Prompted partly by Olsson’s recent *Against Coherence* (OUP 2005), I’ve been thinking about the truth-conduciveness of coherence. There’ve been two recent claims to prove that coherence cannot be truth conducive (in Olsson, and Bovens & Hartmann’s *Bayesian Epistemology*).

I don’t know how many people have looked at this literature. Briefly, the claim (theorem, in fact) is that if

a) the coherence of a set of beliefs is a function of the probability distribution over the believed propositions and

b) the beliefs are formed independently of each other (i.e., when the truth-values of the relevant propositions are fixed, the occurrence of one belief doesn’t affect the probability of the other beliefs occurring),

then

c) there is no possible measure of the degree of coherence of a belief system on which more coherent beliefs are in general more likely to be true,

ceteris paribus.

So I wonder a few things about this:

1) Is (c) incompatible with coherentism? Perhaps some coherentists would like to weigh in.

2) Should the coherentist accept (a) and (b)?

3) Lastly, I’m wondering more generally about the interpretation of claims like “x is conducive to y, *ceteris paribus*.” Olsson says that means: As long as you hold fixed all factors that are independent of x, an increase in x always leads to an increase in y. But I don’t think that’s right. This actually makes a big difference to the impossibility theorem.

Has anyone else thought about this?

Good questions, Jon! First, let me point out that Diettrich and Moretti have shown that coherence can be CONFIRMATON conducive — even in the (c)-type sense (even if it is not truth-conducive in the (c)-type sense). Their paper just came out in Philosophy of Science. I highly recommend that (it’s something I’ve suspected for some time now). Second, I share your worries about the legitimacy of the way “x is conducive to y” is cashed-out here. When I read Bonjour (for instance), it’s not entirely clear to me that this is what he means by “truth-conducive”. Also, Olsson’s characterization can’t be completely correct anyway, since coherence is supposed to be conducive to TRUTH, not to PROBABILITY OF TRUTH. So, I don’t even see how his formulation makes sense (since it should then be about degree of truth, not probability of truth). Anyhow, I look forward to finally talking philosophy with you in person next week!

Thanks, Branden, but my name’s not Jon and you won’t be talking to me in person next week. ðŸ˜‰ The point about truth- versus probability-conduciveness occurred to me, but I took it to be just a little terminological slip: by “truth-conducive”, Olsson just meant conducive to probability of truth.

I have a more serious problem for his criterion though. Suppose you have four variables, where it is known in general that:

y < 10. z = x + y. w = 2x + z. z is clearly w-conducive. But according to Olsson's criterion, the following two cases would constitute a counter-example to the claim that z is w-conducive: Case 1: x = 2. y = 2. z = 4. w = 8. Case 2: x = 1. y = 4. z = 5. w = 7. In case 2, you have a higher value of z but a lower value of w. It's ok to reduce x like this, because x is not independent of z, so you don't have to hold it constant.

Mike and Branden,

Skeptical as I am about the nature of the truth connection in epistemology, I have viewed the B&H result as well as the Olsson result as not much of an issue for coherentism. Moreover, the D&M result is quite reassuring here, especially if the coherentist is inclined to adopt my quasi-Chisholmian take on the truth connection. In rough fashion, the idea is that epistemic justification gives you grounds for thinking that a certain claim is best to believe in the attempt to get to the truth and avoid error. That’s very close to the Chisholmian claim that even though rationality doesn’t yield probability of truth, it does yield the result that it is probable that the claim in question is probable.

There’s stuff to sort out here about the relationships between what I just wrote, what Chisholm claimed, and the D&M result. But I think they are all in the same conceptual neighborhood.

I think I’m going to do a grad seminar on this! Poor students… They’ll have to read B&H, Olsson, and D&M. And of course more background on what confirmation is, right Branden? Gee, I wonder who might be good to read about that…!

Rats, Mike; I thought maybe you’d bite on the invitation to come on over for Branden’s talk! ðŸ™‚ I hear it’s only a 12-hour drive (in good weather…).

Sorry Mike (I often ASSUME that Jon is posting here — I should pay more attention to names!)!

Anyhow, your example is interesting. But, I wonder why you think z is w conducive in your example. Can you explain that? And what do you think the right “ceteris paribus” clause is here?

It’s cool that Jon (really Jon this time!) is doing a seminar on this. There’s some neat stuff out there. I’m still looking forward to discussing this with Jon next week (sorry Mike won’t be there!).

Mike: two brief remarks on (a) and (b).

