Thursday, July 24, 2008

Primitivism about indeterminacy: a worry (x-post from TnT)

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 was indeterminate, one couldn’t know p (think of parallel discussion of “minimal” conceptions ofassumed that every series account of indeterminacy would say that if p 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.


Ross Cameron said...

One thing is that while it seems to be very hard to deny that 'it's indeterminate' is a good answer to 'is it red?', it doesn't look at all obvious that it's a good answer to 'will you be going out tonight?' even if you're an open future theorist. One might take that as a reason to doubt that invoking indeterminacy is the way to characterise the OF thesis - naturally, I don't want to say that. I'd be tempted to say one of two things:

1) Perhaps there are two phenomena that the English 'indeterminate' is ambiguous between: one is unsettledness between truth and falsity, the other is there being no fact of the matter. The first is compatible with bivalence, the latter not. 'It's indeterminate' might be a good response iff there is no fact of the matter as to whether the thing has the questioned property.

2) There's a uniform notion of indeterminacy, and whether 'it's indeterminate' is a good answer depends on the cases. It's a good answer to 'is it red?' but not to 'will you be going out tonight?'. Why? In both cases there's indeterminacy because the corresponding bits of ontology (the state of affairs of it being red, the future event of my going out) neither determinately exist nor determinately fail to exist. But in the latter case our evidence for one answer over another is independent of the grounding ontology: rather, we would cite our present intention to go out, the lack of impediments etc. But our evidence for things being a certain colour tends to be our acquantance with the ontology that makes it true that they are that colour - so it's understandable why, if I intimate that the ontology isn't determinate either way, I thereby tell you that I don't have any evidence for or against its evidence, in a way that I don't with the future case.

I like option (2) better.

Robbie Williams said...

Hi Ross, thanks for this!

I take the point about the putative datum not being so obvious for the future cases as others. If someone were to press this too hard, I would get worried why we think our primitive operator deserves the name "indeterminacy".

I guess that's the worry with (1). The non-primitive conception would fit nicely with how things work in general---and OF indeterminacy just looks like something else. Another thing is if the answer to "what's the relevance of p being indeterminate to my attitude to p?" is just "it's totally irrelevant", then I really do start to wonder what we're dealing with---why we're not just dealing with a kind of contingency, which exhibits similar behaviour.

(2) seems really interesting. The idea I suppose is that ceteris paribus, saying that it's indeterminate whether p will indicate we have no evidence (a bit like the epistemicist reaction). It's a sort of status p can have that rules out a kind of access to p's truth.

And then---to deal with the apparent difference between the cases---we appeal to a special route we can have for evidence in the particular case of the open future, indicating that ceteris aren't paribus in that particular case. That'd be really elegant if you can make it work!

I suppose the issue now is to look at what we need to say about primitive indeterminacy to make this work. We need that certain kinds ("acquaintance with ontology") evidence for or against p are lacking when p isindeterminate. That is a first shot at answering the descriptive challenge. The question then is whether we can explain why p's having this unsettled status has this upshot---the justificatory challenge.

Robbie Williams said...

Incidentally, one thing I've been playing about with in the OF case is to let the primitive indeterminacy come in degrees. And then the answer to the description question is: you should match your credences to the degree of determinacy of the proposition.

There's still justificatory questions to be asked, but it does seem like a clean kind of approach.

Louis said...

Hi Robbie,

I don't work on this stuff and don't know the literature, but here's a very simple-minded answer to the challenge posed by the descriptive and justificatory questions. Let's confine ourselves to the "is that red?" case. "It is determinate that that's red" clearly answers the question. So does "It is determinate that that's not red." "It is indeterminate whether that's red" is true just in case neither of those answers are. So the relevance of the answer to the question is that it eliminates two perfectly good answers. For comparison, a perfectly appropriate answer to "How tall is that pole?" is "Not more than 20 feet."

CHALLENGE: We can pull the same trick with "it's contingent whether that's red", which eliminates both "it's necessary that that's red" and "it necessary that that's not red." So the explanation fails.

