Here’s a basic (and possibly wrong-headed) question. Probably, if I were a better student of logic and/or epistemology, I would see the answer, but at the moment I don’t.

Why do we even recognize a category of inductive inferences (or, as some would have it, inductive standards of inference)? Why not treat all inferences as deductive, but with some sort of probabilistic qualification built into the conclusions of some of those deductive inferences?

That is, instead of characterizing such inferences in these terms …

1. This is a fair, six-faced, cubical die and I shall roll it in the normal way.
So probably
2. I shall not roll a “6.”

3. The first 999 crows I saw were black
So probably
4. The next crow I see will be black.

… why not characterize them in the following terms?

1. This is a fair, six-faced, cubical die and I shall roll it in the normal way.
Therefore (certainly):
2*. Probably, I shall not roll a “6.”

3. The first 999 crows I saw were black
Therefore (“certainly”):
4*. Probably, the next crow I see will be black.

Of course, I see that there’s a difference between the above arguments and standard deductive arguments such as:

5. If Fluffy is a vixen, then Fluffy is a female.
6. Fluffy is a vixen.
Therefore,
7. Fluffy is a female.

But that difference could be expressed in terms of the presence or absence of a probability qualifier in the conclusion, and not in terms of a fundamentally different kind of inference.

So I repeat my question: why do we allow for two kinds of inference, instead of only one?

The conference will focus on three main challenges to religious and moral beliefs:

1. Widespread interpersonal disagreement among intellectual peers on religious and on moral topics provides reason to doubt these beliefs;
2. Belief-source disagreement on moral issues between commonsense moral intuitions and religious belief sources raises doubts about both methods of belief formation;
3. Evolutionary accounts of the origins of our religious and moral beliefs create doubts about these beliefs by undermining our confidence in the reliability of their sources.

Conference Participants:

• Robert Audi                              University of Notre Dame (Philosophy)
• Sarah Brosnan                         Georgia State University (Psychology)
• Kelly James Clark                    Calvin College (Philosophy)
• Stephen Davis                          Claremont McKenna College (Philosophy)
• Kyla Ebels-Duggan                  Northwestern University (Philosophy)
• William FitzPatrick                   University of Rochester (Philosophy)
• John Greco                              Saint Louis University (Philosophy)
• John Hare                                Yale University (Divinity School)
• Kevin Hector                            University of Chicago (Divinity School)
• Timothy Jackson                     Emory University (Candler School of Theology)
• Jordan Kiper                            University of Connecticut (Anthropology)
• Jennifer Lackey                       Northwestern University (Philosophy)
• Dustin Locke                           Claremont McKenna College (Philosophy)
• Charles Mathewes                  University of Virginia (Religious Studies)
• Christian Miller                        Wake Forest University (Philosophy)
• Mark Murphy                           Georgetown University (Philosophy)
• John Pittard                             Yale University (Philosophy & Religious Studies)
• Jeffrey Schloss                        Westmont College (Biology)
• Walter Sinnott-Armstrong        Duke University (Philosophy)
• Richard Sosis                           University of Connecticut (Anthropology)
• Sharon Street                           New York University (Philosophy)
• Ralph Wedgwood                     University of Southern California (Philosophy)
• Erik Wielenberg                        DePauw University (Philosophy)

 Organizers:

• Michael Bergmann                  Purdue University (Philosophy)
• Patrick Kain                             Purdue University (Philosophy)

For more information, including how to register, go to www.knowinginreligionandmorality.com/conference.html.

Our intuitions suggest that, to defeat undercutting evidence, we need to appeal to something independent of what’s undercut.  I think those intuitions are wrong.  Suppose I receive testimony from a reliable source that all my belief-forming methods are unreliable.  Given our “independence intuitions”, this undercutting evidence is impervious to defeat.  Since it undercuts everything, there is nothing to which I can appeal.  Yet the mere generality of the defeater should not make it invincible.

When we realize that the intuitions are wrong, we have some explaining to do.  If undercut evidence can defeat the undercutting evidence, then what’s the problem with trusting the testimony of the car salesman?  And what’s the problem with relying on the wall’s appearing red to give me evidence of my reliability in the context where the wall is lit by red lights?  If our “independence intuitions” don’t explain what’s going on in these cases, why can’t we appeal to the undercut evidence to defeat the undercutting evidence?

