Here is a collection of "Gettier Examples" and other similar scenarios found in various papers on the Internet. For each case, I will provide an analysis from the perspective of the Inferential Contextualist Theory of Knowledge, and the idea of Contextual Decomposition.
Note: Most of these examples are found in many different papers, so I have not provided a specific citation for them. Only where I found an internet reference to the source, have I copied that citation here. If I have missed an appropriate citation, I apologize. If you happen to know the source for any of these examples, I would greatly appreciate the information. And if you are aware of any additional examples that might be relevant, I would also greatly appreciate the information.
Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition:
1. Jones is the man who will get the job, and Jones has ten coins in his pocket.
Smith's evidence for (1) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago. Proposition (1) entails:
2. The man who will get the job has ten coins in his pocket.
Let us suppose that Smith sees the entailment from (1) to (2), and accepts (2) on the grounds of (1), for which he has strong evidence. In this case, Smith is clearly justified in believing that (2) is true.
But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (2) is then true, though proposition (1), from which Smith inferred (2), is false. In our example, then, all of the following are true:
But it is equally clear that Smith does not know that (2) is true; for (2) is true in virtue of the number of coins in Smith's pocket, while Smith does not know how many coins are in Smith's pocket, and bases his belief in (2) on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job.
Edmund Gettier was a victim of the modern philosophical penchant for treating philosophy as "philosophy of language". If one pays attention to the concepts being employed, rather than the words being used, the resolution of this problem is simple. The words "The man" employed in (2) are a verbal short-hand for the concept "Jones". For clearly, in believing (2), Smith is believing that "The man" being referred to is "Jones" and not merely "Some unidentified man". With this conceptual clarification, the equivocation employed in the remainder of Gettier's example becomes clear. Thus understood, (2) is not in fact true, and therefore - consistent with the intuitive analysis - Smith does not have the requisite knowledge.
(see Gettier, Edmund L.; Is Justified True Belief Knowledge?; Analysis 23 ( 1963): 121-123.)
Let us suppose that Smith has strong evidence for the following proposition:
1. Jones owns a Ford.
Smith's evidence might be that Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:
2. Either Jones owns a Ford, or Brown is in Boston.
3. Either Jones owns a Ford, or Brown is in Barcelona.
4. Either Jones owns a Ford, or Brown is in Brest-Litovsk.
Each of these propositions is entailed by (1). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (1), and proceeds to accept (2), (3), and (4) on the basis of (1). Smith has correctly inferred (2), (3), and (4) from a proposition for which be has strong evidence. Smith is therefore completely justified in believing each of these three propositions, Smith, of course, has no idea where Brown is.
But imagine now that two further conditions hold. First Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (3) happens really to be the place where Brown is. If these two conditions hold, then Smith does not know that (3) is true, even though
This is another instance where the "philosophy of language" gets in the way of the meaning of what is being proposed. To answer this case, it is necessary to be clear about the context of the truth and the justification. The case improperly conflates the contexts of the two halves of (3). Unlike the approach of "philosophy of language", there are two separate propositions in play here. And it is necessary to keep clear the roles of truth and justification as they apply to the different propositions. The justification that Smith has, applies only to whether or not Jones owns a Ford. The truth of the proposition applies only to the current location of Brown. By maintaining a consistent context for both the truth and the justification conditions, it is clear that Smith does not know that (3). Although Smith does have the justification to believe that Jones owns a Ford, it is not true that Jones owns a Ford. And of course, as described, Smith has no justification for believing the truth that Brown is in Barcelona.
You have a justified belief that someone in your office owns a Ford. And as it happens it's true that someone in your office owns a Ford. However, your evidence for your belief all concerns Nogot, who as it turns out owns no Ford. Your belief that someone in the office owns a Ford is true because someone else in the office owns a Ford. Call this guy Haveit. Since all your evidence concerns Nogot and not Haveit, it seems, intuitively, that you don't know that someone in your office owns a Ford. So you don't know, even though you have a justified belief that someone owns a Ford, and, as it turns out, this belief happens to be true.
This example is similar to Case 1 above. It confuses the context of the concept "The owner of the Ford" with the preposition "Someone". If you have justification for believing that Nogot owns a Ford, the justification does not apply to "Someone in your office", it applies to Nogot. Extrapolating from the belief that Nogot owns a Ford to the proposition that "Someone in your office" owns a Ford (because Nogot is someone in your office) may be a logically valid inference. But it does not help the situation because it is not true that Nogot owns a Ford.
