This past Saturday “indeterminacy day” was held at Leeds. Or, to give it its more prosaic title: “Metaphysical Indeterminacy: the state of the art”.
There were four speakers (Katherine Hawley, Daniel Nolan, Peter van Inwagen and myself). We had quite a few people turn up from around the country to participate in the discussions—we were very pleased to see so many grad students around—thanks to everyone who came along and helped make the event such fun!
I’m going to write up a short report on what happened for the reasoner (probably focussing more on the intellectual content than on the emergency evacuation procedures that ended in a locked courtyard). But I thought I’d take the chance to post the slides I talked to on the day. They’re available here.
I wanted to do two things with the talk. One was to give an overview of how we’ve been thinking about these things here at Leeds (on reflection, I should have been more explicit that I was drawing on previous work here—particularly joint work with Elizabeth Barnes. I’ve added some more explicit pointers in the posted slides). But I also wanted to go beyond this, to urge that one thing that we want from any “theory” of indeterminacy is some account of its cognitive role—what the rational constraints (if any) believing that p is indeterminate, puts on one’s attitude to p. (To fix ideas, think about chance: knowing that there’s a 0.5 chance of p (all else equal) means you should have 0.5 credence in p. That’s a pretty specific doxastic role. On the other hand, knowing that p is contingent is compatible with any old credence in p).
Now, in the talk, I said that this can help to articulate what people are complaining about when they say that they *just don’t understand* the notion of metaphysical indeterminacy. I reckon people shouldn’t say that the notion of indeterminacy with a metaphysical/worldly source is literally unintelligible (I reckon that’s way to strong a claim to be plausible—Elizabeth and I chat about this a bit in the joint paper). But I’m sympathetic to the thought that someone can complain they don’t “fully grasp” the concept of a specific sentential operator P if they’re entirely in the dark about its cognitive role (how credences in P(q) should constrain attitudes to q). A fair enough answer to this challenge is to say that there are no constraints. For P=it is contingent whether, that seems plausible. But there’s something compelling about the thought that someone who e.g. doesn’t appreciate that something like the principal principle governs chance, doesn’t grasp the concept of chance itself.
What makes the challenge to spell out cognitive role particularly pressing for the view that Elizabeth and I set up in the joint paper, is that we don’t get much of a steer from other aspects of what we say, as to what the cognitive role should be. We say that metaphysical indeterminacy is a primitive/fundamental operator (compare what some would like to say about modality or tense). No help from this about cognitive role—as there might be for someone who said that indeterminacy is a special case of some wider phenomenon whose cognitive role we had a prior grip on (e.g. ignorance). Moreover, in the joint paper the logic of indeterminacy that we defend is pretty thoroughly classical. And so there’s no obvious way of appealing to features of (the putative) logic of indeterminacy to get guidance. Others with a more revisionary/committal take on the logic of indeterminacy may well be able to point to features of the logic as implicitly answering the cognitive role question (that’s a strategy that Hartry Field has been advocating recently).
Some qualifications (arising from good questions put during the workshop, esp. by Daniel Nolan).
(i) I certainly shouldn’t suggest that being able to explicitly articulate the cognitive role of a concept C is required in order to fully grasp C. Surely we can at most require one *implement* the cognitive role (accord with whatever rules it specifies, not necessarily articulate those).
(ii) If one thinks in *general* that concepts are in part individuated by cognitive role, then we’ll have a general reason for thinking that in order for someone to come to fully grasp C, from a position where they don’t yet grasp it, they’ll need to be given resources to fix C’s cognitive role. On this view you won’t count as having attitudes to contents featuring the concept C at all, unless those contents are structured in the way prescribed by C’s cognitive role.
(iii) Even if you don’t go for a strong concept-individuation claim, you might be sympathetic to the general thought that it’s right to classify people as having greater/lesser grasp on a concept, the the extent that they’re deployment of the concept conforms to what’s laid down by its cognitive role.
(iv) There may be cases where we count people as fully competent with a concept, even though they don’t accord to cognitive role, if they’ve regard themselves as having (or can plausibly be interpreted as tacitly believing that there are) special reasons to depart from the cognitive role.
(v) If a theorist whose subject-matter is C doesn’t explicitly or implicitly convey information about the cognitive role of C, it’ll be appropriate for someone without an anterior concept of C, to complain that they haven’t been put in a position to become fully competent deployers of C.
Ok, so claims (i-v) sound eminently suitable for counterexamples—be very pleased to hear people’s thoughts about them in the comments. My thought is that when Elizabeth and I say we’re theorizing about a metaphysically primitive indeterminacy operator, whose logic is pretty much entirely classical—unless we say some more, people are entitled to complain in the way described in (v).
One thing I’d’ve talked about a bit more (if the Fire Alarm hadn’t interrupted!) is various ways of adding bits that implicitly fix cognitive role. Think about the following rather “external” norm of belief:
- One should: believe p only if p is true.
Now, suppose that it’s indeterminate whether p is true (as it will be when p is indeterminate, on the position put forward in the joint paper). Then if it’s determinately true one believes p, it’ll be indeterminate whether the biconditional “believe(p) iff p is true” holds (compare: if A is necessary and B is contingent, then A<–>B is contingent). Likewise, determinately believing ~p in these circumstances leads to it being indeterminate whether you’ve violated the norm.
As Ross pointed out in the talk, on these formulations, suspending belief and disbelief in p is a way of determinately satisfying the norms. Maybe that’s an attractive result. If we strengthened the norms to biconditionals, then (determinately) not believing doesn’t lead to any worse status. And the biconditional versions don’t look implausible as articulating some kind of doxastic ideal: what a believer concerned aiming at the truth, and not resource-limited, should do.
If we leave things here, the conclusion is that when it’s indeterminate whether Harry is bald, it’s indeterminate whether (determinately) believing that Harry is bald violates the truth-norm on belief (and the same goes for other salient options). You can’t come all-out and say that someone who without hestitation *believes Harry is bald* is determinately doing something wrong. But notice: suppose someone without hesitation determinately believes it’s wrong to believe Harry is bald. Then you equally can’t say that it’s determinately wrong to believe what they believe. And of course this iterates!
This seems pretty vertigo-inducing to me. Notice that we shouldn’t ignore the option of it being indeterminate what a subject believes. In that situation, one might *determinately* meet the truth-norm even in biconditional version. (Compare: if A and B are both contingent, it can be necessarily true that A<–>B).
It’s tempting to think that, determinately, what you *should* do in these circumstances is to make it the case that it’s indeterminate whether you believe p. For only then can you avoid the worries about someone criticizing you, and not being not-determinately-wrong to do so! But of course, this really would be something over and above what we’ve said so far.
What *would* enforce the idea that when it’s indeterminate whether p, it should be indeterminate whether you believe p, is the following formulation of the truth norm:
- One should: determinately (believe p iff p is true).
If p is indeterminate, then determinately believing p or determinately not believing p would each violate the claim that the biconditional is *determinately* true, and on the revised formulation, one isn’t doing as one should (and it’s determinately true to say so).
So I think that given the truth-norm (or, better, the narrow-scoped version just laid down) there’s some prospect of arguing that there’s a cognitive role for indeterminacy implicit in the kind of non-revisionary framework of the joint paper. There’s work to do to figure out how to go about meeting these constraints—what sort of mental setup it takes for it to be indeterminate whether you believe p, and what to say about rational action, in particular, given this. But we’ve got a starting point.