Gettier problems
Suppose you wake up in the morning one day, look at the clock, and see that it reads 7:00 AM—for this reason, you believe it is 7:00 AM. As a matter of fact, the time is 7:00 AM. Do you therefore know that the time is 7:00 AM? For millennia, philosophers have toyed with the question of what it means to know something: at what point do you not simply believe a proposition to be true, but also know it? One convincing answer used to be "justified true belief" (JTB). Here, the clock was a convincing justification for your belief that the time was 7:00 AM, and the belief was true because the time was indeed 7:00 AM. Because you had a justified true belief that the time was 7:00 AM, most philosophers before the 1960s would have probably agreed that you also knew that the time was 7:00 AM. In 1963, however, a man by the name of Edmund Gettier changed everything.
Suppose that, unbeknownst to you, the clock is broken. It just happens to be stopped at 7:00 AM. However, by sheer chance, the time is indeed 7:00 AM. In this situation, nothing has really changed from your perspective: you still wake up in the morning, still look at the clock, and still see that it reads 7:00 AM, and based on this reasonable justification, you form a true belief that the time is 7:00 AM. However, in this situation, do you really know that the time was 7:00 AM? Despite having a justified true belief, it seems that we are still missing some prerequisite for knowledge.
This kind of counterexample to the JTB definition of knowledge is known as a "Gettier problem", named after American philosopher Edmund Gettier, who in 1963 published a three-page paper in the journal Analysis that triggered an upheaval in the field of epistemology. I learned about Gettier problems, including this particular example featuring a stopped clock, from a class I took in my freshman year at Berkeley called PHILOS 4: Knowledge and Its Limits; my instructor was Professor Wesley Holliday.
Gettier made two observations regarding JTB. Firstly, it is possible to be justified in believing a proposition that turns out to be false. In the example above, even if you had looked at the broken clock at 7:30 AM, you would have still been justified in believing the time to be 7:00 AM—after all, clocks are usually reliable. Secondly, if you are justified in believing a proposition that entails another proposition, then you would inherently be justified in believing the entailed proposition as well. For example, suppose that your school doesn't start until 8:00 AM; thus, if it is true that the time is 7:00 AM, then it must also be true that school has not started for you yet—in other words the time being 7:00 AM entails that school has not started for you yet. In this case, if you are justified in believing that the time is 7:00 AM, then you are also justified in believing that your school has not started yet.
Gettier's cases
The two specific counterexamples that Gettier proposed in his seminal 1963 paper had nothing to do with clocks, but the basic framework of the counterexamples is similar.
The case of the ten coins
In the first one, Gettier considers the case of two men, Smith and Jones, who have both applied for the same job. Gettier asks us to suppose Smith has strong evidence to believe the following proposition:
(A) Jones is the man who will get the job, and Jones has ten coins in his pocket.
Perhaps, for example, the company's president told Smith that Jones would get the job, and Smith himself counted the number of coins in Jones' pocket a few minutes ago. If proposition (A) is true, then the following proposition must also be true:
(B) The man who will get the job has ten coins in his pocket.
In other words, (A) entails (B). Suppose that because of this entailment, Smith believes (B); that is, Smith believes that the man who will get the job will have ten coins in his pocket. As I mentioned above, if you are justified in believing a proposition that entails another proposition, then you would inherently be justified in believing the entailed proposition as well. Thus, Smith is justified in believing (B) because of the entailment from (A). As a matter of fact, the man who gets the job does have ten coins in his pocket. Because Smith had a justified true belief, could we say that Smith knew that the man who would get the job would have ten coins in his pocket?
Gettier then asks us to imagine that, to Smith's surprise, it is actually Smith himself that gets the job, not Jones, and also to Smith's surprise, Smith also has exactly ten coins in his own pocket. In this case, all of the conditions for justified true belief are still present: Smith was correct to believe that the man who would get the job had ten coins in his pocket, and Smith had reasonable justification for this belief. Yet somehow, a serendipitous quirk in the situation—the man being Smith and not Jones—causes our intuition to reject the proposition that Smith knew that the man who would get the job had ten coins in his pocket.
The case of the Ford
In the second counterexample, Gettier considers the case of Jones's car: a Ford. Gettier again asks us to suppose that Smith has strong evidence to believe the following proposition:
(C) Jones owns a Ford.
The evidence could be that, for as long as he can remember, Smith has always seen Jones drive a Ford, and perhaps right now Jones is offering to give Smith a ride while driving a Ford. Now suppose that Smith has another friend named Brown, and Smith has no idea where Brown is currently. If proposition (C) is true, then all of the following proposition must also be true:
(D) Either Jones owns a Ford, or Brown is in Boston;
(E) Either Jones owns a Ford, or Brown is in Barcelona;
(F) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
In other words, (C) entails (D), (E), and (F). The word or here is used as an "inclusive or". In formal logic, if a proposition is constructed in the form "X or Y", with or being an inclusive or, then as long as one of either X or Y is true, then the entire proposition "X or Y" is true. Engineering students might appreciate this: in electrical engineering, this can be represented by the OR logic gate (typically represented as two switches in parallel: as long as one of the switches is closed, then current can flow through the gate). In this case, if Jones has good reason to believe (C) is true, then he trivially also has good reason to believe that (D), (E), and (F) are all true.
Gettier then asks us to suppose that Jones in fact does not own a Ford (it's a rental), and Brown, by sheer coincidence, is actually in Barcelona. As a result, proposition (E) turns out to be actually true, and as we demonstrated above, it appears that Smith had a reasonable justification for believing (E) to be true as well. But did Smith know that "either Jones owns a Ford, or Brown is in Barcelona"? If you subscribe to the JTB definition of knowledge, it would seem that you would be forced to say yes. Something seems off.
Conclusion (or lack thereof)
Gettier problems proved to be a fatal threat to the JTB definition of knowledge. Today, it seems that few epistemologists still subscribe to that definition, at least without some modification. In my freshman-year philosophy course at Berkeley, I learned about alternative formulations of knowledge that seek to amend or replace JTB in light of Gettier problems. I confess, however, that my memory of those alternative theories has faded to the extent that I do not feel comfortable describing any of them in this blog post. I have also since lost my notes from the class (it's been four years now). For these reasons, I will have to end this blog post here. If these kinds of epistemological conundrums interest you, I encourage you to conduct your own research into those JTB alternatives.
As for me, unfortunately, if I have to be honest, this kind of stuff no longer interests me as much as it used to. Back in high school, I was much more actively interested in philosophy. I spent a nontrivial amount of my time ruminating on abstract philosophical thought processes—I even posted a few such ruminations to this blog: e.g. see my posts on eternity, existence, and teleportation. However, I have found that as I have grown older, I have come to realize a certain futility in these philosophical exercises. Frankly, the freshman-year epistemology class I took at Berkeley was a critical inflection point for my interest in philosophy. I started to find the lectures boring. I could understand why someone might be interested in the question of, "What exactly does it mean to know something?" But as applied to everyday life, such a question seems irrelevant. The question seems so esoteric and so difficult to answer, why should I spend so much time thinking about it?
Of course, I realize the irony of the preceding paragraph in the context of the broader blog post, where I have spent a considerable amount of time continuing to ruminate on these epistemological questions. I suppose that, deep down, I still do recognize that these questions are interesting and merit our attention. However, it seems to me that there are more pressing questions facing the world at the moment to which our attention would be better directed.