Monday, July 31, 2006

The Paradox of the Preface

You write a book. You believe every single sentence in that book. Yet you also write a preface in which you acknowledge that probably something you've said in the book is false. It seems that you believe each claim p1, p2, p3, ... pn, individually but you disbelieve the conjunction (p1 & p2 & p3 & ... & pn). But of course, it follows straightfowardly from p1, p2, p3, ... pn, that their conjunction is true. In denying it, you commit yourself to an inconsistent set of beliefs. We ordinarily think holding an inconsistent set of beliefs is irrational; yet your acknowledging the likelihood of error in the preface seems eminently rational. Hence, the paradox of the preface.

Much has been written about the paradox of the preface, but I want to focus on just one issue here: The challenge it poses for the idea, raised last Monday that we cannot have flatly contradictory beliefs. For if we accept what we might call the conjunctive principle of belief attribution -- the principle that someone who believes A and who believes B also believes A & B -- then it seems to follow that the preface writer has baldly contradictory beliefs: (p1 & p2 & p3 & ... & pn) [from repeated applications of the conjunction principle] and -(p1 & p2 & p3 & ... & pn) [from what he says in the preface].

The solution, I think, is to deny the conjunction principle. On a representational warehouse model of belief, according to which to believe something is to have representations of the right sort stored in an appropriate location in the mind, denying the conjunction principle invites the unsavory conclusion that in order to believe that I got in the car and drove to work I have to represent both "I got in the car" and "I drove to work" and "I got in the car and drove to work". (On the other hand, if the warehouse-representationalist accepts the conjunction principle, she risks sliding into the even more unsavory position of holding that we believe all the logical consequences of our beliefs.)

On a dispositional approach to belief, according to which to believe something is to act, cogitate, and feel in ways concordant with the truth of the proposition in question, there may be room to deny the conjunction principle, without dragging in a suite of redundant representations. The key is to notice that one needn't be absolutely consistently disposed to act in accord with some proposition P to count as believing that P. For example, one can believe in God despite passing fits of irreligiosity. One need only act appropriately generally speaking, most of the time, and when excusing conditions are not present. One need only match the profile of the full and complete believer to a certain degree. (For more on this, see my Phenomenal, Dispositional, Account of Belief.) And what comes in degrees doesn't conjoin.

To see this last point, consider the lottery paradox: It's approximately certain that Jean won't win and approximately certain that Bob won't win and approximately certain that Sanjay won't win, ..., but it doesn't follow that it's approximately certain that no one will win. The uncertainties compound with conjunction. So also, likewise, in the paradox of the preface: I come pretty close to matching the profile of a full and complete believer in each of p1, p2, p3, ... pn, considered individually, but it doesn't follow that I come at all close to matching the dispositional profile of a full believer in the conjunction (p1 & p2 & pn & ... & pn). This point is often made in terms of Bayesian degrees of belief; but I intend it here as a point of set theory, where the relevant sets are sets of dispositions. Having most of the elements of set A and most of the elements of set B does not necessarily imply that one has most of the elements of A+B.

(By the way, I believe it was Jay Rosenberg who first raised this as a puzzle for my rejection of baldly contradictory beliefs, at an APA meeting some years ago.)


B. Michael Payne said...

The preface of Of Grammatology raises opaquely this issue, as well.

B. Michael Payne said...

I'm sorry, I meant to comment more than that. Is there a middle ground between Derridian obscurantism and, well, analytic obscurantism? Taking a cue from Derrida, the problem of preface has to do, doesn't it, with the fact that the author generally writes the preface after he writes the book to which the preface prefaces. It seems perfectly clear to me--and I don't know much about contemporary analytic philosophy--that the disposition/lottery paradox, which you've enunciated in your post, is just one conceptual apparatus by which to talk about one's work.

(I have a friend who thinks that his past self and his future self are different selves and that never the two will meet.)

