Vagueness in Gettier Cases
In a seminal article (Gettier, 1963), Edmund Gettier posed counterexamples to the contemporary analysis of knowledge as justified true belief (JTB). These counterexamples, and the many others invented by other philosophers since, all consist of instances in which someone comes to hold a belief that is true, and that person is completely justified in believing it, but we still shy away from labeling it as knowledge.
One grouping of these “Gettier cases” is epitomized by the familiar barn/barn façade counterexample, which runs thus: A man is driving through the countryside and points out a barn, saying, “That’s a barn,” to his son. Unknown to them, a film crew has erected a number of false barn façades nearby. The father could just as easily have pointed to one of these façades - he wouldn’t be able to tell the difference - but he did in fact point out an actual barn. Does the man know that he spotted a barn? Many would hold that he doesn’t.
I would like to explore just what it is about these types of cases that leads some to doubt the knowledge of the subject. The subject’s belief is brought about in a sufficiently causal way[1] without invoking any false premises[2] or leaving unchecked any hidden “defeater” statements[3]. Why then do some people doubt that the man knows that he spotted a barn?
Well, the contention is that the man, were he in a situation where he had seen a barn façade rather than an actual barn, he still would have pointed it out and said, “That’s a barn”. He still would have believed he had spotted a barn. Therefore, since the results are independent of whether the man was looking at a barn or a barn façade, the man doesn’t know he’s spotted a barn. To put it another way, a non-barn can cause him to believe he’s spotted a barn, so he can’t know when he’s spotted a barn - it could be a barn façade.
Okay, so that’s why someone could object to the man knowing he’s spotted a barn. But shouldn’t this apply when there isn’t a film crew in the area? From the man’s point of view, he’s in exactly the same epistemic position. Unless the film crew, by means of erecting these barn façades, somehow imbue or infect the process of the man seeing the actual barn with some kind of … something, there is no difference between the one case and the other. The only way to accept that the man does have knowledge under a regular case of this process, but doesn’t in the Gettier case of this process, is to accept some such imbuement.
Allowing the proximity of possible counterexamples affect whether or not one has knowledge is a rather metaphysical way of looking at this epistemological problem, and it leads to some other issues besides this imbuement question. To illustrate these, I wish to introduce a different version of the counterexample, which is a little easier to talk about in a general way.
Consider a college cafeteria[4] with one hundred tables, each of which has a salt shaker in the center of it. A person in line (for whatever reason) points at a salt shaker and says to her friend, “That shaker has salt in it.” Unknown to her or her friend, a trickster has filled ninety-nine of the shakers in the cafeteria with sugar, overlooking a single shaker which is still filled with salt. This overlooked shaker happens to be the one that the person in line points out.
There are two problems that this new version of the barn/barn façade case is meant to make clearer. The first is a vagueness in the term “proximity”: Just how close do these possible counterexamples have to be? For example, does it make a difference if the table with the shaker of salt on it is for some reason set apart in a different side of the room from the other tables? In the other room? In another building? Does it make a difference if the film crew set up the barn façades on the other side of the valley from the actual barn the man points out? On the other side of the mountain range? On the other side of the planet?
The other (and, I think, more serious) problem is one of quantification. The intuition in the case above is that the person in line cannot know that the shaker is filled with salt. Is the intuition the same if the situation is reversed? Consider the same situation, except that when the trickster goes to swap the salt for the sugar, the dining staff catches him, and he’s only able to change over a single shaker. Later, the person gets in line and says to her friend, “That shaker is filled with salt,” pointing to a shaker that is near her (yet completely on the other side of the room from the one the trickster managed to swap). Does she know there is salt in the shaker?
The intuition of many is that the person in line does indeed know that there is salt in the shaker. Accepting this intuition, however, reveals a problem because it admits of a continuum of trickster successes. If ninety-nine shakers switched means that the person in line does not know there is salt in the shaker, but a single shaker switched means that she does know, then there should be some number n of switched shakers that keeps the person in line from knowing there is salt in the (correctly identified) shaker, and n - 1 that allows her to know there is salt in the shaker. But, isn’t that too definite a border? It is difficult to agree with the notion that a single switched shaker in the middle of the continuum somewhere changes “S knows that P” from being true to being untrue, or vice versa.
