for want of tracing those ideas which we have, or may have, and for want of finding out those intermediate ideas, which may show us what habitude of agreement or disagreement they have one with another. And thus many are ignorant of mathematical truths, not out of any imperfection of their faculties, or uncertainty in the things themselves, but for want of application in acquiring, examining, and by due ways comparing those ideas. That which has most contributed to hinder the due tracing of our ideas, and finding out their relations, and agreements or disagreements one with another, has been, I suppose, the ill use of words. It is impossible that men should ever truly seek, or certainly discover, the agreement or disagreement of ideas themselves, whilst their thoughts flutter about, or stick only in, sounds of doubtful and uncertain significations. Mathematicians abstracting their thoughts from names, and accustoming themselves to set before their minds the ideas themselves that they would consider, and not sounds instead of them, have avoided thereby a great part of that perplexity, puddering, and confusion, which has so much hindred men's progress in other parts of knowledge. For whilst they stick in words of undetermined and uncertain signification, they are unable to distinguish true from false, certain from probable, consistent from inconsistent, in their own opinions. This having been the fate or misfortune of a great part of men of letters, the increase brought into the stock of real knowledge, has been very little, in proportion to the schools, disputes, and writings, the world has been filled with; whilst students, being lost in the great wood of words, knew not whereabouts they were, how far their discoveries were advanced, or what was wanting in their own, or the general stock of knowledge. Had men, in the discoveries of the material, done as they have in those of the intellectual, world, involved in all the obscurity of uncertain and doubtful ways of talking, volumes writ of navigation and voyages, theories and stories, of zones and tides, multiplied and disputed; nay, ships built, and fleets sent out, would never have taught us the way beyond the line; and the antipodes would be still as much unknown, as when it was declared heresy to hold there were any. But having spoken sufficiently of words, and the ill or careless use that is commonly made of them, I shall not say any thing more of it here.

§. 31. Extent in respect of universality.-Hitherto we have examined the extent of our knowledge, in respect of the several sorts of beings that are. There is another extent of it, in respect of universality, which will also deserve to be considered; and in this regard, our knowledge follows the nature of our

ideas. If the ideas are abstract, whose agreement or disagreement we perceive, our knowledge is universal. For what is known of such general ideas, will be true of every particular thing, in whom that essence, i. e. that abstract idea, is to be found; and what is once known of such ideas, will be perpetually and for ever true. So that as to all general knowledge, we must search and find it only in our minds; and it is only the examining of our own ideas, that furnisheth us with that. Truths belonging to essences of things (that is, to abstract ideas), are eternal, and are to be found out by the contemplation only of those essences: as the existences of things is to be known only from experience. But having more to say of this in the chapters where I shall speak of general and real knowledge, this may here suffice as to the universality of our knowledge in general.

CHAPTER IV.

OF THE REALITY OF KNOWLEDGE.

§. 1. Objection. Knowledge placed in ideas, may be all bare vision. I doubt not but my reader by this time may be apt to think, that I have been all this while only building a castle in the air; and be ready to say to me, "To what purpose all this stir? Knowledge, say you, is only the perception of the agreement or disagreement of our own ideas: but who knows what those ideas may be? Is there any thing so extravagant, as the imaginations of men's brains? Where is the head that has no chimeras in it? Or, if there be a sober and a wise man, what difference will there be, by your rules, between his knowledge, and that of the most extravagant fancy in the world? They both have their ideas, and perceive their agreement and disagreement one with another. If there be any difference between them, the advantage will be on the warm-headed man's side, as having the more ideas, and the more lively. And so, by your rules, he will be the more knowing. If it be true, that all knowledge lies only in the perception of the agreement or disagreement of our own ideas, the visions of an enthusiast, and the reasonings of a sober man, will be equally certain. It is no matter how things are; so a man observe but the agreement of his own imaginations, and talk conformably, it is all truth, all certainty. Such castles in the air, will be as strong holds of truth, as the demonstrations of Euclid. That an harpy is not a centaur, is by this way as certain knowledge, and as much a truth, as that a square is not a circle..

imaginations, to a man that enquires after the reality of things? It matters not what men's fancies are, it is the knowledge of things that is only to be prized; it is this alone gives a value to our reasonings, and preference to one man's knowledge over another's, that it is of things as they really are, and not of dreams and fancies."

§. 2. Answer, not so, where ideas agree with things.-To which I answer, that if our knowledge of our ideas terminate in them, and reach no farther, where there is something farther intended, our most serious thoughts will be of little more use, than the reveries of a crazy brain; and the truths built thereon, of no more weight, than the discourse of a man, who sees things clearly in a dream, and with great assurance utters them. But I hope, before I have done, to make it evident, that this way of certainty, by the knowledge of our own ideas, goes a little farther than bare imagination: and I believe it will appear, that all the certainty of general truths a man has, lies in nothing else. §. 3. It is evident, the mind knows not things immediately, but only by the intervention of the ideas it has of them. Our knowledge therefore is real, only so far as there is a conformity between our ideas and the reality of things. But what shall be here the criterion? How shall the mind, when it perceives nothing but its own ideas, know that they agree with things themselves? This, though it seems not to want difficulty, yet I think there be two sorts of ideas, that, we may be assured, agree with things.

