Coherentism and Inconsistency

Suppose that coherentists can find a solution to the problem of justified inconsistent beliefs. I’ve argued that they can: the argument requires distinguishing between two kinds of necessary falsehoods and between ordinary and epistemic justification.

There’s still somewhat of a problem remaining, however. Given the distinctions above, a necessary falsehood can occur within a coherent belief system. The kinds of inconsistencies that can’t be tolerated await a solution to the question raised in the earlier post about evidence and propositions you’ve never considered. Once we determine how much of the set of logical consequences of your evidence set are evidenced by that set, then we can say exactly what kinds of inconsistent beliefs cannot be part of a coherent system and which can be. The important point, though, is that some impossibilities and perhaps some inconsistencies can be tolerated within a coherent system of beliefs.

On the whole, however, coherentists will be averse to inconsistency, and the question is why.

The usual argument, Lehrer’s, is that inconsistency makes achieving the epistemic goal of believing all and only truths impossible. But once you let in some impossibilities, that argument goes out the window. So what’s left to explain the aversion?

There are two ways to argue here that I see. The first is an “everybody’s in the same boat” argument. That is, point out that every theorist will have a similar aversion to blatant inconsistencies, so whatever explanation is given by, e.g., foundationalists can be given by coherentists. But I don’t know what foundationalists will say either, so even if this line is acceptable, it yields no insight.

The other way is to argue that the intuitive concept of coherence itself is at odds with inconsistency, though perhaps not in the strong way that requires that all inconsistencies are incoherencies. This would be a pleasing result; I just can’t see how it could be developed. That is, what might a coherentist say is involved in the ordinary concept of coherence that puts it at odds with inconsistency but not universally so?


Coherentism and Inconsistency — 6 Comments

  1. Hi Jon,

    What is the distinction between necessary falsehoods that you propose? Is it a distinction between a contradictory proposition (p ^ not-p) and a pair of propositions that are inconsistent, {p, not-p}? Or do you have something else in mind?

  2. The distinction I was thinking of is the distinction between contents from which falsum is derivable in the appropriate logic for the person in question, and metaphysically impossible propositions that are beyond such a derivation.

  3. Ah, ok. So, which kind of necessary falsehood is thought to appear within a coherent belief system? I’m not sure I yet grasp the distinction. Do you have an example of a metaphysically impossible proposition that is beyond derivation?

    Is the idea this: that a set of logically inconsistent propositions, G, may be coherent for an agent S if it is not possible for S to construct a sequence of inference steps from G to falsum within some specified bounds (measured by the length of a sequence) for S or for the class to which S belongs? I take it the idea here is that there may not be a model for G, but that from where S sits with his bounded rationality he cannot, by hypothesis, possibly see it. His (bounded) theory is consistent, even though Cn(G) isn’t. But that would be a distinction between epistemic possibility and logical possibility, wouldn’t it. Is a true statement about large ordinals that is not provably true a metaphysical truth but not a logical truth on your view? Hmm. I’m stuck. I vaguely recall a post in which you thought logical necessity was weaker than metaphysical necessity, and I vaguely remember thinking at the time that I had always considered the order the other way around, or rather, I had thought that metaphysical necessity was no stronger than logical necessity. (Maybe I have too liberal an idea of logical necessity.)

    How my confusion over this bit of metaphysics shakes out may help me to see whether a nice take on belief revision vs. belief updates that Hans Rott presents in the early chapters of his recent book Change, Choice and Inference might be mined for the second line of argumentation that you consider re: coherentism being incompatible with inconsistency.

  4. The best examples are Kripke ones, like water being identical to H2O. So the first thing I want to do is to separate the problem of inconsistent sets of beliefs from examples of this sort, since I don’t see why a coherentist would want to bar believing the opposite of such a claim in a coherent set.

    This point is enough to launch my worry, because once we let in such impossibilities, we can’t object to inconsistent beliefs on grounds that they eliminate the possibility of believing all and only truths.

    Does this help?

  5. Ahhh, ok. What about this line: An inconsistent set of beliefs A offers an agent no chance of believing all and only truths, and the agent can be in a position to know this, which is what makes inconsistent belief avoidance a coherentist epistemic principle. A consistent theory B containing a metaphysically impossible proposition offers an agent no chance of believing all and only truths, but the agent is not (by hypothesis?) in a position of knowing this, so coherence defined w.r.t. metaphysical impossiblity is not a suitable epistemic principle, hence not part of the coherentist credo.

    No? I still have the sense that I am not on point.

  6. Very nice, Greg, I want to think about this some more. At least, even if you’re not in a position to know (in some sense or senses of that phrase), the inconsistencies are knowable a priori, and that’s different from the metaphysical impossibilities.

    But if we can defend the stronger “in a position to know” claim, that would be better, I think.

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