Certain Doubts

Suppose one adopts a closure principle for justification of the following sort:

CLOSURE: If S justifiably believes p and justifiably believes that p implies q, then S is justified in believing q.

Justifiably believing implies believing, in this formulation, but being justified in believing does not.

Suppose one is thinking of the lottery paradox, with n tickets. Suppose also that on your theory you are justified in believing that your ticket will lose. Your theory also endorses the principle that it is impossible to be justified in believing p and at the same time be justified in believing ~p. Finally, suppose you justifiably believe that some ticket will win.

Then consider the following conditional: if ticket 1 loses, then if ticket 2 loses, then . . . if ticket n loses, then it is not the case that some ticket wins. Your ticket is ticket #1, and your evidence is probabilistic. So you come to believe, justifiably, the conditional minus the antecedent about ticket #1. You apply this line of reasoning n times, and get a contradiction.

To save CLOSURE, one might say the following. Once you use your evidence to conclude that ticket 1 loses, the level of confirmation that any remaining ticket will lose is not n-1/n, but rather n-2/n-1. And once you use this evidence to conclude that ticket #2 will lose, your evidence about the remaining tickets gives a confirmation level of n-3/n-2. At some point, the value of n-m+1/n-m is low enough that you it fails to justify believing that the next ticket will lose, so the lottery example isn’t a counterexample to CLOSURE.

Note however that the order of inquiry here makes a difference to what you are justified in believing, if one takes this way out of the problem for CLOSURE. If the tickets are ordered in one way in the conditional with n embedded antecedents, you can come to be justified in believing that ticket #64 will lose. If the antecedents of the conditional are ordered in another way, by the time you get to the question of whether ticket #64 will lose, you’ve already gone far enough that the confirmation level doesn’t justify believing that ticket #64 will lose. So, if you like CLOSURE (or some close cousin of it), and if you like this response to the lottery counterexample to CLOSURE, then you must maintain that the order in which you apply a body of evidence to a set of propositions can make the difference between a claim being justified or not being justified. But how could changing the order of the antecedents in the imagined conditional have this effect? After all, it’s not as if one was unaware prior to drawing the inferences about what one’s body of evidence shows.

So: can one get out of the lottery counterexample without embracing the unusual claim that the order of inference here makes all the difference as to whether a particular belief is justified?

Consider the following principle, one lifted from the same Feldman piece that prompted the last post:

Evidence that there is evidence for P is evidence for P.

I’ll call this principle the “metaevidence” principle. According to this principle, no matter how many repetitions of the phrase ‘there is evidence for’ precede P, it is always true that there is evidence for P.

If the metaevidence principle is true, then evidence and probability look quite different. Suppose it is probable that it is probable that P; it doesn’t follow from this claim that it is probable that P (since a claim can be probable and false). But doesn’t this same reason count against the metaevidence principle? That is, can’t there be evidence for something false? Of course there can. So why do things change when the claim is itself a claim about evidence?

Rich Feldman is one of my very favorite epistemologists. Some of my respect is self-interested: I agree with a vast majority of his expressed epistemological views. But there’s more to it than just self-congratulation involved when I read his stuff. I would say, in fact I will say–here I go, I’m saying it–I’ve never read something he wrote and not learned something philosophically important. I’ve just read another piece of his, on his website. As always, I learned a lot, most of it by becoming convinced by his arguments of points of view he defends.

This time, however, another kind of learning occurred as well, I believe. We might say that what I learned counts as learning in, as our continental brethren might say, the privative mode. I think he endorses the following principle:

If S and S’ are epistemic peers and have shared all their evidence concerning p (and both reasonably believe this conjunction), then it is not possible for S to rationally believe p while S’ rationally believes ~p.
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The comments on my first post about openmindedness make me think that we might need a two dimensional framework for belief. One dimension is that standard Bayesian one of degree of belief. The other, central to the concept of openmindedness, is something like strength or imperviousness of belief. This is a matter of how easily budged the degree of belief is by new information. Your degree of belief might match your evidence precisely, and yet be so firmly entrenched that new evidence either way would not budge your degree of belief. This feature of degree of belief can be measured, though I waver on which of two ideas to use. One idea is to measure it from a from a maximum where the degree of belief is completely petrified, immovable by any possible additional information, toward the other end where the degree of belief is completely vaporous, changeable by any and every piece of new information whatsoever. The other idea is to measure it using the concept of evidence, so that the maximum is a degree of belief impervious to any new evidence, and the minimum where the degree of belief will change with the introduction of any new evidence at all (even if rebutted by other evidence one already possesses).

