termed: it is not in our power to doubt of the existence of a perfon we fee, touch, and converfe with. When fuch is our conftitution, it is a vain attempt to call in queftion the authority of our sense of feeing, as fome writers pretend to do. No one ever called in question the existence of internal actions and paffions, laid open to us by internal fenfe; and there is as little ground for doubting of what we fee. The fenfe of feeing, it is true, is not always correct: through different mediums the fame object is feen differently: to a jaundic'd eye every thing appears yellow; and to one intoxicated with liquor, two candles fometimes appear four. But we are never left without a remedy in fuch a cafe: it is the province of the reafoning faculty, to correct every error of that kind. An object of fight recalled to mind by the power of memory, is termed an idea or fecondary perception. An original perception, as faid above, affords knowledge in its proper fenfe; but a fecondary perception affords belief only. And Nature in this, as in all other inftances, is faithful to truth; for it is evident, that we cannot cannot be fo certain of the existence of an object in its abfence, as when present. With refpect to many abftract propofitions, of which inftances are above given, we have an abfolute certainty and conviction of their truth, derived to us from various fenfes. We can, for example, entertain as little doubt that every thing which begins to exist must have a caufe, as that the fun is in the firmament; and as little doubt that he will rife to-morrow, as that he is now fet. There are many other propofitions, the truth of which is probable only, not abfolutely certain; as, for example, that winter will be cold and fummer warm. That natural operations are performed in the fimpleft manner, is an axiom of natural philofophy: it may be probable, but is far from being certain *. In * I have given this propofition a place, becaufe it is affumed as an axiom by all writers on natural philofophy. And yet there appears fome room for doubting, whether our conviction of it do not proceed from a bias in our nature, rather than from an original fenfe. Our tafte for fimplicity, which undoubtedly is natural, renders fimple operations more agreeable than what are complex, and confequently makes them appear more natural. It de ferves : In every one of the inftances given, conviction arifes from a fingle 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 demonftrated or made evident; which, in oppofition to intuitive knowledge, is termed difcurfive knowledge. This procefs or operation must be explained, in order to understand the nature of reasoning. And as reafoning is mostly employ'd in discovering 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 misled by our tafte for fimplicity to be of that opinion. 2 for for a third fubject, intuitively connected with each of the others by the relation affirmed and if fuch a fubject be found, the propofition is demonstrated; 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 laft ftep of the process is termed a conclufion, being the laft or concluding percep tion. No other reafoning 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 afcertained. To that fcience belong a number of intuitive propofitions, termed axioms, which VOL. III. B b are are 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 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 fhortly 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 refpe&, equal to a third, thẹ one is equal to the other in the fame respect. 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 demonflrate that truth, it is neceflary to fearch for fome other angles that intuitively are equal to both. If this property cannot be difcovered in any one fet of angles, we muft go more leifurely to work, and try to find angles that are equal to the three angles of a triangle. Thefe being difcovered, we next try to find other angles equal to the angles now difco |