reasoning is neceffary, of which afterward.

Human teftimony is another source of knowledge. So framed we are by nature, as to rely on human teftimony; by which we are informed of beings, attributes, and events, that never came under of our

fenfes.

any

The knowledge that is derived from the fources mentioned, is of different kinds. In fome cafes, our knowledge includes abfölute certainty, and produces the highest degree of conviction: in other cafes, probability comes in place of certainty, and the conviction is inferior in degree. Knowledge of the latter kind is diftinguished into belief, which concerns facts; and opinion, which concerns relations, and other things that fall not under the denomination of facts. In contradiftinction to opinion and belief, that fort of knowledge which includes abfolute certainty, and produces the highest degree of conviction, retains its proper name. Το explain what is here faid, I enter into particulars.

The sense of seeing, with very few exceptions, affords knowledge properly fo

VOL. III.

Bb

termed;

In every one of the inftances given, conviction arifes from a single act of perception: for which reafon, knowledge acquired by means of that perception, not only knowledge in its proper fense but alfo opinion and belief, are termed intuitive knowledge. But there are many things, the knowledge of which is not obtained with fo much facility. Propofitions for the most part require a process or operation in the mind, termed reafoning; leading, by certain intermediate steps, to the propofition that is to be demonstrated or made evident; which, in oppofition to intuitive knowledge, is termed difcurfive knowledge. This process or operation must be explained, in order to understand the nature of reasoning. And as reasoning is moftly employ'd in difcovering relations, I fhall draw my examples from them. Every propofition concerning relations, is an affirmation of a certain relation between two fubjects. If the relation affirmed appear not intuitively, we must search

ferves a moft ferious difcuffion, whether the operations of nature be always carried on with the greateft fimplicity, or whether we be not mifled by our tafte for fimplicity to be of that opinion.

fcr

for a third fubject, intuitively connected with each of the others by the relation affirmed and if such a subject be found, the propofition is demonftrated; for it is intuitively certain, that two fubjects connected with a third by any particular relation, must be connected together by the fame relation. The longest chain of reafoning may be linked together in this manner. Running over fuch a chain, every one of the fubjects must appear intuitively to be connected with that immediately preceding, and with that immediately fubfequent, by the relation affirmed in the propofition; and from the whole united, the propofition, as above mentioned, must appear intuitively certain. The last step of the process is termed a conclufion, being the laft 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 comparifon therefore is the only means by which mathematical propofitions are ascertained. To that science belong a number of intuitive propofitions, termed axioms, which are

all

all founded on equality. For example: Divide two equal lines, each of them, into a thousand equal parts, a fingle part of the one line must be equal to a fingle 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 expreffed thus: From two equal lines take equal parts, and the remainders will be equal; or add equal parts, and the fums will be equal. Third: If two things be, in the fame refpect, equal to a third, the one is equal to the other in the fame refpect. I proceed to fhow the use of these axioms. Two things may be equal without being intuitively fo; which is the cafe of the equality between the three angles of a triangle and two right angles. To demonftrate that truth, it is neceffary to fearch for fome other angles that intuitively are equal to both. If this property cannot be discovered in any one fet of angles, we must go more leifurely to work, and try to find angles that are equal to the three angles of a triangle. These being difcovered, we next try to find other angles equal to the angles now difco

vered; and fo on in the comparison, till at last we discover a fet of angles, equal not only to those thus introduced, but alfo to two right angles. We thus connect the two parts of the original propofition, by a number of intermediate equalities; and by that means perceive, that these two parts are equal among themselves; it being an intuitive propofition, as mentioned above, That two things are equal, each of which, in the fame refpect, is equal to a third.

I proceed to a different example, which concerns the relation between cause and effect. The propofition to be demonstrated is, "That there exifts 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 fuch effects, is in the prefent example the fundamental propofition; which is taken for granted, because it is verified by experience. In order to discover the cause of these effects, I begin with an intuitive propofition mentioned above," That every effect adapted

to a good end or purpose, proceeds "from a defigning and benevolent cause,'

99

The