The following case appears in a recent book by Timothy Williamson:
Consider an analogy. I am faced with enormous pile of chocolates. I know that exactly one of them is contaminated and will make me sick; alas, I cannot tell them apart. I have a strong desire to eat a chocolate. I can quite reasonably eat just one, since it is almost certain not to be contaminated, even though, for each chocolate, I have a similar reason for eating it, and if I eat all the chocolates, I shall eat the contaminated one, and my sickness will be overdetermined. No plausible principle of universalizability implies that, in the circumstances, any reason for taking one chocolate is a reason for taking them all; the most to be implied is that, in the circumstances, any reason for taking one chocolate is a reason for taking any other chocolate instead. (Williamson, Knowledge and Its Limits, Oxford: OUP, 2000: 248)
Williamson’s analogy is directed at undermining some simplistic strategies for universalising judgments about what it’s reasonable for one to believe or do. In this case, his ultimate target is principles that attempt to move from its being reasonable to believe each of p and q and r and… to its being reasonable to believe the conjunction of p and q and r and…. Just as it might be reasonable to eat any of chocolate one, chocolate two, chocolate three, and so forth without it being reasonable to eat all of the chocolates, so it might be reasonable to believe any of p, q, r, etc., without it being reasonable to believe all of p, q, r, etc.
Related issues arise concerning knowledge. If you know something, then it must be true. For instance, if you know that this chocolate is uncontaminated, it must be that this chocolate is uncontaminated. Since one of the chocolates is contaminated, it follows that you can’t know, with respect to every chocolate, that the chocolate is uncontaminated. Suppose that you believed, of every chocolate, that the chocolate were uncontaminated. That would involve believing, of the contaminated chocolate, that it was uncontaminated. Since that belief would be false, you could not thereby know that the chocolate was uncontaminated. Hence, you can’t know, with respect to every chocolate, that the chocolate is uncontaminated.
Given that you can’t know, with respect to every chocolate, that the chocolate is uncontaminated, can you know that with respect to any of the chocolates? Considerations of parity suggest that you can’t. In order to know, of any of the chocolates, that the chocolate is uncontaminated, considerations of parity make plausible that your evidential position with respect to that chocolate would have to be better than your evidential position with respect to the contaminated chocolate. However, it’s natural to think that, as the case was described, your evidential positions with respect to contaminated and uncontaminated chocolates do not differ in the required way. If the natural thought is correct, then it seems that you cannot know, with respect to any of the chocolates, that that chocolate is uncontaminated—at least, one can’t know that in advance of eating the chocolate and observing its effects on your health.
In spite of—or in advance of—such considerations, some people seem to be prepared to judge that you can know, with respect to an uncontaminated chocolate, that it is uncontaminated, at least if the number of uncontaminated chocolates is sufficiently high. Suppose, for example, that there are one million uncontaminated chocolates and only one contaminated chocolate. In that case, some people seem to think, it is possible for one to know that a given uncontaminated chocolate is so. However, unless we rig the case so that there is really very little danger of the given chocolate being contaminated—for example, by interposing a pile of 996,347 chocolates between the subject and the contaminated chocolate—the view that you can know here looks to be erroneous. The fact that some of us are willing to judge that you can know in the non-rigged circumstance requires explanation. However, there is no good reason to think that the explanation, or explanations, will make appeal to the correctness of the judgments.
Leaving aside Williamson’s larger aims, his case has the potential to raise a more specific practical question. Suppose that you knew that you were in a situation of the type that Williamson characterises. In that case, how many of the chocolates would it be reasonable for you to eat? I take it that the correct answer to that practical question is dependent on answers to a number of sub-questions, including the following. (1) How many of the uncontaminated chocolates is it reasonable to eat? (2) How many uncontaminated chocolates is it reasonable to believe there are? (3) What degree of sickness following ingestion of the contaminated chocolate is it reasonable to expect? (4) What degree of sickness is it reasonable to endure? But those are not obviously philosophical questions.
Thanks to Aidan McGlynn for suggesting that I consider Williamson’s analogy.