If I were giving a history comprehensive exam...

It seems one can set a history of philosophy comprehensive exam that would be hard and rigorous without knowing almost any history of philosophy—though, of course, to pass or grade, one would have to know a lot. The exam is fun to set. It wouldn't be so much fun to take. Here it is:

Consider the following modal forms of argument:

1. Mp; M(if p then q); therefore Mq
2. Lp; if p then q; therefore Lq
3. L(if p then q); p; therefore Lq
4. M((exists x)F(x)); therefore (exists x)MF(x)
5. L((exists x)F(x)); therefore (exists x)LF(x)

It is generally uncontroversial that (1)-(3) are fallacies; it is fairly widely thought that (4) and (5) are fallacies. Write six essays, each about three or four pages long, satisfying the following rules:

• Each essay chooses exactly one philosopher.
• Each essay chooses exactly one of the argument forms above.
• Exactly two philosophers are chosen from each of the following periods: ancient, medieval and modern (up to the end of the 19th century).
• No two essays concerning philosophers from the same period (ancient, medieval or modern) select the same argument form.
• Each essay identifies a place where the philosopher in persona propria appears to be making use of the selected argument form. The significance of the inference to the philosopher's more major project(s) is discussed, and it is discussed how the project(s) would be affected were the inference invalidated. Then it is discussed whether the philosopher in question could either to defend the inference (perhaps the philosopher has open to her or him a modal logic on which the inference is not fallacious) or somewhat modify the form of argument so as to avoid the modal fallacy (without simply shifting to a different modal fallacy or including a trivializing premise).

Remark: Part of the difficulty of this is that I think it is pretty rare for a great philosopher to commit a modal fallacy. So one will need to show quite a bit of knowledge of the work of great philosophers, or a fair amount of knowledge of the work of not so great philosophers, to do this. Of course, if one knows ahead of time that this question will come up, one will just read up on some really, really bad philosophers from each period.