January 07, 2007

Are Self-Undermining Arguments Self-Undermining?

[The title of the post should be parsed so that it does not ask whether a tautology is true.]

In a post about the epistemology of disagreement, Brian Weatherson argues that the Christensen-Elga-Feldman position is self-undermining:

Roughly, the idea is that if you believe p, and someone as smart as you and as well informed as you believes ~p, then you should replace your belief in p with either a suspension of judgment (in Feldman’s view), or a probability of p between their probability and your old probability (in Elga’s view).

This position is self-undermining because many smart, well-informed people deny it, and so anyone who comes to believe it should suspend judgment in its truth. Brian says, "I think no one should accept a view that will be unacceptable to them if they come to accept it," so he thinks no one should accept the CEF principle.

The principle (S):

(S) No one should accept a view that will be unacceptable to them if they come to accept it

is very appealing, but I'm not sure it can ever provide a reason to reject or suspend judgment on a view that we would otherwise accept. Suppose p is such a view; so long as you don't believe p, the arguments for p are compelling, but if p is true then belief in p is unacceptable. Consider belief in not-p. Since the arguments for belief in p are compelling so long as we do not believe p, if we believe not-p (and are consistent) then belief in not-p is unacceptable if we come to accept not-p. So not-p also falls victim to principle S.

Suspending judgment doesn't quite fall victim to principle S, but it seems to face a similar problem. As I framed the question, the arguments for p are compelling so long as we do not believe p; we don't even have to believe not-p for them to be compelling. Then, once we've suspended judgment on p, we've got no reason to reject p and a good reason to accept it. So we shouldn't suspend judgment. Suspending judgment isn't accepting a view, which is why principle S doesn't apply, but nevertheless it seems reasonable to extend principle S to "No one should suspend judgment on a question if suspending judgment will be unacceptable to them so long as they suspend judgment."

So what should you do when you are convinced by the arguments for a view that will come to seem unacceptable to you when you accept it? I'm not sure. It certainly seems that in such a situation your cognitive limits have become manifest, and you should do what you should do when that happens (which may not always be to suspend judgment). Or perhaps you should oscillate back and forth among the self-undermining views.*

Best of all would be to find a reason why the argument for the self-undermining view is wrong, so that principle S no longer provides your sole reason for refusing to believe in p. On the epistemology of disagreement, that's something I haven't done yet.

*Here's how things might work for the Elga view, that you should adjust your probability to be intermediate between your original probability and your peer's probability. If I only considered my own view of the arguments, I would give a credence of 1 to the Elga view, but there is one other expert who gives a credence of 0 to the Elga view. I now suspend judgment, giving a credence of 0.5 to the Elga view. But it seems that my reasons for giving a credence of 0.5 rather than 1 to the Elga view depend on the Elga view itself, which I am now only giving a credence of 0.5 to.

An equilibrium point may be reached when I assign a credence c to the Elga view that satisfies this constraint: c = (1 - c) + c2/2. Reasoning: insofar as I reject the Elga view, I should trust my own arguments, which convince me of the view; so this component of my credence is 1 - c (degree of credence in not-Elga) * 1 (degree of my confidence in Elga, given not-Elga). Insofar as I accept the Elga view, my credence in it should be midway between my credence in it (c) and my peer's credence (0); so this component of my credence is c (degree of credence in Elga) * c/2 (degree of my confidence in Elga, given Elga). Solving, we get c2/2 - 2c + 1 = 0, or c = 2 - √2 = approx. 0.586.

Giving a credence of 0.586 to the Elga view if you're convinced by the arguments seems consistent, but very weird. I make no particular claims that the previous paragraph gave the right way of calculating c.

Posted by Matt Weiner at January 7, 2007 04:11 PM
Comments

If I only considered my own view of the arguments, I would give a credence of 1 to the Elga view

I should point out that this isn't actually true of me; I think that this view surely isn't right, but I don't have much of an argument why not.

Posted by: Matt Weiner at January 7, 2007 04:34 PM

“Suppose p is such a view; so long as you don't believe p, the arguments for p are compelling, but if p is true then belief in p is unacceptable.”

I wonder whether there ever could be such a p---that is, a p that meets both of the following conditions:

1) So long as you don’t believe p, the arguments for p are compelling.

2) If p is true, then belief in p is unacceptable.*

It seems to me that any p that meets condition (2) will thereby not meet condition (1). Why? Since (S) is true, if (2) is true, then no one should accept p. But if no one should accept p, then the arguments for p cannot be compelling. Thus, if (2) is true, then (1) is false.

