Among these questions is one of much importance which has already been the subject of controversy between Mr. Mill and others; and this question I propose to discuss afresh. Before doing so, however, it will be desirable to glance at two cardinal doctrines of the Hamiltonian philosophy from which Mr. Mill shows reasons for dissenting—desirable, because comment on them will elucidate what is to follow. In his fifth chapter, Mr. Mill points out that “what is rejected as knowledge by Sir William Hamilton,” is “brought back by him under the name of belief.” The quotations justify this description of Sir W. Hamilton’s position, and warrant the assertion that the relativity of {189} knowledge was held by him but nominally. His inconsistency may, I think, be traced to the use of the word “belief” in two quite different senses. We commonly say we “believe” a thing for which we can assign preponderating evidence, or concerning which we have received some indefinable impression. We _believe_ that the next House of Commons will not abolish Church-rates; or we _believe_ that a person on whose face we look is good-natured. That is, when we can give confessedly-inadequate proofs or no proofs at all for the things we think, we call them “beliefs.” And it is the peculiarity of these beliefs, as contrasted with cognitions, that their connexions with antecedent states of consciousness may be easily severed, instead of being difficult to sever. But, unhappily, the word “belief” is also applied to each of those temporarily or permanently indissoluble connexions in consciousness, for the acceptance of which the only warrant is that it cannot be got rid of. Saying that I feel a pain, or hear a sound, or see one line to be longer than another, is saying that there has occurred in me a certain change of state; and it is impossible for me to give a stronger evidence of this fact than that it is present to my mind. Every argument, too, is resolvable into successive affections of consciousness which have no warrants beyond themselves. When asked why I assert some mediately known truth, as that the three angles of a triangle are equal to two right angles, I find that the proof may be decomposed into steps, each of which is an immediate consciousness that certain two quantities or two relations are equal or unequal—a consciousness for which no further evidence is assignable than that it exists in me. Nor, on finally getting down to some axiom underlying the whole fabric of demonstration, can I say more than that it is a truth of which I am immediately conscious. But now observe the confusion that has arisen. The immense majority of truths which we accept as beyond doubt, and from which our notion of unquestionable truth is abstracted, {190} have this other trait in common—they are severally established by affiliation on deeper truths. These two characters have become so associated, that one seems to imply the other. For each truth of geometry we are able