In the series of propositions, A is B, B is C, therefore A is C, the act of mind by which I perceive that A is B, or that B is C, is not of the same nature with that by which I perceive the consequent truth that A is C; no mere repetition of the former act would amount to the latter. There is a new sort of judgment in the latter case, a deduction from the former. In order to reach it, I must not merely perceive that A is B, and that B is C, but must also perceive the connection of the two propositions, and what is involved in them. It is only by bringing together in the mind these two propositions, that I perceive the new truth, not otherwise obvious, that A is C, and the state or act of mind involved in this latter step seems to me a different one from that by which I reach the former judgments. § III.--DIFFERENT KINDS OF REASONING. _Two Kinds of Truth._--The most natural division is that according to the subject-matter, or the materials of the work. The truths which constitute the material of our reasoning process are of two kinds, _necessary_, and _contingent_. That two straight lines cannot enclose a space, that the whole is greater than any one of its parts, are examples of the former. That the earth is an oblate spheroid, moves in an elliptical orbit, and is attended by one satellite, are examples of the latter. _The Difference lies in what._--The difference is not that one is any _less certain_ than the other, but of the one you cannot conceive the opposite, of the other you can. That three times three are nine, is no more true and certain, than that Cæsar invaded Britain, or that the sun will rise to-morrow a few minutes earlier or later than to-day. But the one admits of the contrary supposition without absurdity, the other does not; the one is contingent, the other necessary. Now these two classes of truths, differing as they do, in this important particular, admit of, and require, very different methods of reasoning. The one class is susceptible of _demonstration_, the other admits only that species of reasoning called _probable_ or _moral_. It must be remembered, however that when we thus speak we do not mean that this latter class of truths is deficient in proof; the word probable is not, as thus used, opposed to _certainty_, but only to _demonstration_. That there is such a city as Rome, or London, is just as _certain_ as that the several angles of a triangle are equal to two right-angles; but the evidence which substantiates the one is of a very different nature from that of the other. The one can be demonstrated, the other cannot. The one is an eternal and necessary truth, subject to no contingence, no possibility of the opposite. The other is of the nature of an event taking place in time, and dependent on the will of man, and might, without any absurdity, be supposed not to be as it is. I. DEMONSTRATIVE REASONING.