OK, so my argument assumes what you’re trying to disprove---namely, (S). But doesn’t this show that you’ve begged the question by simply stipulating that p meets conditions (1) and (2)?

* I should add that I think you’ve slightly misrepresented (S) in condition (2). (S) talks about what is acceptable if (S) is accepted (as true) not if (S) is true. But I think our arguments go through just the same.

Posted by: Dustin Locke at January 7, 2007 05:30 PM

Hi Dustin,
First of all, I think you're right about condition (2); I slide back and forth a little there.

As for the main point, what I have in mind is a situation like the following:

There is what looks like a good argument for p.
Accepting p makes it irrational to accept p.
But that's the ONLY reason I have not to accept that argument.

This seems at least possible; at least, for limited creatures such as ourselves who may not have found the flaw in the argument yet.

If so, suppose we reject p on grounds of S. What should we take to be the flaw in the argument for p? It can't be whatever makes it irrational to accept p once I've accepted p; since I don't accept p, this doesn't come into play. It seems that it has to be the self-undermining nature of the conclusion itself. But this isn't a very satisfying explanation of the flaw in the original argument. It seems to me that the argument that p still stands as an attractive nuisance until it itself is undermined.

Things get even worse if not-p has the same problem, as I believe it does in this case. After all, it's not a priori that CEF undermines itself (it depends on the existence of CEF dissenters); and for some people it is (a posteriori_ true that when they evaluate the arguments about disagreement for themselves, as anti-CEF dictates, they find CEF extremely convincing. What are they to do? If they take the anti-CEF position, it dictates that they should evaluate the argument for themselves, which would mean accepting CEF; and there seems to be no more reason to disregard the contingent fact that they find the CEF arguments convincing than that others do not. [Perhaps this means they should suspend judgment.] The situation is somewhat like Andy Egan's counterexamples to causal decision theory, where B is better given that you choose A and A is better given that you choose B.

Now, the logical conclusion to draw may be that there's some yet undiscovered reason you shouldn't be convinced by the argument, and that is in fact what I think about the CEF position. (Although here my ignorance of the reason is probably due to not knowing the issue well enough, so I'm not even a peer.) Still, the S argument doesn't seem to me to provide a reason in itself to reject p; it may indicate the existence of a reason and leave us with more work to determine what that reason is.

Posted by: Matt Weiner at January 7, 2007 07:29 PM

Hi Matt,

"[the S argument] may indicate the existence of a reason [to reject p] and leave us with more work to determine what that reason is."

But if we have a reason to believe that there is a reason to reject p, don't we thereby have a reason to reject p?

Posted by: Dustin Locke at January 8, 2007 09:59 AM

Good question. It's my understanding that something similar is at the heart of the CEF arguments: If we have evidence that there is undefeated evidence for q, don't we thereby have evidence for q? If so, then the acceptance of q by our peer gives us evidence for q, since we have reason to believe that the peer has evidence for q, and we aren't aware of any potential defeaters that the peer isn't also aware of.

You'll note that I haven't answered the question. The situation may be that of the mathematician who's provided an existence proof but would like to actually display the witness; then the mathematician has more work to do, but we (if we aren't intuitionists) wouldn't say that she lacks reason to believe the existence claim.

Still, the person I've described seems to be in a worse predicament than the mathematician. She finds the argument for p convincing even though she has reason to think (so we assume) that there is a flaw in it. This may be more like a mathematician who has an existence proof but has checked all the possible witnesses and found them wanting. Then she knows that she's made a mistake somewhere; but it's not obvious what the proper response is.

[Also, I don't think the last paragraph of my previous comment necessarily follows from the previous paragraph, so the CEF defender might want to disclaim the whole thing.]

Posted by: Matt Weiner at January 8, 2007 10:45 AM

"I wouldn't belong to any club that would have me." -- G. Marx, Dialectical Materialism for Dummies

Posted by: Ben at January 8, 2007 07:19 PM

But how do you know that the other person is as smart and well-informed as you? If they believe not-p, aren't they dummies?

Posted by: Matt's mom at January 9, 2007 09:45 AM

Sometimes clearly not -- if they're in a better position to know, you should adjust your arguments to them; if you're in a better position, you should ignore their opinion. But we're thinking of cases where they have the same credentials, you know them well enough to know that they're not generally batty, and (most important) you're both looking at the same evidence. So it seems presumptuous to say that they're dummies just because you disagree on this question.

Posted by: Matt Weiner at January 9, 2007 03:01 PM