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 ought to do, or what is good and bad in manners, literature and art. Of course in these latter regions of belief any educated person is aware that there is much doubt and controversy; still there are plenty of propositions in each of the regions indicated, which it would seem in ordinary thought as absurd to dispute or qualify as propositions with regard to the most familiar matters of fact. When Charles Lamb took a candle to examine the cerebral bumps of the soap-boiler who affirmed that Shakespeare was a first-rate dramatic writer, it was, I suppose, because the irrefragable certainty of the proposition seemed to render its express statement absurdly superfluous.

Concentrating attention, then, on beliefs that in ordinary thought are certain in the sense explained, let us—with a view to a necessary limitation of our inquiry—take a second distinction. Reflecting upon the beliefs of the truth of which I have no doubt, I perceive that some of them (e.g., the propositions of Euclid) have only derivative or dependent certainty—my belief in them rests on my belief in some other proposition or propositions; while in other cases (e.g., most of the axioms of Euclid) my certitude may be distinguished as primary or independent. In the instance given—as I have personally followed the reasonings of Euclid and satisfied myself as to their cogency—I might employ a clearer antithesis, and say that some of my geometrical beliefs have “intuitive” and others demonstrative certainty. But this antithesis is too narrow for my present purpose. For, firstly, I do not profess to have intuitive certainty with regard to all beliefs for which proof does not seem to be required. I am certain that I read through the three first pages of this essay before I sat down to write the fourth half an hour ago; but it would be contrary to usage to call this certainty “intuitive,” though the belief does not present itself to me as requiring proof. Secondly, I wish to include among beliefs with derivative certainty that comparatively large body of scientific conclusions which I believe to have been scientifically proved, though not to me, and which I accordingly accept on the authority of one or more other persons. Of course, in a wide sense of the word, a statement of my grounds for trusting any conclusion arrived at by some other mind might be called my “proof” of the proposition; but at any rate it would not be scientific demonstration, and it would be odd to call the certainty of any such belief to me “demonstrative certainty”. For simplicity, let us here provisionally disregard any doubts of the authority of others as others: then the distinction will be