The barn/barn façade thought experiment is familiar to most epistemologists. It is intended to present a counterexample to certain causal theories of knowledge; in it, a father driving through the countryside with his son says, ‘That's a barn’ while pointing to a barn. Unbeknownst to the father, however, a film crew is working in the area, and it has constructed several barn façades. While the father did correctly point to a barn when he made his assertion, he could have just as easily pointed to a barn façade, and so, many hold, he does not know that the structure at which he is pointing is in fact a barn.Footnote ¹ If this is so, then it follows that true beliefs formed from reliable causal processes (in this case, vision by a competent observer under normal conditions) may still not qualify as knowledge.

I do not want to comment on the strength of this objection to casual theories of knowledge, but instead would like to present a similar thought experiment that raises quite a different issue. Consider the following case: a certain university cafeteria contains 100 tables, each with a salt shaker in the center of it. A student who has eaten at the cafeteria for years and has used many of the salt shakers to salt his food is giving his young brother a tour of campus; they enter the cafeteria and the student identifies many of the objects: ‘That's the salad bar,’ ‘That's the ice cream machine,’ and, while pointing at a given shaker, ‘That's a shaker containing salt.’ Does the student, who has excellent vision, know that he's pointing at a shaker containing salt? Let's consider some different possibilities. In scenario (1), imagine that a trickster has substituted sugar for salt in all of the shakers save one, which she overlooked, and which happens to be the one at which the student pointed when he made his assertion. Certainly those who feel that the father in the barn/barn façade example did not have knowledge (and perhaps even some of those who say that he did) would here say that the student does not know that he's pointing at a shaker containing salt. In scenario (2), imagine that the trickster only managed to substitute sugar for salt in one of the shakers, and it is a shaker on a table at the far corner of the cafeteria away from where the student is standing. Here the intuition is, I think, that the student does know that there is salt in the shaker at which he is pointing.

The problem arises when we consider a continuum of ‘trickster success’ rates. We said that 99 switched salt–to–sugar shakers results in a verdict of no knowledge possessed, even in the case in which the student points to the one shaker still containing salt, and that one switched salt–to–sugar shaker (at least in the case in which the shaker correctly identified as containing salt is a far distance from the one containing sugar) ought to be taken as an instance of knowledge possession. From this it would seem there is some number of shakers n, such that n switched salt–to–sugar shakers precludes the student from knowing that the shaker at which he is pointing contains salt, and n-1 shakers allows for him to know that the shaker at which he is pointing contains salt (as long as the student isn't pointing at one of the n-1 shakers when he makes his assertion). But it will strike many as absurd to say that one switched shaker marks the difference between ‘S knows that p’ being true from it being false.

Yet to deny there is such a number may also strike many as incorrect. For to say that in the case of a few switched shakers the student possesses knowledge, in the case of nearly all shakers switched he does not possess knowledge, and in between these there are cases in which it is indeterminate as to whether the student knows suggests that ‘knows that’ is not a precise predicate. Put slightly differently, denying any one such number n implies that the principle of bivalence does not in some instances apply to knowledge claims: it can in those instances be neither true nor false that ‘S knows that p.’

As I see it, this example leaves us to choose from three responses. We could agree that ‘knows that’ is a vague predicate; we could take the approach that the epistemist takes with regard to other putative ‘vague’ predicates, i.e. deny there are in fact indeterminate cases, and hold that there is indeed a number n as described above, chalking up our confusion about just what number n is to the limitations of our knowing powers;Footnote ² or third, we could respond along Austinean lines and question the whole enterprise of seeking necessary and sufficient conditions for knowledge possession.Footnote ³ Fred Dretske has made a strong case against the first response,Footnote ⁴ while the second option entails that there are a not insubstantial number of cases in which I possess knowledge but cannot, in principle, ever know that I do. For these reasons, I prefer the third option.