Conditionals in Epistemology

Subjunctives in Epistemology

In epistemology it is widely agreed that in order for a subject to know a proposition, the proposition must be true, and the subject must believe it. It is plain, however, that these requirements will not suffice. What other than truth and belief might be required for knowledge? A number of philosophers, notably Nozick, Dretske, Sosa, and Williamson have suggested that a third (and maybe fourth) condition for knowledge may be formulated using subjunctive conditionals.

According to Nozick and Dretske, a subject knows a proposition p iff: 1) p, 2) BSp, 3) ¬p>¬BSp. This criterion has famously been referred to as the sensitivity requirement; in other words, S knows that p if his belief is sensitive to the truth and falsity of p. Many philosophers have attacked the sensitivity requirement and cited counterexamples. One consequence of the theory is that we do not know that we are not in a skeptical scenario. If we were, for instance, brains in vats deceived into (falsely) believing that we have hands, then, plainly, by hypothesis, we would still believe that we have hands. Nozick was untroubled by this consequence, but, for many contemporary epistemologists, the result is untenable.

Sosa responded to the critiques launched at the sensitivity requirement. He proposed a reversal of the third Nozick-Dretske criterion (see Sosa, "How to Defeat Oppostition to Moore"). His analysis is as follows: S knows that p iff 1) p, 2) BSp, and 3) BSp>p. This is known as the safety requirement. S knows that p if his belief in p is safe iff it could not easily be false. Timothy Williamson has recently endorsed the view in Knowledge and its Limits. It should be evident from this initial formulation that Sosa must reject Lewis' Centering Axiom, that is, the closest possible world to the actual world must be itself. Accepting the centering axiom would render all true beliefs at the actual world safe. This result would trivialize the principle.

Counterexamples due to Juan Comesana have motivated Sosa to slightly alter the saftey principle, and the principle has since undergone several revisions. (See Comesana "Unsafe Knowledge").

Initial Questions

Given the difficuties and lack of concensus in providing an analysis of subjuctive conditionals, one might question the efficacy of bringing them into an analysis of knowledge. Obviously, how we interpret the above mentioned conditionals is going to have an enormous effect on whether or not we determine that a subject knows a given proposition. And, equally obviously, interpreting conditionals in one way rather than another may, then, add to or detract from the plausibility of the theories.

Before delving into the specifics of either theory, one wants to pose the following general question: "Why expect that using conditionals is going to bring us any closer to a conceptual analysis of knowledge? Why think that the concept of knowledge is related to subjunctives?"

Obvious, too, is the fact that the concept of comparative similarity may come in to play when we assess whether or not a subject knows a proposition. Generally, on the Nozick-Dretske picture, a subject will know a proposition if at the closest possible worlds at which that proposition is false, the subject doesn't believe it and at the closest possible worlds at which the proposition is true, S believes it. On the Sosa picture, a subject has knowledge of a proposition if at the closest possible worlds at which the subject believes the proposition, it's true. Which worlds are closest makes all the difference in determining whether or not the subject has knowledge. So if we are to uses subjunctives in epistemology, the idea of comparative similarity, which has never adequately been explained (as demonstrated by the difficulties with the Lewis account), is going to play a central role.

Analyses of Counterfactuals and Analyses of Knowledge

Using subjunctives in epistemology may limit and change the kind of reading we are entitled to give them. For instance, some philosophers have supposed that the best way to interpret a subjunctive is by looking at the A-world(s) identical to the actual world up to the time of the antecedent, and then consider whether or not C is true. Holding everything fixed creates a 'bump,' a large violation of the laws of that world. Problems with this view have been cited, and it has no wide acceptance. Nonetheless, it serves as a good example of how using subjunctives for epistemic purposes dictates the analysis for the subjunctives. observing this is instuctive. If we use subjunctives in epistemology, the bump theory generates absurd results. Consider the following case:

Luther is an obsessive compulsive. He leaves his copy of Crime and Punishment in a particular place on his desk, and checks on it three times. Then he leaves the house. Later in the day he comes to think, "My book is at home right now." He's right. The book is just where he left it. Does Luther know? Intuitively, it seems like it. But consider the sensitivity counterfactual, "If the book weren't at Luther's home right now, Luther wouldn't believe it." If we read the counterfactual with a bump, that is, the book pops out of existence or teleports to some other location at the time of the antecedent, this is certainly going to come out false. Luther won't have knowledge if we permit this reading of the counterfactual.