Feel free to comment on the above quick and dirty argument without consulting the material below the fold.  For those who want to see the argument against our independence intuitions laid out more carefully, see below.

I’ve just completed a mathematics test.  My belief in each answer is highly justified.  But then I’m told by a reliable source that my coffee was laced with a drug that makes mathematical reasoning highly unreliable for at least four hours (it only took 1 to complete the test).  It seems that I should now lower my confidence that my answers are correct.  More generally, when our beliefs are highly justified (but not certain), and we acquire some undefeated evidence that they were formed in an unreliable way, it seems that our beliefs are less justified and, perhaps, no longer justified at all.  More formally, we can appeal to the:

Undercutting Evidence Principle (UEP): If my beliefs in domain D are highly justified (but not certain) at t1 and if, at t2, I acquire evidence that my judgments within D were formed using method M and that M is unreliable, then, unless this evidence is defeated, my beliefs in D are less justified at t2 than they were at t1.

Once I’m informed of the drug, I begin to check my answers.  I consider first question.  I check my calculations and they seem flawless.  I then realize that there are other ways of calculating the answer to the question.  For example, instead of multiplying 4 x 4, I add 4 + 4 + 4 + 4.  I consider an additional five ways of calculating the results to the answer and each time I confirm my original answer.  I undertake a similar investigation for each of the other 9 answers. My new calculations confirm my old ones again and again.  Presumably, these confirmations, when taken together, count as evidence for the reliability of my mathematical reasoning.  Can this evidence raise my justification that my answers are correct (at least partially) back to their original level? Or perhaps even higher than their original level?  Intuitively, many think the answer is clearly no.  These “confirmations” appealed solely to mathematical reasoning.  But that is the very sort of reasoning that my evidence suggests is unreliable.  How can further investigation defeat the undercutting evidence by relying on the very sort of reasoning that is undercut?  At first glance at least, that’s just plain foolish.  Hence, the following principle may seem undeniable:

Independence: A body of evidence E* can defeat undercutting evidence that M is unreliable only if E* was, at least in part, was not obtained via M.

Unfortunately, things aren’t so simple.  We are faced with a contradiction when we consider two other very plausible claims.  Consider first:

Possibility of Global Undercutting (PGU): it is possible to have beliefs that are highly justified at t1 and then acquire evidence at t2 that all of your belief forming methods are unreliable, so all your judgments are/were formed using methods.

PGU is a very weak claim.  It says that it is possible to have beliefs that are highly justified and then acquire evidence that all your beliefs are formed via some unreliable method.  Suppose, for example, that I receive reliable testimony that all my belief-forming methods are unreliable.  This testimony is confirmed by the world’s leading experts.  The most reliable news outlets testify that my beliefs are unreliable, an unfortunate result of an insidious science experiment.  I would say that I have now acquired evidence that all my beliefs are formed by some unreliable method.  Indeed, one might think that this is fairly strong evidence that all my belief forming faculties are unreliable.  I usually confidently believe things on far less impressive testimony.

But when you put UEP and PGU together, it follows that I should reduce confidence in all my beliefs.  Is there any way that I can regain the lost degree of justification?  Not given Independence.  Since it disallows me from appealing to anything undercut and every way I have of forming beliefs is undercut, there is nothing to which I can appeal.  I’m stuck where I am—at least until I gain even more evidence of my unreliability, at which point my justification might decrease even further.  Hence,  invincible counterevidence would be possible.  Yet the mere fact that undercutting evidence is completely general should not make that evidence invincible, as would be the case were Independence true.  In other words:

Anti-Invincibility: A body of undercutting evidence E can’t be invincible, i.e. there must be some possible circumstances in which E is defeated.  Or at the very least, the generality of the undercutting evidence shouldn’t ensure that the defeater is invincible.

Setting aside the possibility that one can acquire new belief forming methods, UEP, Independence, PGU, and Anti-Invincibility form an incompatible tetrad.  UEP, Independence, and PGU guarantee that invincible defeaters are possible, and Anti-Invincibility guarantees that there aren’t any.

