I'm curious about the example in class:
(1) The student in the classroom 384 is smiling.
If I was right in the previous post, we have to distinguish between a sense of indeterminacy and underdeterminacy for (1).
Should we read the Benacerraf dilemma as posing:
(2) It is not clear which student, if any, is the student in question, so there is no such student. (1) could be about any student, so it is about no student.
(3) It is not clear which student, if any, is the student in question, so there is no way of telling if (1) is true or false. (1) could be about any student, so it is not clear which student it is supposed to be about.
It seems like a defense of the reading of (2) would be to appeal to Russell's notation:
(4) (∃x)((Fx & (∀y)(Fy → y = x)) & Gx)
and since just as there is no unique king of France, there is no unique student in the classroom 384, the sentence is false. Nothing is there to satisfy the definite description, so the sentence has to be false.
A defense of the reading of (3) would seem to appeal to a 3-valued logic. There are true sentences, false sentences, and yet-to-be-determined sentences. If we suspected that a spy was in the classroom, and an intelligence agent told us that "The spy is the man who is smiling" it would seem absurd to conclude since there is no unique smiler, that isn't any spy at all. Why wouldn't the agent just say that in that case?
Or imagine a police detective who finds a murder victim. He might construct a story to explain the murder, that a unique individual entered through the bathroom window and hit Jones over the heat with a frozen banana. The detective might conclude that there was some unique x who did this. How would he react if we told him that since anyone could satisfy this condition, no one could?
The defender of the reading of (3) might argue that in reality, not everything is as clear cut as knowing plainly that there is no king of France. We have to wait to see for many claims.
The defender of the reading of (2) might argue that we still in principle have a 2-valued logic, but admit that we have trouble answering about some claims.
It almost seems like the difference between (2) and (3) is whether we need to have evidence to rule something in, or rule something out. (2) seems to argue that if we have no principled reason to accept the claim as true, it must be false. (3) seems to argue that if we have no principled reason to accept a claim as true or to accept a claim as false, we should stay agnostic.
Does anyone have a preferred reading?