where we know by acquaintance a complex fact consisting of certain terms in a certain relation, we say that the truth that these terms are so related has the first or absolute kind of self-evidence, and in these cases the judgement that the terms are so related must be true. Thus this sort of self-evidence is an absolute guarantee of truth.
But although this sort of self-evidence is an absolute guarantee of truth, it does not enable us to be absolutely certain, in the case of any given judgement, that the judgement in question is true. Suppose we first perceive the sun shining, which is a complex fact, and thence proceed to make the judgement “the sun is shining.” In passing from the perception to the judgement, it is necessary to analyse the given complex fact: we have to separate out “the sun” and “shining” as constituents of the fact. In this process it is possible to commit an error; hence even where a “fact” has the first or absolute kind of self-evidence, a judgement believed to correspond to the fact is not absolutely infallible, because it may not really correspond to the fact. But if it does correspond (in the sense explained in the preceding chapter), then it must be true.
The second sort of self-evidence will be that which belongs to judgements in the first instance, and is not derived from direct perception of a fact as a single complex whole. This second kind of self-evidence will have degrees, from the very highest degree down to a bare inclination in favour of the belief. Take, for example, the case of a horse trotting away from us along a hard road. At first our certainty that we hear the hoofs is complete; gradually, if we listen intently, there comes a moment when we think perhaps it was imagination or the blind upstairs or our own heartbeats; at last we become doubtful whether there was any noise at all; then we think we no longer hear anything, and at last we know we no longer hear anything. In this process, there is a continual gradation of self-evidence, from the highest degree to the least, not in the sense-data themselves, but in the judgements based on them.