I take it that the two least plausible claims are Independence and Anti-Invincibility.  Which one should we give up?  Which one is the least plausible?  I don’t have a super strong argument for Anti-Invincibility, but I do want to put a little pressure on Independence.  In the case described above, I have all sorts of testimonial evidence that suggests all my belief forming methods are unreliable.  Independence entails that, even if I were to acquire rather convincing evidence that the whole thing is an elaborate gag, this evidence still could not restore me to my original level of justification.  And that seems rather counterintuitive, and it reinforces the intuition that the mere generality of undercutting evidence should not make it invincible.  I think, therefore, that we should reject Independence.

I do not post this to cast aspersions or to accuse.  Rather, in the spirit of the undergraduate women students at Northwestern who recently started the WiPhi (“Women into Philosophy”) group here in the NU Philosophy Department, I post this to challenge the epistemology community.   With these excellent undergraduates (and the many, many others like them all over the world) in mind, I challenge us to see whether, within a period of a few years, we might change our practices in such a way that, far from being seen as not particularly women-friendly, epistemology will be, and will come to be seen as, one of the most women-friendly subdisciplines within philosophy.  (Of course, this should be part of an effort to make philosophy as an entire discipline more women-friendly, as well as more friendly to all underrepresented groups; but perhaps this smaller and more focused effort can help these larger aims.)

In order to ensure that this effort has a fighting chance, I think it is important at the outset to offer proposals with which everyone working in epistemology (or near enough) might agree.  I offer the following suggestions in that spirit (and other suggestions are welcome as well).

First, there are some large-scale efforts that I would propose: (1) program chairs for epistemology conferences or workshops are urged to take all reasonable measures to ensure a happy gender representation, both among the invited sessions and among the chosen submissions; (2) editors of epistemology volumes and special editions of journals are urged to take all reasonable measures to ensure a happy gender representation among contributors; (3) those teaching epistemology should ensure that at least some women epistemologists are on the syllabus, to be read and discussed; and (4) those on search committees for positions defined to include epistemology should make sure to give extra scrutiny to all of the applications from women candidates, and also to familiarize themselves with the various ways in which such applications are dismissed prematurely, or on insufficient evidence.

But there are also some efforts which, though perhaps on a smaller scale, are ones each one of us can make: (5) let’s be aware of the phenomenon Sally Haslanger calls the “micromessages” we communicate to others, and (to the extent this is feasible) aim to address these in our own behaviors; (6) let’s recognize and resolve to address the various ways in which women get unfairly treated at conferences (raised hands not acknowledged at all, or acknowledged only late in a session; points made not acknowledged at all, or only acknowledged after a male colleague makes essentially the same point after her, thereby illustrating a form of what Miranda Fricker calls “epistemic injustice”; other, more subtle exclusions from group conversations; etc.); (7) let’s recognize and resolve to address the various ways in which women get unfairly treated in the classroom; and finally (8) let’s all attend to the empirical work that is being done by many excellent scholars regarding the reasons for the low numbers of women in philosophy (as compared to other disciplines), and let’s all resolve to act in small ways and big to address these.

I should add that I do not think it is wise to conflate the aim of making epistemology more women-friendly with the aim of increasing the visibility and prevalence of feminist epistemology.  My point here is not against feminist epistemology – not at all.  It is rather that the role of feminist epistemology within epistemology should be settled by the outcome of philosophical reflection and discussion among epistemologists (including but not limited to feminist epistemologists).  By my lights, conflating these two aims would be unfair both to women in epistemology (as it would implicitly regard them as having to work in feminist epistemology), and to feminist epistemology (as it would assume that the case for the significance of feminist epistemology requires something beyond the normal give-and-take of philosophical exchange).  It is an open question how the aim to increase the women-friendliness of epistemology bears on the aim of increasing the visibility of feminist epistemology.  I think that is as it should be.

I am well aware that I have no official standing to offer this challenge, other than as a concerned person whose research life is mainly in epistemology.    I can only hope that this challenge is understood in the spirit in which I offer it: made out of a sense of commitment to (and love for) epistemology, in the face of a concern I have with this aspect of the state of our field.  It is my further hope that many other epistemologists find themselves in the same position, and will join in the efforts to address this matter head-on, without defensiveness.

