I have been thinking about the following dialogue for some time. It consists of some arguments I've come up with for both sides, and includes the idea of Russel's teapot.
Suppose X is a proposition which
1) Implies various propositions about the physical universe.
2) There is no empirical justification for X
3) There is no empirical justification that X is false
4) Suppose there are countably many mutually exclusive propositions, one of which is X, and each of which satisfy (1), (2), and (3).
Fred Argument 1:
Fred: It's about time you admitted X is false!
George: I require empirical justification to believe this proposition that X is false. There is none.
Fred: But surely you believe that there is no teapot in orbit of Jupiter? I intuit that this is absurd, yet we agree that there is no empirical justification for or against it, just like proposition X. Do you not then believe that proposition X is false?
George: I believe that there is no teapot in orbit of Jupiter, but not that proposition X is false. I would be justified in saying that such a teapot does not exist because someone would have had to put it there. In this respect, this claim is unlike proposition X.
Fred: How do you know that there is not a non-man-made teapot orbiting Jupiter?
George: I would infer by the laws of thermodynamics that the odds of a teapot assembling by chance alone are quite small.
Fred pauses to think.
Fred Argument 2:
Fred: Ok. I agree that my former argument cannot convince you. But X is a member of a countable set of mutually exclusive propositions, each with no empirical justification for or against. If one assigns a probability to each one, and chooses a threshold to represent "very unlikely", only a finite amount of propositions could not be very unlikely. From this we can infer that proposition X is probably very unlikely.
George: I object that you are not warranted in assigning a probability space to this scenario. Such probabilities would stem from the existence of evidential justification of some sort, which for proposition X there is not. To give you an example of what I mean, consider the specific proposition that there is a fairy with a wing of a certain specific color whose RGB value is (10, 80, 128).
Fred: that would look quite nice.
George: but there are countably many distinct propositions, one for each natural number: there exists a fairy with a wing of certain specific color whose RGB value is (10, 80, 128 2^(-n) ). I reject your inference that one can say anything about how likely each one is, and I do not believe that there are no fairies.
Fred: I see that this will not convince you either then. To me, it is self evident that fairies of any sort do not exist.
The question is, what position is justified on proposition X, if indeed there is enough information to take one? What philosophical views are there that weigh in on this matter? As pointed out by Conifold, An answer to this question necessarily involves giving one's view on epistemic justification. I would like not to suppose that Fred and George share such a view, but for the answer to give possible viewpoints and where they stand in promoting the arguments involved.