The Gettier problem shook the classic definition of knowledge. For centuries it was certain that there was a stable definition of the concept of knowledge that was already known in Plato’s time. But the Gettier problem pointed to a systematic flaw in this definition.
The standard analysis of knowledge
The Gettier problem is completely impossible without a prior understanding of the classical definition of knowledge. I have therefore already written an introduction to this topic, which you should definitely read here before you devote yourself to this article in detail. Nevertheless, I will shortly clarify the conditions mentioned there again at this point.
The initial question, of course, is the condition for knowledge, so what is knowledge? We saw that we spoke of propositional content and viewed knowledge (at least as a rule) in a subjective form. This leads us very quickly to the idea that knowledge must somehow have something to do with opinion or conviction.
But it is far from enough if we say that a person knows x because he means x or is convinced of it. There are still more components missing, such as the criterion of truth. What I am convinced of must also correspond to reality.
Finally, we had to realize that knowledge needs something like a justification to justify our opinion. So we came up with the classic definition of knowledge, which until Gettier had been considered inviolable for 2000 years: Knowledge is true, justified conviction.
Gettier versus the standard analysis
Edmund L. Gettier showed in a three-page essay from 1963 that this conception of knowledge does not cover everything and therefore falls short. The three conditions, namely truth, justification and conviction, are necessary, that is, each indispensable for knowledge, but unfortunately not enough together.
It can be shown that with a few basic assumptions, which almost everyone accepts, one can construct cases in which all the conditions of knowledge according to the classical definition are met, but we would never speak of knowledge. Here is an example from everyday life:
As early as 1948 in Human Knowledge, Bertrand Russell had shown, using the example of a stopped clock, that the extensive conception of knowledge as a true [justified] opinion was wrong: If Hans’ alarm clock stopped at 5:00 p.m., but Hans didn’t notice it and looks at his alarm clock at 5:00 p.m. the following day, he has a justifiable true opinion that it is exactly 5:00 p.m. however, no one will claim that Hans acquired knowledge that it was 5:00 p.m. 
Problematization of the alarm clock example
The problem in such a case is simple. Somehow we are confronted with a coincidence, but remain justified in our conviction. The fact that there is no knowledge is now received differently. Some immediately see that this is the case, while others first ask what the problem is. Why is that not knowledge?
Gettier justifies this on the one hand by a fundamental understanding of the nature of knowledge and on the other hand by intuition, which is by no means stupid. When we speak of knowledge, we mean something that happens to be true, something infallible that applies with full conscientiousness.
If we consider these coincidences, such as the alarm clock example and the following Gettier examples, as knowledge, our concept of knowledge becomes vague, almost arbitrary. I have already mentioned one example against chance in the article on the definition of knowledge and I would like to add another one here:
All those who consider chance to be insignificant for the problem of the definition of knowledge would have to speak of knowledge in this case too: Suppose I go to a woman who poses as a fortune teller. She predicts that I will meet an inspector on the train at exactly 4:39 pm the next day and that actually happens. Would we really want to talk about knowledge here?
Gettier’s basic assumptions
Now that we have cleared away the first pebbles, we can finally get to the specific subject of this topic, namely Gettier’s essay Is Justified True Belief Knowledge? including his two cases. Right at the beginning he mentions two prerequisites that we have already implicitly mentioned.
1) Fallibilism – One can be justified in believing something that is wrong.
In the sense of “justified” in which it is a necessary condition for S ‘knowledge of P that S then be justified in believing that P, it is possible that someone is justified in believing something that is in Reality is wrong. 
Does that sound plausible? It should. Gettier’s assumptions are both harmless. It is best to use simple everyday examples as a guide: I believe that Maria is in Berlin. Why do I believe that? Quite simply: Your friend Tim, who is considered reliable, has assured me.
So I am justified in believing that Maria is in Berlin. In fact, Tim was wrong and Maria flew to Hamburg at short notice. The fact that the truth is now absent does absolutely nothing to change my justification.
2) Deductive unity – Here: justification is preserved.
If S is justified in believing P, and if PQ follows, and if S concludes from P to Q and accepts Q as a result of this inference, then S is justified in believing that Q. [ibid.]
The second assumption looks much more complicated because of the many letters – but it is not. Let’s use an example from everyday life again: This time Maria is in the swimming pool. From where I know this? She told me, yes maybe I even saw her there.
