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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 any of our fenfes.

The knowledge that is derived from the fources mentioned, is of different kinds. In fome cafes, our knowledge includes abfolute 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. Τα explain what is here faid, I enter into particulars.

The fenfe of feeing, with very few exceptions, affords knowledge properly fo termed:



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 fenfe of feeing, as fome writers pretend to do. No one ever called in queftion 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 instances, is faithful to truth; for it is evident, that we cannot be fo certain of the existence


of an object in its abfence, as when prefent.

With refpect to many abstract 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*


* I have given this propofition a place, because 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 Gimplicity, which undoubtedly is natural, renders fimple operations more agreeable than what are complex, and confequently makes them appear more natural. It deBb 2 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 fenfe 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 procefs or operation in the mind, termed reafoning; leading, by certain intermediate fteps, to the propofition that is to be demonstrated 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 reafoning. And as reafoning is moftly employ'd in difcovering relations, I fhall draw my examples from them. very 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.


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 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 laft ftep of the procefs is termed a conclufion, being the last or concluding perception.

No other reafoning affords fo clear a notion of the foregoing procefs, 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 science belong a number of intuitive propofitions, termed axioms, which are


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