Page:Russell - The Problems of Philosophy, 1912.djvu/220

216 altered to be more and more like the blue, becoming first a blue-green, then a greeny-blue, then blue, there will come a moment when we are doubtful whether we can see any difference, and then a moment when we know that we cannot see any difference. The same thing happens in tuning a musical instrument, or in any other case where there is a continuous gradation. Thus self-evidence of this sort is a matter of degree; and it seems plain that the higher degrees are more to be trusted than the lower degrees.

In derivative knowledge our ultimate premisses must have some degree of self-evidence, and so must their connection with the conclusions deduced from them. Take for example a piece of reasoning in geometry. It is not enough that the axioms from which we start should be self-evident: it is necessary also that, at each step in the reasoning, the connection of premiss and conclusion should be self-evident. In difficult reasoning, this connection has often only a very small degree of self-evidence; hence errors of reasoning are not improbable where the difficulty is great.