There are many (a)-type “supervenience” assumptions in Bayesian epistemology. It is also typically assumed that degrees of confirmation supervene on the agent’s credences (at the time the confirmation judgment is made). I think that’s false (this is one of the main motivations I have for abandoning Bayesian confirmation theory in favor of a more general inductive-logical approach). I guess a coherentist would want coherence to supervene on SOME “internal” set of properties. But, I guess you’re asking: why would the supervenience base have to be the agent’s credences? I also think that’s a good question (not usually even addressed by Bayesians — like their other supervenience assumptions).

As for (b), this does seem troubling for a coherentists, no? After all, their view seems somewhat “holistic” (at least about justification). By the way, the “independence” assumption that actually plays a role in the theorems is also defined in terms of credences. So, it really should be couched in terms of a kind of probabilistic independence, under the agent’s credences. The way (b) is stated above makes it sound like an “external” kind of independence. But, I don’t see how that can imply anything about relations among the agent’s credences.

Branden —

Yeah, I’m sorry I can’t hear your talk. I like the paradox of confirmation (is this the one where every proposition confirms every proposition?)

1.

z is w-conducive?I was actually thinking that my example would be recognized as the very paradigm of one factor being conducive to another — that is, when the latter is literally the sum of the former and something else. But I don’t want to give a general criterion, because it will probably turn out to be wrong. Perhaps if you have some funny business going on (like where the “something else” requires subtracting the first factor) you could have a case in which A isn’t conducive to B even though B is equal to A plus something. But there’s no funny business in my example — stuff is just being added together.2.

Condition (a):This stuff is in the paper I’ve been working on. (Starting this topic is my sneaky way of getting more ideas for the paper.) I was thinking that we might want the supervenience base to include information about the beliefsources, including things like whether some pair of beliefs were produced by the same source or different sources, rather than just the initial probabilities of the propositions the beliefs are about (+ their boolean combinations).3.

Condition (b):Yes, you’re right. The way I said that made it sound external. The claim that some beliefs were formed independently sounds like a causal claim, which could not be secured by any assumptions about anyone’s credences. Anyway, it seems to me the coherentist should definitely reject this assumption. I made the conditional independence assumption in my 1997 paper criticizing coherentism, but now I think I can’t justify it.4.

Credences:I’m more sympathetic to objective bayesianism, with logical probabilities and such, than subjective bayesianism. I didn’t take Olsson, Bovens, or Hartmann to be assuming an interpretation of probabilities in terms of credences per se. But it’s entirely possible that that’s an oversight on my part.Let me encourage all of you to pursue this research project of trying to clearly identify important epistemic features of our beliefs which are not reducable to our related probabilities. It is not clear to me that such features exist, at least in the finite case.

W.r.t. Robin Hanson’s remark in 8, I think a good portion of epistemologists would be inclined to change the signs: that is, I imagine them pressing,

try to clearly identify important epistemic features of our beliefs thatarereducible to probabilities. For it has seemed clear to many that such featuresdo notexist.I do not offer this contrary remark by way of an endorsement. Rather, my motivation is this. To effect a useful bridge between formal epistemology (broadly construed) and traditional epistemology, it is necessary that we pay particularly close attention to the literature and aim of each field. For there is considerable overloading of terms, philosophical sophistication matched with clumsy mathematics, and vice versa, and, on top of this still, a tendency for each field to take a different view about the proper ends for our theorizing about knowledge.

Given this, the stage is perfectly set for people to talk right past one another.

Nice point, Greg. It’s also very easy not only for the sides to talk past each other, but to think to themselves that the other side is just confused and not doing real epistemology… And, of course, I have an antidote, which is value-driven epistemology. Having to say why and how one’s theorizing matters is a really good way of forcing one to distinguish between different projects and see the value of other projects at the same time.

Mike–I think (a) is so specific to a certain kind of Bayesianism that the Olsson result has no implications for coherentism itself (even if one assumes that there needs to be the kind of truth connection that is under attack here). (a) is the sort of principle Lehrer would be attracted to, though I don’t think he’d quite endorse it, but it is fairly obvious that BonJour (of the 80’s) could not endorse it.

Also, can you motivate (b) a bit here? When I read it, I think it is hopelessly unrealistic with respect to the actual psychology of belief formation. Perhaps the defense is that a coherentist ought to be committed to the conditional itself (that a and b imply c) without being committed to the antecedents themselves?

There is an alternative argument that avoids dependence on (b).

Define the “opinion set” O for a person S as the set of propositions on which S forms an opinion, i.e., the set of Pj (for j=1 through n) such that either S believes Pj or S believes the negation of Pj. One can prove that for all Pj in O, Prob(Pj is true/S Bel Pj)=Prob(S Bel Pj/Pj is true), provided only that (1) n is finite and (2) S’s beliefs are consistent.

