From what has been said it is evident that, both as regards intuitive knowledge and as regards derivative knowledge, if we assume that intuitive knowledge is trustworthy in proportion to the degree of its self-evidence, there will be a gradation in trustworthiness, from the existence of noteworthy sense-data and the simpler truths of logic and arithmetic, which may be taken as quite certain, down to judgements which seem only just more probable than their opposites. What we firmly believe, if it is true, is called _knowledge_, provided it is either intuitive or inferred (logically or psychologically) from intuitive knowledge from which it follows logically. What we firmly believe, if it is not true, is called _error_. What we firmly believe, if it is neither knowledge nor error, and also what we believe hesitatingly, because it is, or is derived from, something which has not the highest degree of self-evidence, may be called _probable opinion_. Thus the greater part of what would commonly pass as knowledge is more or less probable opinion. In regard to probable opinion, we can derive great assistance from _coherence_, which we rejected as the _definition_ of truth, but may often use as a _criterion_. A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually. It is in this way that many scientific hypotheses acquire their probability. They fit into a coherent system of probable opinions, and thus become more probable than they would be in isolation. The same thing applies to general philosophical hypotheses. Often in a single case such hypotheses may seem highly doubtful, while yet, when we consider the order and coherence which they introduce into a mass of probable opinion, they become pretty nearly certain. This applies, in particular, to such matters as the distinction between dreams and waking life. If our dreams, night after night, were as coherent one with another as our days, we should hardly know whether to believe the dreams or the waking life. As it is, the test of coherence condemns the dreams and confirms the waking life. But this test, though it increases probability where it is successful, never gives absolute certainty, unless there is certainty already at some point in the coherent system. Thus the mere organization of probable opinion will never, by itself, transform it into indubitable knowledge. CHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE