3-place and 2-place epistemic predicates

If you’re attracted at all to relevant alternatives theories in epistemology, you’ll find some attraction in the contrastivist suggestion that some epistemic predicates are 3-place predicates. For example, you might be attracted to the idea that knowledge is best represented in terms of S’s knowing that p rather than q, instead of simply in terms of S’s knowing that p.

Here’s a question about such an approach: can this contrastivist suggestion be maintained “all the way down”? That is, if we suppose that knowledge is best represented as a 3-place relation, and we hold that justification is necessary for knowledge, can we also hold that justification is as well? If so, then we should talk in terms of S’s being justified in believing p rather than q, instead of simply in terms of S’s being justified in believing p. Furthermore, if you’re an evidentialist, you’ll want to understand justification in terms of evidence, so to go contrastivist all the way down will require making sense of the idea of something’s being evidence for p rather than q, but not evidence for p rather than r (making, of course, the entirely reasonable assumption that what is justified is a function of the quality of one’s evidence).

I’m not sure, however, how to understand the idea of something’s being evidence for p rather than q.

I can make sense of the idea if we explain it in some way to 2-place predicates. For example, if we try to clarify the nature of evidence in terms of the language of probability, the view isn’t 3-place all the way down. The best we could say is that p is more probable on e than q is, or we might compare likelihoods here, comparing the probability of e on p with that of e on q. Each of these approaches is a comparison between two 2-place predicate claims, not a 3-place predicate claim. (I believe this point applies to Sober’s idea of constrastive confirmation, where some evidence confirms p as opposed to q, since this three-place relation is defined in terms of likelihoods.) The same happens if we clarify evidence for p rather than q in terms of what rules out q but leaves it open whether p, and if we use Schaffer’s language of what one has proven rather than presupposed: we’ll get a relation between premises and conclusion for what is proven, not some three-place relation. So in all these cases the fundamental epistemic notions will not be three-place relations.

If we suppose that the fundamental notions will not be three-place notions, is this a problem? It’s not obvious if it is, but here’s a thought. If the basic notions are at least one place less than contrastivists hold is true of other epistemic notions, why does the additional place enter into the picture? For example, suppose that the fundamental notion is e’s being evidence for p. Then we can define a notion of justification in terms of the totality of one’s evidence constituting evidence for p. And from there, it looks as if we can extend the account to one of knowledge, as long as p is true, believed, and one’s justification ungettiered. Where in this story does the need for a third relata enter? If there is no good answer here, we should want contrastivism to be three-place “all the way down.”


3-place and 2-place epistemic predicates — 10 Comments

  1. Martijn, let me get you to explain a bit more. If we suppose that the basic epistemological concepts are 3-place relations, we should expect that knowledge is too, if these basic concepts are necessary for knowledge. That expectation can be overridden: for example, suppose the basic notions come in degrees, we might still explain away the idea that knowledge comes in degrees by appealing to the fact that truth and perhaps belief don’t. If we can’t explain it away, we should agree with Hetherington that knowledge comes in degrees, too.

    I must admit that this explanation against degrees of knowledge is a bit mysterious. But suppose we accept it: knowledge doesn’t come in degrees even though some of its parts do. Then we might hold that knowledge is an n-place relation even if some of its part are not n-place relations.

    Even so, this view seems to carry an explanatory burden that the other view doesn’t. That is, if justification is a 2-place relation, and knowledge a 2-place relation, that is satisfying in virtue of symmetry if nothing else. It’s only when they diverge that we need, or ask for, an explanation.

    I’m not sure I agree with this last paragraph, but it’s the view I’d like to hear what you think about it, since I take it you think it’s mistaken.

  2. Hi Jon and Martijn,

    It seems to me that, whether knowledge is a two-place or three-place relation, there will be structural differences between knowledge and evidence, and knowledge and belief as well.

    Start with belief. This seems to be at least a three-place relation, between a subject, a proposition, and a degree: s believes p to degree x. Likewise for evidence: s has evidence for p to degree x. That’s why we get constructions like “s believes p more than s believes q” and “s completely/mostly/partly believes p”, as well as “s has more evidence for p than for q” and “s has conclusive/strong/decent/weak evidence for p”. But knowledge, whether it is a 2-place relation between a subject and a proposition, or a 3-place relation including a contrast, does not seem to come in degrees (pace Hetherington). So structural match seems out of the question for everyone.