If we adopt such a two-dimensional framework for belief, we have another potential account of openmindedness. Strength of belief can be appropriate or inappropriate, and closemindedness occurs where one’s strength of belief is excessive. It is this strength of belief that underlies the disposition of being resistant to learning. Closemindedness is therefore the excess with feeblemindedness (where one’s degree of belief is too easily moved) the deficiency, and openmindedness the mean.

In the prior post I suggested requiring that degree of belief exceed warrant for closemindedness, but given the two-dimensional framework, that seems wrong. Suppose your degree of belief is deficient, you are doxastically timid, so to speak, but your timidity is firmly entrenched. If it is impervious to additional evidence, I would think that is still closeminded.

Wayne Riggs has a new paper up on his website that has me thinking about openmindedness again (by the way, Wayne, I think Greg Pappas had a piece on this topic once in the Peirce Transactions). Two questions are central here: what is openmindedness and why is it a valuable character trait? On the latter score, I recall Pappas’s answer was metaphysical: openmindedness is important because the world is in flux, and without openmindedness, our belief system would be frozen while the world changed.

This answer seems to me mistaken on two grounds. First, being closeminded does not require an inflexible belief system. So a closeminded person could change attitudes across time. Second, the fact that the world changes needn’t affect the closeminded unless their closemindedness undermines or negatively affects their achievement of some epistemic good. On this score, it appears that an infallible person wouldn’t need to abandon his/her closemindedness.

For these two reasons, the right answer to the question of the significance of openmindedness is epistemic rather than metaphysical. Openmindedness is important because we are fallible, not because the world is in flux. Moreover, even if the world were changeless, fallibility itself would be a sufficient account of the importance of openmindedness.

Wayne’s proposal is one concerning the epistemic good in relation to which openmindedness has value. On Wayne’s account, the value in question is understanding, not either true belief or knowledge. He seems to agree, though, that it is our fallibility that makes openmindedness important for securing the epistemic good in question.

The last question is about the nature of openmindedness. Wayne first quotes John Dewey (wouldn’t it be amazing if we found an adequate definition from this source?):

This attitude may be defined as freedom from prejudice, partisanship, and other such habits as close the mind and make it unwilling to consider new problems and entertain new ideas.

So, according to Dewey, openmindedness is freedom from prejudice and partisanship. Clearly, we need to do better than this (only political independents turn out to be openminded on this account… and only so long as they remain uncommitted). Wayne objects as well, but turns immediately to the issue of the value of openmindedness, where has a lot of interesting things to say. But I want to know what openmindedness is as well as knowing why it is a virtue.

The Dewey quote is especially unhelpful in this regard. Partisanship in the epistemic realm might involve either of two ideas: either holding beliefs, or having a degree of belief not in line with what the evidence warrants. Neither idea provides a necessary condition for openmindedness: you don’t have to free yourself of beliefs to be openminded, and you don’t have to correlate strength of belief with quality of evidence to avoid closemindedness (on the latter score, not that intellectual meekness and doxastic insecurity are not examples of closemindedness). The idea of intellectual prejudice suggests the same sort of idea: believing something prior to acquiring any good reasons to believe it. But that is simple irrationality, not closemindedness. Closemindedness has something to do with one’s response to new ideas and new information.

