192 In every one of the instances given, conviction arises from a single act of perception: for which reason, knowledge acquired by means of that perception, not only knowledge in its proper sense but also opinion and belief, are termed intuitive knowledge. But there are many things, the knowledge of which is not obtained with fo much facility. Propositions for the most part 'require a process or operation in the mind, termed reasoning ; leading, by certain intermediate steps, to the proposition that is to be demonstrated or made evident; which, in opposition to intuitive knowledge, is termed discursive knowledge. This process or operation must be explained, in order to understand the nature of reasoning. And as reasoning is mostly employ'd in discovering relations, I shall draw my, examples from them. Every proposition concerning relations, is an affirmation of a certain relation between two subjects. If the relation affirined appear not intuitively, we must search а ferves a moft ferious difcuffion, whether the operations of nature be always carried on with the greatest fimplicity, or whether we be not misled by our taste for fimplicity to be of that opinion. for for a third subject, intuitively connected with each of the others by the relation affirmed : and if such a subject be found, the proposition is demonstrated; for it is intuitively certain, that two subjects connected with a third by any particular relation, must be connected together by the fame relation. The longest chain of reasoning may be linked together in this manner. Running over such a chain, every one of the subjects must appear intuitively to be connected with that immediately preceding, and with that immediately subsequent, by the relation affirmed in the proposition ; and from the whole united, the proposition, as above mentioned, must appear intuitively certain. The last step of the process is termed a conclufron, being the last or concluding perception. No other reasoning affords fo clear a notion of the foregoing process, as that which is mathematical. Equality is the only mathematical relation; and comparison therefore is the only means by which mathematical propositions are ascertained. To that science belong a number of intuitire propositions, termed ax:oins, which VOL. III. Вь are are all founded on equality. For example: Divide two equal lines, each of them, into a thousand equal parts, a single part of the one line must be equal to a single part of the other. Second: Take ten of these parts from the one line, and as many from the other, and the remaining parts must be equal; which is more shortly expressed thus: From two equal lines take equal parts, and the remainders will be equal; or add equal parts, and the sums will be equal. Third : If two things be, , in the same respect, equal to a third, the one is equal to the other in the same refpect, I proceed to show the use of these axioms, Two things may be equal without being intuitively fo; which is the case of the equality between the three angles of a triangle and two right angles. To demonstrate that trut!, it is necessary to Search for fome other angles that intuitively are equal to both. If this property çannot be discovered in any one set of angles, we must go more leisurely to work, and try to find angles that are equal to the three angles of a triangle. These being discovered, we next try to find other angles equal to the angles now discovered ; and fo on in the comparison, till at last we discover a set of angles, equal not only to those thus introduced, but alfo to two right angles. We thus connect the two parts of the original proposition, by a number of intermediate equalities; and by that means perceive, that these two parts are equal among themselves; it being an intuitive proposition, as mentioned above, That two things are equal, each of which, in the same respect, is equal to a third. I proceed to a different example, which concerns the relation between cause and effect. The proposition to be demonstrated is, “ That there exists a good and in telligent Being, who is the cause of all the wife and benevolent effects that are produced in the government of this world.” That there are such effects, is in the present example the fundamental proposition'; which is taken for granted, because it is verified by experience. In order to discover the cause of these efiects, I begin with an intuitive proposition mentioned above, “ That every effect adapted to a good end or purpose, proceeds from a designing and benevolent cause.” B b 2 The The next step is, to examine whether man can be the cause : he is provided indeed: with some share of wisdom and benevolence; but the effects mentioned are far above his power, and no less above his wifdom. Neither can this earth be the cause, nor the sun, the moon, the stars ; for, far from being wife and benevolent, they are not even fenfible. If these be excluded, we are unavoidably led to an invisible being, endowed with boundless power, goodness, and intelligence; and that invisible being is termed God. Reasoning requires two mental powers, namely, the power of invention, and the power of perceiving relations. former are discovered intermediate propofitions, equally related to the fundamental proposition and to the conclusion: by the latter we perceive, that the different links which compose the chain of reasoning, are all connected together by the same relation. We can reason about matters of opinion and belief, as well as about matters of knowledge properly fo termed. Henee reafoning is distinguished into two kinds demonstrative, and probable. Demon Irative By the |