There is a variation of this case. Suppose that the evidence justifying your belief that someone in your office owns a Ford is "impersonal". Perhaps you see a Ford in the company parking lot on a daily basis. And you have good reasons for believing it is neither rented nor leased. In this case, you need to maintain the context of "The owner of the Ford you see in the parking lot" and the "Someone in the office". If that particular Ford happens to be owned by "Someone in the office", then you do have the knowledge. But if that particular Ford does not belong to Haveit, and is not owned by someone in your office, you do not have the knowledge. The fact that Haveit owns a Ford is irrelevant, because it is the wrong Ford.
Here, the particular flaw in the reasoning is a deduction from a false belief. The conclusion that someone in your office owns a Ford is based on two premises. One, that someone in your office is waxing a Ford. And two, that the person waxing the Ford owns the Ford. It is this second premise that is false. This case is considered a "Gettier Example" because of the already mentioned penchant for modern philosophers to confuse the conceptual contexts of prepositions.
If you look at the case carefully, you will see that there is a chain of reasoning involved. You see Nogot waxing the Ford. You believe that Nogot is "Someone in your office". So you can deduce that "Someone in your office is waxing a Ford". You believe that anyone who waxes a car must own the car he is waxing. So you conclude that Nogot owns the Ford. And you then conclude that "Someone in your office owns a Ford". But the context of this belief is that the "Someone" involved is Nogot. So the fact that Haveit owns a Ford is not relevant to whether your belief is knowledge. All your justification applies only to Nogot and not to all other people in your office.
You're in the meadow, and you see a rock which looks to you like a sheep. So you say to yourself "There's a sheep in the meadow." In fact there is a sheep in the meadow (behind the rock, where you can't see it).
Once again - a confusion over the context of the concepts involved. The justification for the belief that "There is a sheep in the meadow" is the belief that "That thing over there is a sheep". And that is the false premise that renders the conclusion a belief rather than knowledge.
It looks to you like there is a pillar 100 feet ahead. But in fact there's a mirror 50 feet ahead of you, and what you're seeing is a pillar off to your left. As it turns out, though, there is a pillar 100 feet ahead of you, you just can't see it.
The same as Case 5. The justification for the belief that there is a pillar 100 feet ahead, is the belief that the pillar you are seeing is ahead of you. And that is the false premise that renders the conclusion a belief rather than knowledge.
Consider whether an executive knows whether her secretary is in his office. Suppose that she looked into the office and saw, sitting behind the desk, a figure who looked to her exactly like her secretary. We may suppose that she would be completely justified in accepting that her secretary is in his office. However, it may be that the person sitting at the desk is her secretary's identical twin brother. The real secretary is hiding behind the office door, waiting to leap up and surprise her. So it is true that the secretary is in the office, the executive accepts that it is true, and she is completely justified in so accepting that he is.
She is not completely justified in accepting that he is in his office. The unspecified premise is that the person sitting behind the secretary's desk, and who looks like her secretary, is in fact her secretary. All of the justification that the executive brings to bare on her belief is mis-directed because of this false first premise. Once again, it is a problem of consistent context. The context of the justification for the belief is not the context of the truth of the proposition.
Tommy comes across some evidence that his wife is sneaking around. She isn't at work when she's supposed to be, he finds some matches from a fancy nightclub in her car, and so on. When he asks his wife where she's been, she is evasive. This gives him some evidence for believing that his wife is having an affair. As a matter of fact, there is a simple explanation for all the evidence that Tommy has encountered: his wife is planning a surprise birthday party for him. But as it also turns out, his wife is having an affair, with her old boyfriend in Chicago. But she's very discreet about it, and so hasn't left any clues lying around. This is a case where Tommy has a true belief that his wife is unfaithful, and it's just an accident that his belief is true. Yet it seems intuitively correct to say Tommy doesn't know that his wife is unfaithful.
The problem here is similar to those above. The case is deliberately designed to hide a critical premise. To resolve the apparent contradiction, one need only be cognizant of that missing premise. The reason it seems intuitively correct to say that Tommy doesn't know, is that intuitively we are aware of the significance of that missing premise even if we are not conscious of it. In this case the missing premise is that the evidence Tommy is seeing is evidence of his wife fooling around. And as specified in this case, that premise is false. Therefore, any justification based on that premise is invalid.
Tommy goes on a business trip to Chicago, checks into his hotel, and goes up to his room. By accident, he gets off the elevator on the wrong floor, and opens the wrong door. But the door does open, and there is his wife, in bed with her old boyfriend. In this case, too, Tommy has a true belief that his wife is being unfaithful to him. And in this case, too, it seems to be just an accident that Tommy has a true belief about this. But in this case, we do want to say that Tommy knows that his wife is being unfaithful.
And of course, in this case, that missing premise is in fact true. So justification based on that premise is now valid.