    Is this mysterious? Is some sort of explanation of structural divergence needed? I don’t think much of an explanation is needed. Consider some other 3-place contrastive relations. So consider the ternary contrastive relation of preference: s prefers a to b. It is natural to think that this is founded on ternary-contrastive relations of desiring: s desires a to degree x. Then it is a necessary condition on s’s preferring a to b, that (s desires a to degree x, s desires b to degree y, and x>y). Where does the contrast argument arise in the preference relation, if preference is founded on desire? I think the natural answer here woule just be: the contrast arises simply from the nature of what preference is. Likewise I would say that, if there is a contrast argument in the knowledge relation, it arises simply from the nature of what knowledge is.

  3. Jonathan, I agree with everything you say here, especially with the last part that if there is a contrast argument in the knowledge relation, it arises from the nature of what knowledge is. But I don’t know what that explanation is yet. In the case of preference, for example, the necessary condition you cite doesn’t explain the tertiary character of preference. If it were a sufficient condition, I’d be satisfied, but it’s not. What is needed in addition is some appeal to interference in the satisfaction of both desires, or at least the possibility of such. When we talk of preference, we imply something about what a person would choose when allowed only one option.

    In the case of knowledge, can we say something similar? We have a certain degree of evidence for p and a different degree for q, and the former is greater than the latter. The question then is what else involved in the nature of knowledge gets us contrastive knowledge that p rather than q. Well, p and q need to be contrasts, but that’s not something about the nature of knowledge, and is insufficient anyway.

    Here’s one explanation that would work if true: belief itself is contrastive, and belief is part of knowledge. Or maybe the idea is that when one knows, one also believes, and when one believes a claim, it is always in the context of rejecting competitor claims. I’m not sure these claims are true, but if they are, they’d give me what I’m looking for.

    As you might notice, it is not at all that clear what I’m looking for, though! Maybe there’s no problem here. In fact, maybe the problem results from the assumption I’ve made here that a good explanation will cite a sufficient condition, and maybe reflecting on why that’s false (assuming it is) would get me not to wonder about this anymore. But I can’t tell yet…

  4. Jon,

    Perhaps the underlying question here is, what determines the adicity of a given relation R? The determinants of the adicity of K will explain why K is 2-place or 3-place or whatnot, if anything can.

    I take it that what determines adicity is the number of logically independent parameters needed to determine a truth-value. So the contrastivist will explain the ternicity of K by arguing that one needs to fix a contrast parameter to determine whether K obtains. She will cite cases in which it seems that s knows that p rather than q1, but fails to know that p rather than q2. (For instance, Dretske’s painted mule case works like this–the zoo-goer seems to know that the beast is a zebra rather than a normal mule, but does not seem to know that the beast is a zebra rather than a pained mule.) She will also cite conceptual role considerations (for instance, the use of knowledge ascriptions to identify who is able to answer questions). Or do you think something is missing in this line of explanation?

    By the way, I don’t think we need to appeal to mutual exclusivity in the preference case. That I prefer a to b leaves open how I feel about a&b. Though if you think that mutual exclusivity would bolster the explanation here, keep in mind that in the case of knowledge, the contrastivist requires that p and q be mutually exclusive. Would that bolster the explanation for you?

    (As you can probably tell, I’m struggling a bit to understand exactly what sort of explanation you are looking for. Though if you think that we need a sufficient condition on K to explain the adicity of K, I would say that no one (binary theorist or contrastivist) has offered any informative sufficient conditions, so no one is in a position to offer that sort of explanation.)

  5. Jonathan,

    I don’t think the issue I’m concerned about would arise if ordinary language were clear about the adicity of knowledge ascriptions. When considering explanations of the variety of knowledge ascriptions, I don’t think the 2-placers or the 3-placers have a compelling case. The next stage is, I think, the theoretical virtues of either approach, which is where I take the present discussion to be playing out. I’m thinking here of your arguments comparing contextualist accounts with contrastivist accounts.

    What I’d really like is something in between, and symmetry considerations look like a nice place to look. So if the basic account of knowledge is in terms of evidence, and evidence in terms of probabilities (of the right sort!), then all else being equal one would expect the adicity of knowledge to be that of probability. That’s the part of Hetherington’s position that looks right to me: if the defining conditions come in degrees, so should knowledge.

    In neither case is the “all else equal” clause satisfied, so there’s no compelling argument here. But suppose we ask Hetherington’s question: if justification comes in degrees, why doesn’t knowledge? That sounds like a question that deserves an answer. The beginning of an answer is that there is more to knowledge than justification and not all of the additional elements come in degrees. And maybe all that remains to an adequate explanation here is to cite the facts of ordinary language and cite the aberrance of talk about knowing one thing better than another.

