this connection has often only a very small degree of self-evidence; hence errors of reasoning are not improbable where the difficulty is great.
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.