Tuesday, May 15, 2007

Coherence and Comprehension

Responding to my post on verificationism and base facts, Jim Ryan writes:
I wonder whether Richard's view entails that one can understand an incoherent term (such as "square with only three sides"). After all, "I know what it means, I understand it, but I just don't see how it could be rendered coherent" sounds Richardesque. I suppose he might say that the incoherence precludes comprehension. But that seems arbitrary. Why won't he also allow that evidential vacuity precludes comprehension, as well? Again I say that the mind is large and its imagination powerful. It can imagine a logically impossible thing (especially if it's in a sort of dreamy state: try it, you can do it. Or if the contradiction is buried deep enough, you can accomplish the task in a clear-headed state.) It can mistake this for comprehension. It can imagine the correct application of an evidentially vacuous term (e.g., "zombie") and mistake this for comprehension, too. How can Richard distinguish these two, such that in the latter case there is in fact no mistake?

Granted, our claims to understanding are fallible -- one can't be certain that further reflection won't reveal some hidden incoherence in a notion. There's a gap between prima facie conceivability and ideal conceivability. A nice example of this is the Grim Reaper paradox:
There are countably many grim reapers, one for every positive integer. Grim reaper 1 is disposed to kill you with a scythe at 1pm, if and only if you are still alive then (otherwise his scythe remains immobile throughout), taking 30 minutes about it. Grim reaper 2 is disposed to kill you with a scythe at 12:30 pm, if and only if you are still alive then, taking 15 minutes about it. Grim reaper 3 is disposed to kill you with a scythe at 12:15 pm, and so on. You are still alive just before 12pm, you can only die through the motion of a grim reaper's scythe, and once dead you stay dead. On the face of it, this situation seems conceivable — each reaper seems conceivable individually and intrinsically, and it seems reasonable to combine distinct individuals with distinct intrinsic properties into one situation. But a little reflection reveals that the situation as described is contradictory. I cannot survive to any moment past 12pm (a grim reaper would get me first), but I cannot be killed (for grim reaper n to kill me, I must have survived grim reaper n+1, which is impossible). So the description D of the situation is prima facie positively conceivable but not ideally positively conceivable.

How should we interpret this? I guess I am a bit tempted by the line Jim attributes to me: "I can understand the set-up, I know what it means, and I see that it's incoherent!" But this trades on an equivocation. I can understand each of the descriptive components in isolation, but that's all. It remains a total mystery how they fit together -- what is supposed to happen after the strike of 12? It can't be understood. It's incoherent. But I repeat myself.

It's not arbitrary to say that "incoherence precludes comprehension." On the contrary, it's analytic! Coherence just is comprehensibility. To call something "incoherent" is precisely to say that it cannot be comprehended by any rational mind whatsoever. (Of course, something coherent but complicated might be "incomprehensible to me" in the limited sense that, due to my contingent cognitive limitations, I simply happen to not understand it. But that's not the relevant sense of the term here.)

On the other hand, I just don't see any reason to think that evidential vacuity precludes comprehension. And I do see reasons -- in the form of apparently coherent counterexamples (zombies, multiverses, etc.) -- to reject such a stringent requirement.

Jim concludes:
Richard needs to say what is the difference between "comprehensible" and "suspiciously incomprehensible" other than a feeling of "I've got it!" I don't trust that feeling. I need epistemic, evidential terms.

That seems fair enough, given how fallible such intuitions are. The difference between true and false intuitions is a matter of fact that won't always be transparent to us, namely: would further reflection lead me to change my mind?

1 comment:

  1. I think of it this way: if a hypothesis is incoherent, then (1) its truth-conditions cannot be understood; but (2) the reason why its elements fail to cohere can be understood.

    If someone thinks an incoherent hypothesis is coherent, then their lack of understanding on the second count is what leads to their mistaken sense of understanding on the first.


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