Now, if S’s beliefs are coherent (on some appropriate measure that takes into account logical, evidential, probabilistic and other such relations), it may well not be the case that the probability of a given belief occuring is independent of the other beliefs that occur. But the crucial question is whether the coherence of S’s beliefs makes it any more likely that S will believe Pj simply because Pj is true and S takes an opinion on it.

Putting the argument more intuitively, suppose we start with some rather large set of propositions, and from these we select some suitably interesting, coherent subset to be our set of beliefs. The question as to truth-conduciveness is whether a proposition is more likely to be true given that it is selected. But we could equivalently focus on the question whether true members of the initial set are more likely than false members to be selected. If the probability of selection is independent of truth or falsehood, then the coherence of the subset likewise is not truth conducive.

Stephen: can you show me the proof of the result you state to the effect that Prob(Pj is true/S Bel Pj)=Prob(S Bel Pj/Pj is true)?

Jon,

Although I’m not advocating either (a) or (b) — ultimately, I think the coherentist should reject them — I do believe they have some initial plausibility.

(a)The idea behind (a) is that coherence is a matter of how well propositions support each other, which is reflected in facts about the probability distribution over those propositions — e.g., whether one prop is more likely given the others, etc. To skirt the debate over exactly how “support” should be understood (sorry, Branden), we just put the condition in terms of the probability distribution in general, rather than stating the specific features of it that make propositions “mutually supporting”.

You’re right that BonJour wouldn’t have accepted (a), even when he was a coherentist, because he includes things like having “explanations”, which probably doesn’t supervene on the probabilities, as part of coherence. But one might argue that probabilistic relations are at least

a large partof coherence, and so it is of interest to see whether this aspect of coherence is truth-conducive.(b)When he gives his analogy of congruent witness testimonies, BonJour says something about the witnesses giving “independent” reports. So this conditional independence assumption is supposed to be something the

coherentistwants to require, as a condition for coherence to be useful. The idea is that if a pair of witnesses are listening to each other’s testimony to figure out what they should say, then the fact that they cohere doesn’t tell us much. But if theyindependentlygive reports that turn out to cohere, then this fact is a reason to think the reports are true.You’re right that the condition is unrealistic — perfect independence is unlikely to be satisfied in any real cases. But the claim on the part of the anti-coherentist is that this independence assumption is a sort of ideal case favorable to coherentism — so if coherence isn’t truth-conducive (even) in

thiscase, coherentism is in serious trouble.Branden, for starters, take a “negation” in a broad sense to mean “contradictory,” so that A and -A are each in this sense negations of the other. Thus, if I believe A, both A and -A are in my opinion set (and likewise if I believe -A). The opinion set can then be thought of as consisting of pairs of propositions, where each element of the pair is the contradictory of the other. My belief set is a selection set that takes one and only member from each pair. Under these conditions the proportion of propositions selected that are true equals the proportion of true propositions selected, provided that the opinion set is finite. (Extending to the infinite case would require the axiom of choice.)

The proof is just that 1) given the way the opinion set is defined, the number of propositions selected from the opinion set equals the number of true propositions in the set; and 2) the set of true selected propositions is identical to the set of selected propositions that are true, so these also have the same number of members. Thus the proportion of true popositions selected equals the proportion of selected propositions that are true.

Hello all,

(Kind of in a rush; I’ll try to flesh out these comments tomorrow and read what everyone else had to say.)

Jonah Schupbach and I are just finishing up a paper objecting to B&H’s interpretation of the impossibility result in the first chapter of _Bayesian Epistemology_. I’ll throw out a few of our gripes. First, some (many?) who believe that, ceteris paribus, coherence is truth-conducive will *also* believe that other theoretical virtues are c.p. truth-conducive (an example of someone who seems to want to take this kind of approach: Tim McGrew in “Confirmation, Heuristics, and Explanatory Reasoning”). These folks should not buy B&H’s interpretation of the impossibility result. By varying reliability, B&H are varying the explanatory power of the hypothesis that R_1,…,R_n are true given that one has received REPR_1,…,REPR_n. What B&H are doing is keeping coherence constant, varying r, and noticing that the posterior probability is wacky (not behaving the way B&H think the Bayesian Coherentist needs it to behave). The problem is that B&H fail to notice that the Bayesian Coherentist who holds that explanatory power is c.p. truth-conducive is *absolutely fine* with that result. After all, the “criss-crossing” happens *precisely* at the points at which, for the first time, one info-set’s explanatory power becomes greater than that of the other! So, the result may be interpreted as showing that Bayesian Coherentists need some additional commitments if they’re going to avoid such problems.

-Adam

Quick terminological note: I’m using “truth-conducive” to mean conducive to probability of truth.