§. 4. As, first, all simple ideas do.-First, The first are simple ideas, which since the mind, as has been shown, can by no means make to itself, must necessarily be the product of things operating on the mind in a natural way, and producing therein those perceptions which, by the wisdom and will of our Maker, they are ordained and adapted to. From whence it follows, that simple ideas are not fictions of our fancies, but the natural and regular productions of things without us, really operating upon us; and so carry with them all the conformity which is intended, or which our state requires; for they represent to us things under those appearances which they are fitted to produce in us; whereby we are enabled to distinguish the sorts of particular substances, to discern the states they are in, and so to take them for our necessities, and to apply them to our uses. Thus the idea of whiteness or bitterness, as it is in the mind, exactly answering that power which is in any body to produce it there, has all the real conformity it can, or ought to, have, with things without us. And this conformity between our simple ideas, and the existence of things, is sufficient for real knowledge.

§. 5. Secondly, all complex ideas, except of substances.Secondly, All our complex ideas, except those of substances, being archetypes of the mind's own making, not intended to be the copies of any thing, nor referred to the existence of any thing as to their originals, cannot want any conformity necessary to real knowledge. For that which is not designed to represent any thing but itself, can never be capable of a wrong representation, nor mislead us from the true apprehension of any thing, by its dislikeness to it: and such, excepting those of substances, are all our complex ideas. Which, as I have shown in another place, are combinations of ideas, which the mind, by its free choice, puts together, without considering any connexion they have in nature. And hence it is, that in all these sorts the ideas themselves are considered as the archetypes, and things no otherwise regarded, but as they are conformable to them. So that we cannot but be infallibly certain, that all the knowledge we attain concerning these ideas, is real, and reaches things themselves. Because in all our thoughts, reasonings, and discourses of this kind, we intend things no farther, than as they are conformable to our ideas. So that in these, we cannot miss of a certain and undoubted reality.

§. 6. Hence the reality of mathematical knowledge.-I doubt. not but it will be easily granted, that the knowledge we have of mathematical truths, is not only certain, but real, knowledge; and not the bare empty vision of vain insignificant chimeras of the brain; and yet, if we will consider, we shall find that it is only of our own ideas. The mathematician considers the truth and properties belonging to a rectangle or circle, only as they are in idea in his own mind. For it is possible he never found either of them existing mathematically, i. e. precisely true, in his life. But yet the knowledge he has of any truths or properties belonging to a circle, or any other mathematical figure, are nevertheless true and certain, even of real things existing because real things are no farther concerned, nor intended to be meant by any such propositions, than as things really agree to those archetypes in his mind. Is it true of the idea of a triangle, that its three angles are equal to two right ones? It is true also of a triangle, wherever it really exists. Whatever other figure exists, that is not exactly answerable to the idea of a triangle in his mind, is not at all concerned in that proposition. And therefore he is certain all his knowledge concerning such ideas, is real knowledge: because intending things no farther than they agree with those his ideas, he is sure what he knows concerning those figures, when they have barely an ideal existence in his mind, will hold true of them also, when they have a real existence in matter; his consideration being barely of those figures,

§. 7. And of moral.—And hence it follows, that moral knowledge is as capable of real certainty, as mathematics. For certainty being but the perception of the agreement or disagreement of our ideas; and demonstration nothing but the perception of such agreement, by the intervention of other ideas, or mediums, our moral ideas, as well as mathematical, being archetypes themselves, and so adequate and complete ideas; all the agreement or disagreement which we shall find in them, will produce real knowledge, as well as in mathematical figures.

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§. 8. Existence not required to make it real.-For the attaining of knowledge and certainty, it is requisite that we have determined ideas and to make our knowledge real, it is requisite that the ideas answer their archetypes. Nor let it be wondered, that I place the certainty of our knowledge in the consideration of our ideas, with so little care and regard (as it may seem) to the real existence of things: since most of those discourses, which take up the thoughts, and engage the disputes, of those who pretend to make it their business to enquire after truth and certainty, will, I presume, upon examination, be found to be general propositions, and notions in which existence is not at all concerned. All the discourses of the mathematicians, about the squaring of a circle, conic sections, or any other part of mathematics, concern not the existence of any of these figures, but their demonstrations, which depend on their ideas, are the same, whether there be any square or circle existing in the world, or no. In the same manner, the truth and certainty of moral discourses abstracts from the lives of men, and the existence of those virtues in the world whereof they treat: nor are Tully's Offices less true, because there is nobody in the world that' exactly practises his rules, and lives up to that pattern of a virtuous man, which he has given us, and which existed no where, when he writ, but in idea. If it be true in speculation, i. e. in idea, that murder deserves death, it will also be true in reality of any action that exists conformable to that idea of murder. As for other actions, the truth of that proposition concerns them not. And thus it is of all other species of things, which have no other essences, but those ideas which are in the minds of men.

§. 9. Nor will it be less true or certain, because moral ideas are of our own making and naming.-But it will here be said, that if moral knowledge be placed in the contemplation of our own moral ideas, and those, as other modes, be of our own making, what strange notions will there be of justice and temperance? What confusion of virtues and vices, if every one may make what ideas of them he pleases? no confusion nor disorder in the things themselves, nor in the reasonings about them; no more than (in