Actually, I'm thinking rather on the fly, when you're looking at a particular belief you may say that you believe in it or you don't. You could look at discrete arguments in this way. You may agree with A1, A2, A3... An. And as you pointed out, you may not not agree with their conjunction. This seems paradoxical. But what if you looked at the above arguments like this: A1+2, A2+3+4, A1+4+6, A6+45+99... You may still be said to agree with A1, A2, A3...An, but you may only agree with certain ways of their fitting together. (Or of their not fitting together.)

What I'm trying to get at is a point Wittgenstein makes in the Philosophic Investigations: Namely, that when you're analyzing a red colored square, say, what's to stop you from calling it a red square with an orthogonal transparent square. Or half of a red rectangle. Or two red triangles.

I've never prefaced a book, but I've prefaced a lot of my statements. (The preceding sentence, in fact, was such a preface.) I think what a preface does is to signal to the audience how you want them to take what you're saying; that is, how you want the audience to analyze your statements, maybe, in the way I described above. When you analyze them in a different way, you might get confused. It might seem paradoxical.

Anonymous said...

Hi Eric,

Giving up the conjunction principle is probably the most elegant way of getting rid of the problem. So I'm inclined to agree with you in that. (By the way, this was Kyburg's original reaction to the lottery paradox in 1961.) I was once moved by Mark Kaplan's interesting defense of the principle saying in effect that we need it in order to make sense of our everyday practices of giving deductive arguments. But I have come to think that his defense is not really convincing if we are dealing with rather long conjunctions as here in the preface paradox.

Nevertheless, there is something about your solution that strikes me as problematic. You say: "The key is to notice that one needn't be absolutely consistently disposed to act in accord with some proposition P to count as believing that P."

For my taste there is too much psychology in here. Notice that at core the preface and lottery paradoxes are genuinely NORMATIVE puzzles: given the preface situation, would it be epistemically rational for me to believe the conjunction etc? Saying, as you do, that believing that P just doesn't require being absolutely consistently disposed to act in accord with P seems to be beside the point. The problem seems to be not so much about making sense of belief attributions, but about what we SHOULD believe in certain circumstances.

Now it may be true that 'believe' is vague to some extent which the dispositional account captures, but this should not preclude making sense of the preface puzzle. Perhaps, it is a virtue of (or even a requirement for?) an adequate account of belief that it allows to formulate those paradoxes about RATIONAL belief.

(By the way, Jay Rosenberg is really a good commentator - although I have even seen him sleeping during presentations he then cleverly comments on!)

Eric Schwitzgebel said...

Michael: I agree with your impression that there are many different ways to see the puzzle. Philosophers so often seem to think there's only one really right way to see through a problem; but I'm inclined to think that philosophy is more a domain of decisions and alternative conceptualizations with different competing values than a domain of clean truth.

Mike, you raise an excellent point. I wonder, can I go Bayesian for the normative aspect of the puzzle? You believe all the p's .95, say. Normally, if you conjoin them, you end up with a lower degree of belief -- perhaps even below .5. The question, then, is how to hook up the normative Bayesian stuff with the descriptive dispositional stuff. I don't have all the details worked out. For example: Is feeling absolute confidence in P, when asked, part of the standard dispositional profile for believing that P, so that someone who doesn't feel such confidence fails completely to match the profile? There are probably alternative ways in which such questions could be worked out, without logical inconsistency.

B. Michael Payne said...

If you believed something 95%, does that mean that every one time in twenty you would, perhaps, believe the exact opposite?

Eric Schwitzgebel said...

Tone doesn't come across very well in plain text, so I'm not sure in what vein you made that last remark, Micheal, -- but the standard Bayesian thing to say would be that if you believe 95% you would (or alternatively should) be willing to wager $0.95 on a bet that pays $1 if you're right and $0 if you're wrong. But actually, I find that way of thinking a bit of a straitjacket: There are many ways of being in-between or ambivalent or lacking confidence -- including just what you said. Maybe Antonio sincerely professes belief in God nineteen times out of twenty and atheism once!