But accepting that the person in line knows in the reversed case while not knowing in the original case while not admitting to such a number n is an even worse problem. For it is tantamount to saying that there are cases in between the higher and lower ends of the spectrum that are indeterminate. This suggests that “knowledge” and the predicate term “knows that” are imprecise and vague.
Ablondi draws three options from such a state of affairs. We could agree, he says, that “knows that” is simply a vague predicate. We could agree with the epistemist, and say that there is indeed some such n. Or we could agree with Kaplan (Kaplan, 1985) that the analysis of knowledge is a worthless endeavor.
But to come to this particular choice between these three options, we had to agree in the first place to allow the proximity of possible counterexamples to affect the truth-value of “S knows that P”. I do not think that this is correct. Because it has these three problems, I deny that the proximity of possible counterexamples has any affect on the truth-value of “S knows that P”. We are left then to pick between two options, which are prior to the three options Ablondi offers us: Either the man has knowledge in both the case of a solitary barn or one surrounded by barn façades, or he doesn’t have knowledge in either case.
The Gettier case strongly suggests that the man does not have knowledge that he has seen a barn. After all, he could just as easily have been pointing at a barn façade. Given what we have just said, then, we must conclude that he doesn’t even know in the case of a solitary barn that he’s seen a barn. Someone could come build a bunch of barn façades nearby next week.
We have just stumbled into the problem of induction. Because, as the analysis of knowledge is currently laid out, the only thing left to knowledge is justified true belief with no possible counterexamples, which is to say knowledge is logico-mathematical truths. But this is problematic if we are to have any kind of epistemic theory, such as physics or evolution.
The fact that the analysis of knowledge leads to the problem of induction stands in contrast to Kaplan’s contention that the analysis of knowledge is a worthless endeavor. Kaplan argued that all the Gettier cases were “set up to fail”. In a sense, he is correct - all the cases are set up in such a way that they do not question the subject’s knowledge of a deductive truth[5]. They instead question the subject’s knowledge of an inductive truth, such as “That is a barn” or “There is salt in that shaker”. It is indeed precisely because of the nature of induction that there is able to be a Gettier case concerning such justified true beliefs at all.
Now, it is outside the scope of this paper for me to attempt to solve the problem of induction, and I am not coming down on one side or the other in the debate. But I do hold that it is the fact that the subject is making an induction that leads people to doubt the knowledge of the subject in this particular type of case. Of course Gettier cases are set up to fail, because they all question knowledge of an inductive conclusion. I suspect that it is this fact that leads people to go along with the other types of Gettier cases as well.
[1] For a good description of the causal revision of JTB, see Goldman, 1967.
[2] For a good description of (and interesting attack on) the no-false-premise revision of JTB, see Feldman, 1974.
[3] For a good description of the indefeasibility revision of JTB, see Lehrer and Paxson, Jr., 1969.
[4] This case was invented, to my knowledge, by Dr. Fred Ablondi in his unpublished article “Epistemic Vagueness?”.
[5] Or, if they do, then said truth is in some way based on inductive truth(s). For instance, the original Gettier case, in which the subject is justified in believing “Smith owns a Ford”, and therefore is justified in believing “Smith owns a Ford, or Jones is in Barcelona”. It turns out that Smith doesn’t own a Ford, but Jones is in Barcelona. So the subject has a justified true belief of a logical statement or of a logical truth without it being based entirely on logical grounds.
Works Cited
Ablondi, Fred, 2008? “Epistemic Vagueness?” Unpublished. Note: There is little information that is relevant in this article that wasn't included in the above work. If you have any questions, ask me. If you have a lot of questions, I'll post it.
Feldman, Richard, 1974. “An Alleged Defect in Gettier Counter-Examples”, Australasian Journal of Philosophy 50, no. 1.
Gettier, Edmund L., 1963. “Is Justified True Belief Knowledge?” Analysis, vol. 23. 121-23.
Goldman, Alvin I., 1967. “A Causal Theory of Knowing”, The Journal of Philosophy, 355-72.
Kaplan, Mark, 1985. "It's Not What You Know That Counts", The Journal of Philosophy, 350-63.
