"Michael was not born in Germany" cannot stand alone as S's belief about Michael's birthplace. Current conventional practice leads to our claiming otherwise, and in doing so it also results in saying that all three individuals share the exact same belief about Michael's birthplace.
They - quite clearly - do not.
The only way to properly discriminate between the three individuals is to report their belief as Q because P, where P is any of the three beliefs written above. Upon doing so, we find Gettier's problem dissolved. Justified false belief is not a problem for JTB. — creativesoul
Well, that clarifies a great deal, and I agree that this dissolves the Gettier problem.
But I do have qualifications.
First, is this a diagnosis that you would accept? Gettier thinks that beliefs, propositions and sentences neatly align with each other. Each belief, proposition and sentence is clearly distinct from all other beliefs, propositions and sentences. I doubt that he would accept that, but his formulation of the problem sweeps all the complexities under the carpet and trades on the resulting ambiguities.
Second, if you focus on "Michael was not born in Germany" and the fact that all three people would agree on that, you will think that they all have the same belief, and with reason. If you focus on the fact that they each have a different reason for believing that, you will think that they all have different beliefs, and with reason. So I prefer to stick with what I have just said and refuse to adopt either that they do, or that they do not, have the same belief. So long as the situation is clear, which it is, the classification doesn't matter very much. Or at least, I need to be persuaded that it matters, and for what purposes.
I observe that this issue seems to me to parallel the problems that Wittgenstein had with the colour exclusion problem - which, if I have the history right, eventually led to him abandoning logical atomism.
Third, (the Gettier problem seems to have a kind of gravity in that one cannot help returning to it), I think that there is a real problem which he also exploits. The quickest way to articulate this is through an example.
Suppose S is waiting at a bus stop and observes to T that the bus will arrive soon, meaning in the next five minutes. S is justified in believing this, because he has checked the timetable. The bus arrives six minutes later. Was S right or not? Did S know, or not? Again, suppose that the bus that was supposed to arrive has broken down and a replacement bus has been sent out and manages to arrive within five minutes. Was S right or not? Did S know or not? One could invent such cases indefinitely.
Another example, drawing on Gettier's first case. (I should look up the article here, but I'm going to chance my arm and work from memory). The target proposition in this case is "The person who is appointed will have ten coins in their pocket". This proposition turns out to be true, but not in the way that S expects. In this case, S's belief and the truth are nested in different contexts and I would say that the differences are such that Smith does not know. I think (though it is hard to be sure) that all Gettier problems turn on this issue.
The point here is an application of what we've agreed about beliefs. Sometimes belief/knowledge may be confirmed in ways that S has not taken into account; such cases may or may not impinge on a knowledge claim, and even result in an undecidable case. In practice, what we say will depend on the context, particularly what matters to our project at the time.
That's an imperfect formulation of the issue but I hope it takes us forward a bit.