Contemporary Epistemology: Infinitism

In my break from blogging, I've read a lot about how contemporary epistemologists think beliefs can be justified. There are three typical suggestions as to how this can be done: foundationalism, traditional coherentism, and infinitism. The first says that a belief is justified if it 1) itself is or 2) is eventually inferred from a [justified] basic belief, a belief which is itself not inferred from anything else. The second says that the justification of a belief is circular: premises used to support an allegedly justified belief will actually evidence themselves as being premised upon on the very belief in question. The third says that beliefs require justification via a series of non-repeating, non-ending beliefs. There are variations within these frameworks - some say justified beliefs can be based on "unjustified" foundations; some hold to a non-traditional coherentism which actually turns out to be a sort of foundationalism - but in general, the idea that justified beliefs end somewhere, repeat, or neither end nor repeat are taken to be comprehensive alternatives to global skepticism, the conclusion that no beliefs can be justified.

Most contemporary epistemologists aren't global skeptics, so most contemporary epistemologists are obliged to defend one of the above structural theories. Historically, a usual point of departure for such defenses has been a quick dismissal of infinitism by arguing that an infinite regress is somehow vicious. But in the past 15 years, infinitism has experienced increasing support in the philosophic community. Each philosopher has his own specific emphases and disagrees with others on certain points, but among others, Peter Klein, Scott Aikin, David Atkinson, Jeanne Peijnenburg, Jeremy Fantl, and John Turri have defended it.

As is often the case, however, the proponents of a theory are often the first to mention its weaknesses, even if unwittingly. For instance, in "Modest Infinitism" (link), Fantl writes:

It is true that infinitism (on my construal) will give no answer to the question of what degree of justification is required for knowledge. But infinitism is not the only epistemic theory with this difficulty. Any fallibilistic epistemic theory will have trouble specifying a non-arbitrary threshold for knowledge. Certainty is too high a threshold (because the theory is fallibilistic), and any degree of justification less than certainty seems arbitrary. To solve this problem we might want to say that the degree of justification required for knowledge varies according to non-epistemic features of your situation. The degree of justification required for knowledge would thus be determined by context (for example, your stake in the belief being true). Whether one is tempted by a view like this (and it is open to the infinitist to adopt it), the difficulty infinitism runs into in setting a threshold for knowledge is not unique to infinitism and therefore cannot be decisive against it. (pg. 559)

While I have seen Klein, Atkinson, and Peijnenburg make the same appeal to pragmatic contextualization to specify the degree threshold, I have yet to see anyone specify how to non-arbitrarily choose it. So Fantl's conclusion is ironic, given that Klein and others principally reject foundationalism for allegedly requiring that one arbitrarily choose what to hold as a basic belief. Even more ironic is the fact that earlier in his article, Fantl explains how a foundationalist can avoid arbitrarity, an explanation which is strikingly similar to what I have argued on this blog regarding necessary and sufficient conditions for knowledge:

We can ask why self-justifying reasons are self-justifying. If the traditional foundationalist has an answer, it seems like it must involve some metajustificatory feature. If the traditional foundationalist has no answer, it seems like the view has arbitrary foundations. (See BonJour, Structure, 30-3, for a similar argument.) 

However, the traditional foundationalist can argue that completely self-justifying reasons are not self-justifying in virtue of some metajustificatory feature, nor are they arbitrary. It may be that certain reasons have to be assumed to be self-justifying if skepticism is to be avoided. This is a rather familiar form of rationalist argument for the existence of a priori justification. Here, the main implication of these arguments is that there might be a way to non arbitrarily show that we need to take certain reasons to be completely self-justifying without requiring that there be a metajustificatory feature which makes those reasons self-justifying. What convinces us we need to take those reasons to be self-justifying need not make them self-justifying. (pg. 544) 

So Fantl himself has put a certain kind of foundationalism in a rather favorable light, only to reject it himself. Why? Because such foundationalism cannot admit of degrees. But interestingly, as often as infinitists [rightly] complain that foundationalists beg the question by using the concept of "warrant-transfer" to falsify infinitism - which I'll get to in a moment - here we see just the reverse; foundationalism is ruled out because it proves too much. Or, more simply, foundationalism is ruled out because it proves. But so what?

