First, As to the first sort of agreement or disagreement, viz.  identity or diversity.  It is the first act of the mind, when it has any sentiments or ideas at all, to perceive its ideas; and so far as it perceives them, to know each what it is, and thereby also to perceive their difference, and that one is not another.  This is so absolutely necessary, that without it there could be no knowledge, no reasoning, no imagination, no distinct thoughts at all.  By this the mind clearly and infallibly perceives each idea to agree with itself, and to be what it is; and all distinct ideas to disagree, i. e. the one not to be the other:  and this it does without pains, labour, or deduction; but at first view, by its natural power of perception and distinction.  And though men of art have reduced this into those general rules, what is, is, and it is impossible for the same thing to be and not to be, for ready application in all cases, wherein there may be occasion to reflect on it:  yet it is certain that the first exercise of this faculty is about particular ideas.  A man infallibly knows, as soon as ever he has them in his mind, that the ideas he calls white and round are the very ideas they are; and that they are not other ideas which he calls red or square.  Nor can any maxim or proposition in the world make him know it clearer or surer than he did before, and without any such general rule.  This then is the first agreement or disagreement which the mind perceives in its ideas; which it always perceives at first sight:  and if there ever happen any doubt about it, it will always be found to be about the names, and not the ideas themselves, whose identity and diversity will always be perceived, as soon and clearly as the ideas themselves are; nor can it possibly be otherwise.

5.  Secondly, Of abstract Relations between ideas.

Secondly, the next sort of agreement or disagreement the mind perceives in any of its ideas may, I think, be called relative, and is nothing but the perception of the relation between any two ideas, of what kind soever, whether substances, modes, or any other.  For, since all distinct ideas must eternally be known not to be the same, and so be universally and constantly denied one of another, there could be no room for any positive knowledge at all, if we could not perceive any relation between our ideas, and find out the agreement or disagreement they have one with another, in several ways the mind takes of comparing them.

6.  Thirdly, Of their necessary Co-existence in Substances.