not another without which there could be no. knowledge. This is done without labour or deduction, by the natural power of perception and distinction. The first exercise of this faculty is about particular ideas; and no rule can make us more certain that the ideas we call by one name are not those called by another. Whenever any doubts happen, they will be found to be about the identity of the names, and not of the ideas.

The next sort of agreement may be called Relative and is the perception of the relation between any two ideas, when they are compared for the sake of finding out whether they agree or not.

The third sort of agreement or disagreement concerns the Co-existence of qualities in the same subjects; and this belongs particularly to substances. Thus when we pronouncegold to be fixed; we only know that fixedness, or a ower to remain in the power fire unconsumed, is an ide, always accompanying a particular set of properties which constitute our idea of gold.

The last kind is the of Real Existence agreeing with any idea; or its laving a being out of the mind.

All then that we can know of any idea is-whether it is distinct;-whether it always coexists with some other idea in the same subject; whether it has this or that relation to some other idea;-and whether it has a real existence without the mind.

Thus; blue is not yellow, is of identity; two triangles upon equal bases between two parallels are equal, is of relation; iron is susceptible of magnetical impressions, is of coexistence; God is, is of real existence.

Though identity and coexistence are truly nothing but relations, yet they are so peculiar as to deserve distinct consideration.

There are two kinds of knowledge, actual and habitual.

The first is the present view the mind has of the agreement or disagreement of its ideas, or of their relation to one another.

The last is the certainty of the truth of a proposition, from a recollection of the perception we formerly had of the agreement or disagreement of the ideas it consists of.

There are two degrees of habitual knowledge: the one is of those truths where we have an intuitive knowledge of the relation between the ideas; the other of those, where we recollect our conviction, without remembering the proofs. In this case a man may seem rather to believe his memory, than to know; and it once seemed to me a sort of assurance between opinion and knowledge; but I find it comes not short of perfect certainty. The agreement or disagreement of two ideas in a proposition is in this case perceived by the intervention of other

ideas than those which first produced our perception of the truth or falsehood of the proposition: for instance, a person remembers, that is, he knows (for remembrance is but the reviving of some past knowledge) that he was once certain of the truth of the proposition: " that the three angles of a triangle are equal to two right ones;" and the intervening idea, by which he now knows this, is the immutability of the same relations between the same immutable things: hence what he once knew to be true, he will always know to be so, as long as he can remember that he once knew it. It is upon this ground, viz. our perception that the same ideas will eternally have the same habitudes and relations, that particular demonstrations in mathematics afford us general knowledge. As the memory however is not always so clear as actual perception, and decays more or less in all men through length of time, this, among other differences, shews us that demonstrative knowledge is much less perfect than intuitive.

CHAP. II.

OF THE DEGREES OF OUR KNOWLEDGE.

THE different clearness of our knowledge seems to me to lie in the different ways by which the mind perceives the agreement or disagreement of any of its ideas. Sometimes we perceive the agreement or disagreement of two ideas without the intervention of a third: and this we call Intuitive Knowledge : because here the Truth is perceived by bare Intuition, without the pains of examination and proof; thus, we perceive that a circle is not a triungle, that three are more than two, and equal to two and one. All the certainty of our knowledge depends on this Intuition; and there can be no greater: in so much, that in the next degree of knowledge, which I call demonstrative, this intuition in all the connexions of the intermediate ideas is necessary to attain certainty.

We cannot always by immediate comparison or juxta-position, discover the agreement or disagreement of two ideas; but perhaps remain completely ignorant, or can get no farther than probable conjecture: the mind then by the intervention of other ideas seeks to discover this agreement; and this

process is called Reasoning, and the knowledge we attain demonstrative knowledge. Thus, the mind cannot immediately perceive whether the three angles of a triangle agree with two right ones: it endeavours then to discover some other angles which shall agree with the three angles, and with two right ones, and by these intervening ideas it perceives that the three angles of a triangle and two right angles do exactly agree. These intervening ideas are called proofs, and a quickness in discovering and applying them is called Sagacity.

Though this knowledge be certain, its evidence is not so clear, nor our assent to it so ready, as in Intuitive knowledge.

In Demonstrative Knowledge there is a great abatement of that full assurance which accompanies intuitive knowledge; like a face reflected by several mirrors, where, as long as the similitude is preserved there is knowledge, but with a greater degree of dimness in every successive reflection, till its agreement with the object is not at first sight so knowable.

Each step in a chain of reasoning must have intuitive evidence, and be remembered, in order to make our knowledge certain: but as in long deductions the memory cannot always retain the proofs, this knowledge is less perfect than intuitive, and men often embrace falshood for demonstration. I imagine that the necessity of this intuition in every step of a demonstration gave rise to the axiom "that all