REPLY: While the necessity claims, like the corresponding determinacy claims, are factive, they can fail by dint of how red the indicated thing might have been in different circumstances, not how red it in fact is. Since the question at hand is in the first instance a question only about how red the indicated thing is in actual circumstances, "it is contingent whether..." does not directly address the question asked. But presumably a primitivist about indeterminacy would say that the truth or falsity of "it is determinate that that's red" is determined by how red the indicated thing is in actual circumstances, not how red it might have been under counterfactual circumstances. So "it is indeterminate whether that's red" doesn't have the same problem.

An further interesting challenge is in effect proposed by Ross: Why *isn't* "indeterminate" an appropriate answer in the case of an open future? That I'm not sure about.

- Louis deRosset

Robbie Williams said...

Hi Louis,

Thanks for this---it's an really interesting way of thinking about the question. I agree that if we could say why "it's determinately red" is a relevant response to "is it red?", then that'd be a great start. And it does seem intuitively like there should be something to say about why that is relevant.

Let's suppose that the red/non-red cut-off was somewhere between patches x and y. And suppose that the determinate red/not det red cut-off is at x, and the not det red/det not red cut-off was at y (it shouldn't matter if we replace the precise assumptions with something a bit looser). Then if I say "it's indeterminate whether that patch is red", I convey the information that it's in the range x to y. So I convey information about it's degree of redness, even if I don't directly address the question of whether it's red or not. Typically, when I'm asking the question "is it red", I am interested in various bits of info about the patch's colour---and so the determinacy-info then seems a reasonable thing to provide.

(I wonder though---if this is *all* the information we get, why does it seem silly to keep on asking the question: "right---thanks for telling me it's indeterminate---but I really need to know whether it's red or not, so can you tell whether, in addition it being indeterminate whether it's red, it's also red?". For all we've said so far, such questions might make perfect sense: e.g. where what we care about the red/not-red question itself, rather than degrees of redness. Now, maybe there's some Gricean story that'd help out a bit (that by saying "it's indeterminate" you implicate that you don't know the answer to the red/non-red question... but I'm not sure whether that'll explain all the data in the vicinity).

One thing that's interesting about the above is that it leans heavily on special features of the "red" example---that we've got an underlying approximately continuous quantity and can make sense of patches getting redder or less red. The extension of "indeterminate whether it's red" then carves out an interesting range of values of this quantity.

In other cases, we just won't have that sort of setup. The OF scenario is a natural illustration of that---there's nothing like an underlying comparative structure for the "determinately" verdicts to pick up on. But of course---*that* might be an advantage, since it's relevant to your second challenge---why "it's indeterminate" seems an irrelevant answer to "will there be a sea-battle?".

So the strategy you're suggesting seems to me an essentially local one---looking on a case by case basis at determinacy-verdicts, and figuring out whether local factors are going to explain how we answer questions. One of the nice things about that is that it's so theoretically unloaded---it seems everyone should think through this stuff to filter out "noise" before their own theory kicks in. And of course, it might turn out to explain everything we want it to, which'd be extremely nice.

Just to kick off the local examination. One kind of case where the answer "it's indeterminate" seems at least in the offing, but where there's no obvious comparative structure, are weirdo personal identity thought experiments. Presented with strange twists on teleportation cases, lots of people's first reactions are "there's no fact of the matter about whether someone would survive that case". But it's not obvious that they've got in mind some underlying structure of personal identity cases about which "it's indeterminate" conveys information. After much theorizing, we might diagnose some such structure, but we're after what we convey by determinacy-information pre-theoretically. So I wonder what's going on here?

One idea would be to strip back to the bare bones---rather than appeal to degrees of some underlying quantity, just say that "it's indeterminate whether I survive" conveys that the proposition that I survive fails to have the factive Q-property, nor the anti-factive Q* property. And as you suggest (unlike necessity and impossibility for example) the possession of these Q/Q* properties are fixed by the same sort of factors that determine questions of survival.

For myself, I think I still need some more elaboration before I know why information about these Q/Q* properties are relevant to our original question (I want something like the sort of supplementation that was available in the red/not-red case). The personal identity case really brings this out, I think, because it's pretty intuitive that our concerns are structured around the question of survival/non-survival---and we're just far less interested in the subvening properties (unless we're Parfit).

So while I think the suggestion you make is really helpful, I think the puzzles still arise in a range of cases.