See, while there are discrepancies here and there among infinitists, one core agreement seems to be that all justification is probabilistic and, hence, provisional. This is an assumption prevalent among contemporary epistemologists, and infinitists have helped themselves to it. This has worked out nicely for infinitists in some respects.

For instance, it allows them to appeal to probabilistic support for beliefs instead of relying on a deductive inference by which one could see the inheritance of a truth value from one proposition to another. What would be so bad about such a transfer theory? What would be so bad is that infinitism has no place for it. Justification of a proposition can't be inherited from a reason whose justification is inherited from another reason whose justification is inherited from another reason ad infinitum, because then we have a sort of argumentative analogy to a moral theory in which, since there is never an end good, there can never be a method by which we could judge any so-called means to be good. Everything is an instrument to and for nothing with the relevant feature possessed intrinsically, so there is no means of determining that any one of the links in the chain actually possesses the feature. At most, there is only a series of conditionals: "if this is justified or good, then that is justified or good." And in the case of justification, even the justificatory status of these conditionals gets called into question.

Perhaps the above could be phrased better, but in any case, Klein, Atkinson, Peijnenburg, etc. have acknowledged the force of the gist of this argument, which is usually the point at which the objection arises that justification doesn't have to be construed as a transfer. Rather, it can simply "emerge" from a set of propositions. b probabilistically supports a, which is probabilistically supported by c, which is probabilistically supported by d, ad infinitum. The degree to which b probabilistically supports a can differ from the degree to which c probabilistically supports b (though each will by definition be more probable than not). So there is no strict transfer here. Furthermore, the degree to which a is justified is defined by the limit of a series of summed products, so justification has thereby "emerged" from a whole string of reasons. This seems to be the infinitist's response to foundationalism, and so far as a foundationalist accepts the principle that justification comes in degrees, he may find it hard to fight infinitism without hurting his own cause.

But here's where the niceness ends, because I don't see why the foundationalist should have to grant the probabilistic assumption in the first place. The only reason I have seen given for the rejection of infallibilism is that it rules out too much of what we want to say we know. But that's ad hoc, not an argument. On the other hand, Gettier cases provide an actual argument as to why there can be no such thing as fallible "knowledge" (in the epistemic sense).

Furthermore, just as I have yet to see an infinitist explain how he has non-arbitrarily chosen a specific threshold for "knowledge," I have yet to see an infinitist explain how he has non-arbitrarily assigned probabilities. Does the infinitist have a reason for his assertion that b probabilitistically supports a to degree n? When and how did his capacity to non-arbitrarily assign probabilities arise? How does one non-arbitrarily adjudicate a disagreement?

And then what about the mathematical principles which the infinitist utilizes? In many of Peijnenburg's and Atkinson's papers, they append mathematical "proofs" as to how the convergence and determination of the limit of an infinite series is possible. Are these proofs not infallible? Are there no necessary truths? Can what is probable be improbable? When we reject these things, are we not worse than admitted skeptics?

I haven't even mentioned the old finite mind objection - that we as humans can't hold an infinitude of beliefs and so can't be infinitists. There has probably been more written on this objection than any other. And yet even here, I think infinitists are being put on their heels a bit. Klein has said that the requirement that one actually believe an infinitude of propositions would reduce infinitism to absurdity, but the alternative he provides does not give us any assurance that the point at which we stop providing reasons for a belief is not the point at which the justification for our belief begins to dip below whatever threshold we've "established." In other words, another arbitrarity problem.

I think the popularity of infinitism has brought to light more problems than answers. Still, it is interesting reading, and I'll look forward to this book coming out next year. Until then, I guess I'll be satisfied with google scholar and the library. Ok, back to hibernation.