    But we can’t do that with the adicity question. In fact, I’m not sure even you are convinced that knowledge is 3-place, are you? I’m thinking of the beginning of your paper where you cite different versions of contrastivism and say you’ll develop one version of the view, but you don’t give an argument that it’s the correct version of the view. And, though I’m going on memory alone here, I seem to recall thinking that your arguments about the superiority of contrastivism over contextualism didn’t really require the 3-place view. What do you think?

  6. Jon,

    Perhaps your quandry can be resolved by considering the “fact” that conditional probability (for example) is not really a “two-place relation” after all. It is a two place function. But if we want to represent functions in terms of relations, we gain one more “place” — i.e., a two-place function represents (or is represented by) a three place relation. Indeed, for the probability involved in evidential support, it may be plausible to go for four-place-ism. The “primitive” relation may be “a supports b at least as strongly as c supports d”. I believe one can set down a set of axioms for this four place relation, and then show with a representation theorem that on a rich enough algebra of propositions (containing enough lotteries, for example) that one can “represent” such relations by unique conditional probability functions — that is, the relation will hold between a, b, c, and d just in case P[b|a] is greater than or equal to P[d|c] for the representing probability function P. This should not seem too surprising if you are familiar with the “structural representation” literature. In fact, the way Hartry Field does physics without numbers is by starting with congruence and betweenness relations, and showing how to get all of the mathematical structure of Newtonian physics back, including force functions, etc. Might this help with the issue that’s troubling you?

  7. Jim, I think this does help, though it pushes me more toward Jonathan’s remarks. I was hoping for symmetry here between knowledge and basic epistemic notions because (i) the appeal to usage doesn’t settle the adicity of knowledge and (ii) it’s hard to show that the 3-place relation view has theoretical advantages over every 2-place view. So I was hoping the symmetry point might give a reason to go one way rather than another on adicity. Your points about probability make it harder to give an argument from symmetry for either view. Maybe there is no alternative but to compare the implications of the theories in the standard way, and that my hope for a third way to argue for one view over the other just won’t work…

  8. It seems to me that there must be a way to make sense of the idea of e’s being evidence for p rather than q, assuming that the idea of S’s knowing that p rather than q is intelligible –though whether this should be understood as involving a three-place relation and whether it comports with the sense in which knowledge is said to be contrastive is unclear to me. Understood in terms of probabilities, it seems the idea can’t be that p is more probable on e than q is, as that could be true if e is evidence for both p and q. Or is e’s being evidence for p rather than q supposed to be compatible with e’s being evidence for both p and q? In fact it doesn’t seem right to say that e is evidence for p rather than q if e rules out q but not p. Maybe the idea is that e is evidence for p rather than q if e is evidence for p, independently of whether it is evidence for q. This does seem to be a comparison between two two-place relations. But what worries me is that it seems that this is clearly not the sense in which ‘S’s knows that p rather than q’ is supposed to be understood. That is, it should not be understood as meaning that S knows that p, independently of whether S knows that q. Does this seem right? I am not sure I fully grasp the problem here but it seems to me that you are onto something.

  9. Hi Jon,
    What I had in mind was something like this. I am not convinced that we need to ask for an explanation only when the fundamental notions are n-place relations and knowledge is a m-place relation. And the reason is that I donĂ¢??t see any principled reason to think that the number of the relata of the fundamental notions has any impact on the number of the relata of knowledge (or vice versa). I completely agree that symmetry is important, but I am just not sure that we can take symmetry to indicate that there is some necessary connection between the amount of places in knowledge and the amount of places in the fundamental notions, so that only in the case of assymetry we are in need of an explanation. Does this make sense?

  10. Martijn, I understand your point, though I remain slightly puzzled. Suppose we define the relation of addition in terms of the successor function: x+y is to be understood as applying the successor function y times to x. The successor function is a one-place function, so if we represent such a function as a relation, we get a two-place relation.

    Now, suppose I had been perplexed, wondering why addition is a two-place relation, when it is defined in terms of a one-place function: the difference in places perplexes me. You then make Jim’s point above: one-place functions need a place added to be represented as relations, so there is no asymmetry here.

    Ah, my perplexity is now gone. But why? It makes sense for it to be relieved if symmetry in the account eliminates the need for further explanation, but not otherwise.

    But, as I said in a previous comment, I’m not sure there is anything to this worry anymore. I need to think about it some more…

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