And so far I have been dealing only with ideas with regard to what happened in the past. These seem to me to be the cases which offer the most numerous and most certain exceptions to the rule that we can verify our true ideas. With regard to particular past events, either in their own lives or in those of other people, men very frequently have ideas, which it seems highly improbable that any man will ever be able to verify. And yet it is certain that a great many of these ideas are true, because in a great many cases we have both the idea that the event did happen and also the idea that it did not, when it is certain that one or other of these ideas is true. And these ideas with regard to past events would by themselves be sufficient for my purpose. If, as seems certain, there are many true ideas with regard to the past, which it is highly improbable that anyone will ever be able to verify, then, obviously, there is nothing in a true idea which makes it certain that we can verify it. But it is, I think, certainly not only in the case of ideas, with regard to the past, that it is doubtful whether we can verify all the true ideas we have. In the case of many generalisations dealing not only with the past but with the future, it is, I think, obviously doubtful whether we shall ever be able to verify all those which are true; although here, perhaps, in most cases, the probability that we shall not is not so great. But is it quite certain, that in all cases where scientific men have considered hypotheses, one or other of which must be true, either will ever be verified? It seems to be obviously doubtful. Take, for instance, the question whether our actual space is Euclidean or not. This is a case where the alternative has been considered; and where it is certain that, whatever be meant by "our actual space," it either is Euclidean or is not. It has been held, too, that the hypothesis that it is not Euclidean might, conceivably, be verified by observations. But it is doubtful whether it ever will be. And though it would be rash to say that no man ever will be able to verify either hypothesis; it is also rash to assert positively that we shall--that we certainly can verify the true hypotheses. There are, I believe, ever so many similar cases, where alternative hypotheses, one or other of which must be true, have occurred to men of science, and where yet it is very doubtful whether either ever will be verified. Or take, again, such ideas as the idea that there is a God, or the idea that we are immortal. Many men have had not only contradictory ideas, but contradictory beliefs, about these matters. And here we have cases where it is disputed whether these ideas have not actually been verified. But it seems to me doubtful whether they have been. And there is a view, which seems to me to deserve respect, that, in these matters, we never shall be able to verify the true hypothesis. Is it