The bartender asks “Do all three of you want a beer?”
The first logician says “I don’t know”.
The second logician says “I don’t know.”
The third logician says “Yes.”
The bartender asks “Do all three of you want a beer?”
The first logician says “I don’t know”.
The second logician says “I don’t know.”
The third logician says “Yes.”
If any logician hadn’t made up his mind, then the answer to “do all of you want a beer” would be False, i. e. No.
The idea that a Yes/No question can have any other state is not possible for these cartoonish logicians.
(Of course, “logicians” do not exist. The closest thing in real life are mathematicians and computer scientists who are trained in logic, and these people known that the real world works differently than the simple logic presented in this joke, so your point is valid at some level, but it doesn’t invalidate the joke)
Well, then, what would you call a professor of logic?
Logicians certainly do exist. Some of them might be called mathematicians or philosophers but that doesn’t mean they’re not logicians.
So these logicians of yours, do they all want a beer?
Yes, humans who study logic and specialize in it exist, and you can call them logicians, but the point is that they have a much broader understanding of math, philosophy and different modes of logic than the “logicians” used in these jokes, who are caricatures that paradoxically are called logicians, but at the same time only follow a very basic mode of logic that is taught in undergraduate classes.
Such logicians do not exist and cannot exist.