Lehrer, Keith and Thomas D. Paxson, Jr., 1969. “Knowledge: Undefeated Justified True Belief”, The Journal of Philosophy, 225-37.
One grouping of these “Gettier cases” is epitomized by the familiar barn/barn façade counterexample, which runs thus: A man is driving through the countryside and points out a barn, saying, “That’s a barn,” to his son. Unknown to them, a film crew has erected a number of false barn façades nearby. The father could just as easily have pointed to one of these façades - he wouldn’t be able to tell the difference - but he did in fact point out an actual barn. Does the man know that he spotted a barn? Many would hold that he doesn’t.
I would like to explore just what it is about these types of cases that leads some to doubt the knowledge of the subject. The subject’s belief is brought about in a sufficiently causal way[1] without invoking any false premises[2] or leaving unchecked any hidden “defeater” statements[3]. Why then do some people doubt that the man knows that he spotted a barn?
Well, the contention is that the man, were he in a situation where he had seen a barn façade rather than an actual barn, he still would have pointed it out and said, “That’s a barn”. He still would have believed he had spotted a barn. Therefore, since the results are independent of whether the man was looking at a barn or a barn façade, the man doesn’t know he’s spotted a barn. To put it another way, a non-barn can cause him to believe he’s spotted a barn, so he can’t know when he’s spotted a barn - it could be a barn façade.
Okay, so that’s why someone could object to the man knowing he’s spotted a barn. But shouldn’t this apply when there isn’t a film crew in the area? From the man’s point of view, he’s in exactly the same epistemic position. Unless the film crew, by means of erecting these barn façades, somehow imbue or infect the process of the man seeing the actual barn with some kind of … something, there is no difference between the one case and the other. The only way to accept that the man does have knowledge under a regular case of this process, but doesn’t in the Gettier case of this process, is to accept some such imbuement.
Allowing the proximity of possible counterexamples affect whether or not one has knowledge is a rather metaphysical way of looking at this epistemological problem, and it leads to some other issues besides this imbuement question. To illustrate these, I wish to introduce a different version of the counterexample, which is a little easier to talk about in a general way.
Consider a college cafeteria[4] with one hundred tables, each of which has a salt shaker in the center of it. A person in line (for whatever reason) points at a salt shaker and says to her friend, “That shaker has salt in it.” Unknown to her or her friend, a trickster has filled ninety-nine of the shakers in the cafeteria with sugar, overlooking a single shaker which is still filled with salt. This overlooked shaker happens to be the one that the person in line points out.
There are two problems that this new version of the barn/barn façade case is meant to make clearer. The first is a vagueness in the term “proximity”: Just how close do these possible counterexamples have to be? For example, does it make a difference if the table with the shaker of salt on it is for some reason set apart in a different side of the room from the other tables? In the other room? In another building? Does it make a difference if the film crew set up the barn façades on the other side of the valley from the actual barn the man points out? On the other side of the mountain range? On the other side of the planet?
The other (and, I think, more serious) problem is one of quantification. The intuition in the case above is that the person in line cannot know that the shaker is filled with salt. Is the intuition the same if the situation is reversed? Consider the same situation, except that when the trickster goes to swap the salt for the sugar, the dining staff catches him, and he’s only able to change over a single shaker. Later, the person gets in line and says to her friend, “That shaker is filled with salt,” pointing to a shaker that is near her (yet completely on the other side of the room from the one the trickster managed to swap). Does she know there is salt in the shaker?
The intuition of many is that the person in line does indeed know that there is salt in the shaker. Accepting this intuition, however, reveals a problem because it admits of a continuum of trickster successes. If ninety-nine shakers switched means that the person in line does not know there is salt in the shaker, but a single shaker switched means that she does know, then there should be some number n of switched shakers that keeps the person in line from knowing there is salt in the (correctly identified) shaker, and n - 1 that allows her to know there is salt in the shaker. But, isn’t that too definite a border? It is difficult to agree with the notion that a single switched shaker in the middle of the continuum somewhere changes “S knows that P” from being true to being untrue, or vice versa.