Maybe there is something to the Dewey’s idea, as follows. A closeminded person is given to extreme degrees of belief, extreme because they outrun quality of evidence. This approach allows that closemindedness can come in degrees. Having a weaker degree of belief than the evidence warrants is not a sign of closemindedness, but having a stronger degree of belief can be (i.e., is necessary for). The result of such is the characteristic closeminded response to new ideas and information: they are rejected on the basis of some assumed quality of evidence correlated to strength of belief, even though the quality of evidence possessed is not up to the task. Instead, all that is present is the exaggerated degree of belief, and a response that presupposes a perfect calibration between quality of evidence and degree of belief. So, maybe a good start is to think of closemindedness as involving a disposition to respond to new information or ideas on the basis of an exaggerated degree of belief rather than on the basis of the quality of actual evidence possessed.

Does this sound on the right track? I should note immediately that there are going to be finkish disposition problems here: cases where a person’s beliefs are perfectly correlated with evidence, but where the stimulus of new ideas and information itself creates the disposition to respond on the basis of a heightened degree of belief (in part because the stimulus causes the heightened degree of belief (or causes one to behave as if one has such a heightened degree of belief?)). If a person is characteristically this way, it is hard to classify them as not closeminded, but I’m not quite sure what to say about such a case at present.

Fake Barn Country is having a lively discussion on Foley’s work, gypsy lawyer counterexamples as well as other topics in epistemology. Some of the discussion I’ve been part of as the lone defender of my illustrious mentor’s views, and I thought it would be interesting to see here what kind of reception there is to the primary motivator of Dick’s view that Gettier examples can always be explained in terms of the lack of true beliefs. The primary motivator is, I think, Dick’s Swampman case, where a new creature arises from the swamp as a result of a lightning strike, with a strikingly broad and comprehensive range of truths within its expressive powers (I’d call them beliefs, but at this point, I don’t want to have to go into the externalist worry about this): ask Swampman anything you wish, and he’ll produce a correct answer and be able to construct an explanatory answer as well that is both thorough and complete. Moreover, his answering in this fashion is counterfactual-supporting, so can’t be counted as mere luck (though of course it involves luck to have the ability itself). Swampman is thus much more intellectually impressive than any of us, and Foley’s assessment is that we’d have to admit that Swampman knows a whole lot more than any of us.

Any takers? Any critics?

I just received in the mail from Blackwell my copy of the new book, Sosa and His Critics, featuring, of course, essays about CD’s own Ernest Sosa, many of them by CD-ers, the majority of them on Sosa’s epistemology, together with Sosa’s replies, all edited by CD’s own John Greco. It looks great, Ernie & John. Congratulations!

The first Philosopher’s Carnival, a collection of some items that have appeared on philosophy weblogs, is here. The plan, I believe, is to put up items every week or so at this site.

Clayton Littlejohn sent me an interesting email about justification, and with his permission I’m quoting it here so that our discussion can be available to others as well. Clayton’s questions are about the relationship between personal and doxastic justification, as expressed in locutions such as “S is justified in believing p” and “S’s believing p is justified”, respectively. Since his discussion is several paragraphs long, I’m going to put the entire quotation plus my comments on it below the fold.

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Think about traditional theories of perception, such as the theory of appearing, sense-data theories, or adverbial theories. Each of these theories is aimed at a metaphysical question, the issue of what the immediate object of perception is, if any (so the adverbial theory is deflationary here). As such, these theories aim to say what something about the given in sensory experience, or what is immediate, or what it is that we are directly acquainted with (again, if anything). When epistemologists approach this metaphysical question, one of the central issues is whether or not the metaphysical entity in question is “conceptual”.

The central epistemological questions involved in perception go beyond this metaphysical question. The aspects of perception that are relevant to knowledge include its motivating and justifying capacities with regard to belief. The first issue raises the spectre of ethical internalism (and perhaps noncognitivism) in epistemology, since perceptual states seem to be purely cognitive, and yet they motivate belief in much the same way that desires motivate action. The second issue raises the questions of epistemological internalism/externalism and many others as well.

Given this background, why is the issue of conceptual content addressed in answering the metaphysical question? The question of conceptual content is most directly a question about how it could be that perception justifies belief. If perceptual states have content, then the connection between that content and the content of a belief can be rationally intelligible to the perceiver and so yield justification as a result; if not, then some other, perhaps reliabilist, story will have to be told. If the metaphysical objects of perception have conceptual content, then that helps with the justification question; but if not, it’s not obvious that anything follows.

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