“But where does this default entitlement come from?” It needn’t “come from” anywhere: entitlement isn’t a fluid whose creation needs explanation. Probably the best view is that we simply have an attitude of regarding some beliefs as entitled under some circumstances, others not; and we regard some of them as entitled in absence of evidence for or against, even though there might someday be evidence that disconfirms them. And to put it crudely, there are no “facts about entitlement”, there is nothing beyond these attitudes; we can evaluate attitudes as good or bad, but such evaluation is not a “factual” enterprise.

Full paper here, titled “Recent Debates about A Priori.”

Suppose we grant the premise that dogmatism is incompatible with CB.  Why in the world should we conclude that the CB wins?  Why shouldn’t we reject CB instead?  The latter view does have a number of virtues, but it is not as though dogmatism has nothing going for it.  And CB has a number of well-known problems.  So I repeat: if dogmatism and CB are incompatible, why should the Classical Bayesian win?

Here is a way of approaching the question: if the incompatibility between CB and dogmatism depends on the most controversial features of Classical Bayesianism, then dogmatism should win.  For example, I find it implausible that a rational human being should assign a credence to every proposition or a credence of 1 to every necessary truth.  I take it that these implausible claims are entailed by CB.  To whatever extent the incompatibility arises because of CB’s commitment to either of those two claims, dogmatism should win and we should rework CB.  If, however, the incompatibility relies only on the least controversial features of CB, then CB should win.  Perhaps an example of something uncontroversial would be: if S assigns a credence to both P and P or Q, S is irrational for assigning P or Q a lower credence than P.

My suspicion is that you can only derive the incompatibility by relying on the most controversial features of dogmatism, such as the claim that I suffer a rational failing if I don’t assign every proposition a credence.  Suppose I might reasonably fail to assign a credence to the proposition (~D) that  I’m not being deceived into thinking there is a hand.  That is, suppose that, prior to having an experience as of my hand, ~D has no probability for me (perhaps because I have no information one way or the other, I’ve never considered ~D, etc.).  Now what’s the problem with the dogmatism allowing this: my experience provides me with justification to believe that I have a hand, and then, from my justified belief that I have a hand, I justifiably deduce ~D?

I admit that I’m worse than an idiot when it comes to formal epistemology, so this post is intended as a request for information as much as it is intended as a defense of dogmatism.  And let me also stress that I’m not against formal epistemology.  If dogmatism wins, then we shouldn’t give up on formal epistemology; rather, we should improve our formal modelling techniques.

(Btw: Peter Kung’s “On Having No Reason: Dogmatism and Bayesian Confirmation” provides a defense of dogmatism that may be a more intelligent way of pushing some of the points I make in this post.  But perhaps Peter wouldn’t like to be associated with ideas that may be worse than idiotic.)

A and B are actions, and q is a proposition. The symbol stands for preference, so the account says that you believe a claim just in case the ordering of your conditional preferences isn’t affected by adding that claim to the condition. Later in the article, Brian notes that this formulation needs to require that p and q are consistent, but I think that restriction doesn’t go far enough. If p and q are probabilistically or evidentially in tension, the account is subject to counterexample.

Consider this case. Given that it seems to me that I’m not married, I prefer leaving my wedding ring in the drawer to wearing it. But given that it seems to me that not I’m married but actually married, my preferences reverse. But I do in fact believe that I’m married.

The fix strikes me as simple, however: Just restrict q to propositions independent of p. Would love to hear, though, if that can’t work. (For Weatherson aficianados, I should note that the quantifiers above are restricted, but that the restrictions in question don’t rule out counterexamples of this sort. I’ll leave it to the reader to verify that I’m right about this.)

[UPDATE: I fixed the original garbled example, sorry for any confusion! And a bit more below the fold.]

We can generalize as well. Identify q as something that is evidence against something p you believe. For example, let q= the objective chance of p is nearly zero, or let q=the evidence against p is (nearly) conclusive. So, if p is that today is 4/13/2012, something I believe, my preferences for driving to DFW early in the morning over sleeping in favor the latter, given q. But given both p and q I prefer to drive, since I want to get to Gonzaga for the conference on that day.