But accepting that the person in line knows in the reversed case while not knowing in the original case while not admitting to such a number n is an even worse problem. For it is tantamount to saying that there are cases in between the higher and lower ends of the spectrum that are indeterminate. This suggests that “knowledge” and the predicate term “knows that” are imprecise and vague.
Ablondi draws three options from such a state of affairs. We could agree, he says, that “knows that” is simply a vague predicate. We could agree with the epistemist, and say that there is indeed some such n. Or we could agree with Kaplan (Kaplan, 1985) that the analysis of knowledge is a worthless endeavor.
But to come to this particular choice between these three options, we had to agree in the first place to allow the proximity of possible counterexamples to affect the truth-value of “S knows that P”. I do not think that this is correct. Because it has these three problems, I deny that the proximity of possible counterexamples has any affect on the truth-value of “S knows that P”. We are left then to pick between two options, which are prior to the three options Ablondi offers us: Either the man has knowledge in both the case of a solitary barn or one surrounded by barn façades, or he doesn’t have knowledge in either case.
The Gettier case strongly suggests that the man does not have knowledge that he has seen a barn. After all, he could just as easily have been pointing at a barn façade. Given what we have just said, then, we must conclude that he doesn’t even know in the case of a solitary barn that he’s seen a barn. Someone could come build a bunch of barn façades nearby next week.
We have just stumbled into the problem of induction. Because, as the analysis of knowledge is currently laid out, the only thing left to knowledge is justified true belief with no possible counterexamples, which is to say knowledge is logico-mathematical truths. But this is problematic if we are to have any kind of epistemic theory, such as physics or evolution.
The fact that the analysis of knowledge leads to the problem of induction stands in contrast to Kaplan’s contention that the analysis of knowledge is a worthless endeavor. Kaplan argued that all the Gettier cases were “set up to fail”. In a sense, he is correct - all the cases are set up in such a way that they do not question the subject’s knowledge of a deductive truth[5]. They instead question the subject’s knowledge of an inductive truth, such as “That is a barn” or “There is salt in that shaker”. It is indeed precisely because of the nature of induction that there is able to be a Gettier case concerning such justified true beliefs at all.
Now, it is outside the scope of this paper for me to attempt to solve the problem of induction, and I am not coming down on one side or the other in the debate. But I do hold that it is the fact that the subject is making an induction that leads people to doubt the knowledge of the subject in this particular type of case. Of course Gettier cases are set up to fail, because they all question knowledge of an inductive conclusion. I suspect that it is this fact that leads people to go along with the other types of Gettier cases as well.
[1] For a good description of the causal revision of JTB, see Goldman, 1967.
[2] For a good description of (and interesting attack on) the no-false-premise revision of JTB, see Feldman, 1974.
[3] For a good description of the indefeasibility revision of JTB, see Lehrer and Paxson, Jr., 1969.
[4] This case was invented, to my knowledge, by Dr. Fred Ablondi in his unpublished article “Epistemic Vagueness?”.
[5] Or, if they do, then said truth is in some way based on inductive truth(s). For instance, the original Gettier case, in which the subject is justified in believing “Smith owns a Ford”, and therefore is justified in believing “Smith owns a Ford, or Jones is in Barcelona”. It turns out that Smith doesn’t own a Ford, but Jones is in Barcelona. So the subject has a justified true belief of a logical statement or of a logical truth without it being based entirely on logical grounds.
Works Cited
Ablondi, Fred, 2008? “Epistemic Vagueness?” Unpublished. Note: There is little information that is relevant in this article that wasn't included in the above work. If you have any questions, ask me. If you have a lot of questions, I'll post it.
Feldman, Richard, 1974. “An Alleged Defect in Gettier Counter-Examples”, Australasian Journal of Philosophy 50, no. 1.
Gettier, Edmund L., 1963. “Is Justified True Belief Knowledge?” Analysis, vol. 23. 121-23.
Goldman, Alvin I., 1967. “A Causal Theory of Knowing”, The Journal of Philosophy, 355-72.
Kaplan, Mark, 1985. "It's Not What You Know That Counts", The Journal of Philosophy, 350-63.
Lehrer, Keith and Thomas D. Paxson, Jr., 1969. “Knowledge: Undefeated Justified True Belief”, The Journal of Philosophy, 225-37.