It's easy to see how this case can generalize. Bumps present a problem for the safety view too, though the difficulty is a bit subtler. Consider a case of counterfactual belief:

Peter is an extermely careful and reliable historian of the Civil War. At the actual world, at time t, he does not believe p, some true proposition about the Civil War, because, by happenstance, he has never come across some definitive piece of evidence for p. Now consider the counterfactual, "If Peter were to believe p at t, then p would be true." Imagine the closest possible worlds at which Peter believes p at t. On the bump theory, these worlds are identical to the actual wold untill at t, the belief magically pops into Peter's head." On the Safety analysis, Peter would have knowldge. But, this result is intuitively unattractive. Note that in the candidate worlds, Peter had ablsoutely no evidence for p.

So, when we assess which worlds are the closest A-worlds, we are going to have to consider worlds in which there isn't exact mach up to the time of the antecedent, if subjunctives are going to be of any use in epistemology.

The fact that sensibly using subjunctives in epistemology may force us to tailor our account of them may be considered a vice or a virtue. Perhaps, in figuring out a way to analyze subjunctives so that they can do epistemic work, we could learn the right way to analyze the subjunctives. Perhaps we would get an account that has very little to do with the way subjunctive actually work. The result depends on whether there is any natural link between the two. Since there is no absolute consensus about the analysis of knowledge or subjunctives it is difficult to say whether or no the project is useful or misguided.

Concerns about Similarity

Related worries arise from the fact that on the standard reading of subjunctive conditionals, truth and falsity depends on whether or not C is true at the closest A-world(s). It is generally accepted that the Lewis analysis of similarity cannot be made to work. And no one since has able to clarify the concept. So, one wonders whether or not epistemologists are misguided in attempting to put the concept to work for them. Even a course-grained notion of similarity is going to put traditional skeptical hypotheses, like the BIV hypothesis, or Descartes demon deceiver far away from us in modal space. Almost none of the facts in those worlds match the facts of our world. That is, of course, the result epistemologists are looking for. But, all skeptical scenarios needn't be like that.

Consider counter-entropic cases like the one presented by Adam Elga (see Elga, "Statistical Mechanics and the Asymmetry of Countefactual Dependence"). I will not recreate all the details of the case, but, an extremely crude sketch may point to the problems I have in mind. Elga suggests an example in which a world with a different past from our own can converge to our world (that is, share our exact future) via a tiny isolated breach of the laws. So, the world has a very different past, but, but the world follows the actual laws with the exception of the one isolated breach. After the convergence, the world matches our own world exactly.

Though initially not conceived of in this way, the world in Elga's example is a skeptical world. People have memories and traces of events that never occurred. But, with the exception of the tiny breach, this world shares our laws. Further, there is a good deal of match with respect to particular matters of fact. From our perspective, there is no means of differentiating this world from the actual world. Yet people believe all sorts of false things there.

How similar to the actual world is this world? Well, it's not clear. It is intuitively much closer to it than BIV worlds. With only a crude notion of similarity on hand, epistemologists don't have much in the way of a principled reason of ruling it out. Cases like this cause potential problems for an analysis like Sosa's, which crucially depend on our not being deceived in worlds that are close to the actual world..

If assessing subjunctives depends on similarity, then, epistemologists might be wise not to muddy the waters. Alternativley, if the similarity relation could be sysetmatized, it my prove a useful tool in analyzing knowledge and counterfactuals. The prospects of this, however, remain dubious (See Kutach, "Similarity is a Bad Guide to Counterfactual Truth," 2006).

None of these comments are conclusive. Whether or not applying counterfactuals to epistemology is a fruitful practice largely remains to be seen.