now.
Also I think that talking about information content in terms of sets of situations wasn’t as innocent as I originally thought, since that seems to entail the Fieldian answer. (I was thinking in terms of a classical probability measure over the powerspace of situations, but of course that won’t be classical w.r.t the algebra of propositions, since the set of situations supporting ~p isn’t the complement of the situations supporting p.)
That said, doesn’t that just show that the primitive indeterminacy view is compatible with some of the updating procedures?
Actually, I’m beginning to think the updating problem has less to do with the source of the indeterminacy, and more to do with the fact that you admit an extra truth value (i.e. true/false/indeterminate.)
An analogy, if you learn that p is false, your credence in p goes to 0, and your credence in ~p to 1. That shouldn’t have anything to do with your theory of truth and falsity. Correspondence theorists, coherence theorists, or someone who thinks truth is just a primitive property, should all say the same thing.
Similarly, any theory that adds an extra truth value, whether it’s invoked by metaphysical indeterminacy, semantic indecision, or what have you, is going to have something strange going on with the probability (since, depending on the details, the the propositions will no longer form a Boolean algebra.) The only reason that the primitive indeterminatists don’t have an immediate answer to the updating question is because there are various *logical* options you might take (you might treat ~p as ‘p is indeterminate or false’ and do things classically, or you might go the Fieldian route, etc…)
So it seems to me the reason updating question is left undetermined has nothing to do with taking indeterminacy as primitive, and more to do with the extra truth value. Does that sound right, or have I completely misunderstood something?
Hi Alistair, Yup, I think that’s it! Glad you find it convincing. Though, given I actually like the primitivist view, maybe I shouldn’t be too glad…
Hi Andrew. One thing that seems relevant is that it was no essential part of primitivism as I was conceiving of it for the purposes of this post, that it play the role of an extra truth value. If indeterminacy did lead to failures of bivalence, then I think we’d have some traction on both the descriptive and the justificatory questions in the way you sketch. Actually, in an earlier paper I actually combined primitivism with a (supervaluation-style) third-value position where indeterminacy required a truth-value gap. But I’m not now convinced of the motivation for that.
It is true, though, that you can supplement primitivism with various views that give you the answer. Both supervaluation-style views and LEM-rejecting views naturally go with the “rejectionism” (in the sense of the post)—and as I read him, Hartry uses something like the above argument to motivate his favoured rejectionist take. Notice that if this were the line, the Barnes and Cameron primitively open future thing would start to look very weird—in particular, we’d have to reject all future contingents. But the Fieldian doesn’t have to think of that as a bug—he could just say that it was a false step to think of the future as primitively indeterminate. On the other hand, the folks who do want to think of the future as primitively unfixed—Barnes and Cameron—are quite clear that their primitive indeterminacy predicate is not supposed to induce failures of bivalence that might motivate rejectionism—and that’s also the view explored in the Barnes and Williams joint paper…). The people who are really in trouble are traditional Aristotelians, thinking that indeterminacy leads to bivalence failures for future contingents.
What I’d like to do with the above dialectic is just force people (inc. me) to commit one way or another… strategic silence shouldn’t be an option!
By the way, Ross Cameron suggests an interesting line of attack for the primitivist at the X-posted version of the above over at:
http://metaphysicalvalues.blogspot.com/2008/07/primitivism-about-indeterminacy-worry-x.html
I see. I guess I hadn’t considered the possibility that something might be true, and yet indeterminate. I find that thought kind of difficult to get my head around. If not inconsistent it seems to be one of those peculiar situations where we can never expect to find a clear example. (And it seems we can *never* have a determinate example of a indeterminate truth, because of Fitch like paradoxes.)
Anyway, I’ll have to read the papers you referenced, and then maybe I can get a better grip on how these things work!
Yeah–though on this route the idea is that the sentence is true or false, and indeterminate which (compare: supervaluationists saying that a patch can either be red or not red, but indeterminate which). There’s no off-the-bat commitment to having to assert that S is true and indeterminate, anymore than for the supervaluationist there’s any commitment to having to assert that a patch is red, and indeterminately so.
What to say in the context of modals (“it might be that”) is one of the topics of the joint paper with Elizabeth I linked to above…