So I am entirely justified in believing this first statement (P). For example, the first statement includes the following statement (Q): Mary is not at home. Since I am justified in believing P and Q follows from P, I am also justified in believing Q in it. Very easily.
The whole problem of the Gettier cases can therefore be summarized as follows:
Since it is possible that a person S is justifiably convinced of a false thesis P and can furthermore infer a derivation Q from P, which in turn is true, it is entirely possible to arrive at true beliefs from false assumptions. A conviction gained in this way then in no way represents knowledge, although Q is true, S believes that Q is true and S ‘belief that Q is true is justified. 
Coins & Job – The first Gettier case
I don’t want to simply copy Gettier’s two examples into this article, because in such a form you can simply read them here in the original. Rather, I will describe the two cases analogously and make an attempt to align their structure on the basis of the principles already mentioned.
Case 1: Smith and Jones apply for the same position. Smith is justified in believing Jones will get the job. The HR manager told him that. This later turns out to be wrong, but as we have seen it doesn’t change the justification. Also, Smith saw that Jones had 10 coins in his pocket. He now concludes:
The one who is going to get the job has 10 coins in their pocket.
This is where deductive closeness comes in, because the statement, “Whoever will get the job has 10 coins in his pocket” implies that Smith is convinced that Jones will get the job and that he has seen Jones 10 Has coins.
In terms of deductive unity, Smith now has a justified belief . It turns out, however, that Smith got the job and he happened to have 10 coins too, which he didn’t know about (which is not at all absurd). Accordingly, the condition of truth is also present, namely in the statement that was derived from the false one.
All the conditions of the classical definition of knowledge are fulfilled: the statement ›The one who will get the job has 10 coins in his pocket‹ is true, Smith is justified in believing it because he derived it from a statement for which he had very good reasons (we remember: the personnel manager gave him his justification) and for these reasons the opinion is available anyway.
Intuitively, however, we wouldn’t speak of knowledge because this strange factor of chance plays a role. 
Ford & Barcelona – The second Gettier case
The second part is much more difficult without a basic understanding of logic. It therefore seems quite constructed, even very strange and remote from everyday life, but basically it is constructed exactly like the first case – it even presupposes an indirect assumption that the protagonist (Smith) is a very rational person.
Case 2: Smith is justified in believing that Jones owns a Ford because he only ever saw Jones drive in a Ford. He knows no whereabouts of his other friend Brown. He now closes three statements …
- … first, that Jones owns a Ford or Brown is in Boston.
- … second, that Jones owns a Ford or Brown is in Barcelona.
- … third, that Jones owns a Ford or Brown is in Brest-Litovsk.
These statements are all derived from the justified statement ›Jones owns a Ford‹, because the introduction of an (inclusive) OR link can be done without hesitation. After all, the truth of any statement like “I am a person” does not change if I make the following compound statement out of it, for example: “I am a person or the earth is flat”.
In the case of the inclusive or, the overall statement is true if either one of the partial statements is true or both together. In other words, both partial statements have to be wrong for the whole statement to be wrong. Under no circumstances should we confuse this with our either-or from everyday language.
The rest works analogously to the first case. Because of the deductive unity, Smith is again absolutely justified in believing all three statements. The statements are true if and only if one of the conditions is true or both together.
It then turns out that Jones doesn’t own a Ford, just drives a rental car and Brown is actually in one of the three cities, for example in Barcelona. According to this, there is truth, since a condition of his statement is fulfilled, justification also by the first statement from which the three were derived and conviction anyway.
Here, too, all the conditions of the classic definition of knowledge are met, but there is no intuitive knowledge. After all, Smith didn’t really know Brown was in Barcelona, did he? 
Development after the Gettier cases
Finally, the question arises as to whether these Gettier cases can actually be solved. What happened after 1963? Of course there were many original solutions, but it is noteworthy that the definition of knowledge is still being worked on today because nothing definite could be found.
It would probably take 20 more articles to get any idea of what was being done to further handle the Gettier cases. All of this belongs to the larger group of topics of epistemology – including, above all, the clarification of the concept of justification. In conclusion, I would just like to say the following:
The Gettier cases should remind us that even a definition that has long been considered approved does not have to be final. Above all, we should always remember that we must not simply accept the sacred title of inviolability and leave it in blissful rest. After all, the 2000-year-old standard analysis of knowledge would otherwise never have been exposed as flawed.