Between the clear daylight of certain knowledge and the dark night of absolute ignorance comes the twilight of probability.  We find ourselves dependent on opinion and presumption, or judgment based upon probability, when experience and demonstration leave us in the lurch and we are, nevertheless, challenged to a decision by vital needs which brook no delay.  The judge and the historian must convince themselves from the reports of witnesses concerning events which they have not themselves observed; and everyone is compelled by the interests of life, of duty, and of eternal salvation to form conclusions concerning things which lie beyond the limits of his own perception and reflective thought, nay, which transcend all human experience and rigorous demonstration whatever.  To delay decision and action until absolute certainty had been attained, would scarcely allow us to lift a single finger.  In cases concerning events in the past, the future, or at a distance, we rely on the testimony of others (testing their reports by considering their credibility as witnesses and the conformity of the evidence to general experience in like cases); in regard to questions concerning that which is absolutely beyond experience, e.g., higher orders of spirits, or the ultimate causes of natural phenomena, analogy is the only help we have.  If the witnesses conflict among themselves, or with the usual course of nature, the grounds pro and con must be carefully balanced; frequently, however, the degree of probability attained is so great that our assent is almost equivalent to complete certainty.  No one doubts,—­although it is impossible for him to “know,”—­that Caesar conquered Pompey, that gold is ductile in Australia as elsewhere, that iron will sink to-morrow as well as to-day.  Thus opinion supplements the lack of certain knowledge, and serves as a guide for belief and action, wherever the general lot of mankind or individual circumstances prevent absolute certitude.

Although in this twilight region of opinion demonstrative proofs are replaced merely by an “occasion” for “taking” a given fact or idea “as true rather than false,” yet assent is by no means an act of choice, as the Cartesians had erroneously maintained, for in knowledge it is determined by clearly discerned reasons, and in the sphere of opinion, by the balance of probability.  The understanding is free only in combining ideas, not in its judgment concerning the agreement or the repugnancy of the ideas compared; it lies within its own power to decide whether it will judge at all, and what ideas it will compare, but it has no control over the result of the comparison; it is impossible for it to refuse its assent to a demonstrated truth or a preponderant probability.