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 questions, as there is about many fundamental propositions in Mathematics and the Natural Sciences.

Now, it is precisely questions of this sort, about every one of which there are serious differences of opinion, that I wish to discuss in this book. And from the fact that so much difference of opinion exists about them it is natural to infer that they are questions about which it is extremely difficult to discover the truth. This is, I think, really the case. The probability is, that hardly any positive proposition, which can as yet be offered in answer to them, will be strictly and absolutely true. With regard to negative propositions, indeed,—propositions to the effect that certain positive answers which have been offered, are false,—the case seems to be different. We are, I think, justified in being much more certain that some of the positive suggestions which have been made are not true, than that any particular one among them is true; though even here, perhaps, we are not justified in being absolutely certain.

But even if we cannot be justified either in