Jill reads in the newspaper that the president of her country has been assassinated. In fact, this story is true. However, the president's associates have mounted a campaign to suppress the story, and they've been broadcasting false reports on all the television stations that the president is OK, the assassin actually only killed a bodyguard. Jill is blissfully unaware of all this misleading evidence. The newspaper she read happens to be the only news source that's reporting the true events. All of Jill's peers, on the other hand, have heard the misleading TV reports and aren't sure whether or not the president was really killed. It is suggested that Jill has a justified true belief that the president was assassinated, but she doesn't have knowledge, because there is all this misleading evidence abroad in her community, which she has only managed to avoid by sheer luck.
In this case, the problem is resolved by recognizing that there are more than one perspective from which the judgment can be made. Jill can validly judge that she has sufficient justification for her belief in a true proposition that her belief qualifies as knowledge. Other people (including us) who aware of all the apparently defeating evidence, would judge that there isn't sufficient justification for Jill's belief to qualify as knowledge. We cannot expect infallibility in judgments about whether some justified belief is knowledge. If the underlying proposition is true, one person can judge that the justification is sufficient. Another can judge that the justification is insufficient. This may result from differences in their respective degrees of confidence in the justificatory evidence. Or it may result, and in this case, from differences in the nature of the evidence available.
The president's associates are sitting in the TV studio, saying into the microphone "No really the president is OK, it was somebody else who got killed." The fact that they are saying this is a potentially defeating piece of information. If Jill were to learn of it, it would defeat her justification for believing the president had been assassinated. But suppose that in this case, unlike the earlier case, the associates' speech never gets broadcast to the public. (Maybe the TV producers think it would be wrong to deceive the public in the way the associates want.) So all the newspapers and TV stations carry the correct report about the president's assassination.
In this case, it is unclear to me why the authors consider this a "Gettier Problem". There is a potentially defeating piece of evidence out there (the fact that the associates are saying what they're saying). But it's so remote, nobody knows about it except the associates themselves and a few TV crew. Since Jill is unaware of this information it does not block her justified true belief about the president from counting as knowledge. Even those involved in preparing the misleading evidence are aware that the evidence being offered is false. No one is in a position to judge that the evidence is insufficiently justifying to qualify Jill's belief as knowledge.
(See Lehrer, Keith; Theory of Knowledge 2nd Edition; Westview 1990)
You see Tom Grabit hide a book underneath his jacket and sneak out of Widener Library. On the basis of this, you form the justified belief that Tom stole a library book. As it happens, your belief is true. However, unbeknownst to you, Tom's mother was going around today telling people that Tom was thousands of miles away, and that Tom's evil twin John was visiting Harvard. The fact that Tom's mother said this is a potentially defeating piece of evidence. If you were to learn of it, it would defeat your justification for believing that Tom stole the book. However, as it turns out, it really was Tom who stole the book. Tom has no twin brother and his mother is a compulsive liar.
In this case, it seems like you should count as knowing that Tom stole the book. The testimony of a compulsive liar, which you never hear, should not block your justified true belief about Tom from counting as knowledge.
(see Goldman, Alvin. 1976. "Discrimination and Perceptual Knowledge." The Journal of Philosophy 73, pp. 771-791.)
Suppose there is a county in the Midwest with the following peculiar feature. The landscape next to the road leading through that county is peppered with barn-facades: structures that from the road look exactly like barns. Observation from any other viewpoint would immediately reveal these structures to be fakes: devices erected for the purpose of fooling unsuspecting motorists into believing in the presence of barns. Suppose Henry is driving along the road that leads through Barn County. Naturally, he will on numerous occasions form a false belief in the presence of a barn. Since Henry has no reason to suspect that he is the victim of organized deception, these beliefs are justified. Now suppose further that, on one of those occasions when he believes there is a barn over there, he happens to be looking at the one and only real barn in the county. This time, his belief is justified and true. But its truth is the result of luck, and thus his belief is not an instance of knowledge.
I would disagree with Goldman on this case. This case is similar to the one above. There is some potentially defeating information available "out there" that Henry is unaware of. Does this render his conclusion about this particular barn merely a belief? I think not. I think that Henry can validly claim to know in this case that what he is looking at is a barn. In the other cases, where he was looking at a barn-facade, he cannot validly claim to know it is a barn he is seeing, because it is not a barn. However, since we are in possession of the defeating additional information, we can conclude that Henry's belief is not knowledge. This harkens back to the confidence scale of belief. Henry is sufficiently confident in his belief that he claims to know it is a barn. We, in possession of more information, see that Henry's confidence is misplaced and properly conclude that Henry does not know that it is a barn.