This study will show how Bertrand Russell's argument which purports to show that we do not know that the sun will rise tomorrow is similar to the argument which purports to show that we don't know that there is a sun, or, indeed, that there is any other physical object at all.
The purpose of Russell's argument, as presented in Chapter 6 ("On Induction") of his book The Problems of Philosophy, is to see if we can rationally extend the realm of knowledge to matters beyond our "private experience." The basis of the inquiry is the argument that "It must be known to us that the existence of some one sort of thing, A, is a sign of the existence of some other sort of thing, B, either at the same time as A or at some earlier or later time, as, for example, thunder is a sign of the earlier existence of lightning" (p. 60).
With respect to the argument at hand, then, Russell is seeking to discover if we can conclude that the sun will rise tomorrow (B) because the sun has risen every morning in the past, as far as we know. The question boils down to "whether the laws of motion will remain in operation until to morrow" (p. 61).
The principle being investigated by Russell in this and in any similar argument is the principle of induction. This principle holds that "When a thing of a certain sort A has been found to be associated with a thing of a certain other sort B, and has never been found dissociated from a thing of the sort B, the greater the number of cases in which A and B have been associated, the greater is the probability that they will be associated in a fresh case in which one of them is known to be present" (p. 66).
In other words, the more the laws of the physical universe hold true --- from sunrise to sunrise day after day --- the more likely it will be, the more probable it will be, that the sun
However, this does not mean that we have proved that the sun will rise tomorrow. We are merely stating, based on past...