apprehenfion of any thing, by its diflikeness to it; and fuch, excepting thofe of fubftances, are all our complex ideas; which, as I have showed in another place, are combinations of ideas which the mind by its free choice puts together, without confidering any connec tion they have in nature. And hence it is, that in all these forts the ideas themselves are confidered 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; becaufe in all our thoughts, rea fonings and discourses of this kind, we intend things no farther than as they are conformable to our ideas; fo that in these we cannot mifs of a certain and undoubted reality. : 6. Hence the Reality of Mathematical Knowledge. I DOUBT not but it will be eafily granted, that the knowledge we have of mathematical truths, is not only certain, but real knowledge, and not the bare empty vifion of vain infignificant chimeras of the brain and yet, if we will confider, we shall find that it is only of our own ideas. The mathematician confiders the truth and properties belonging to a rectangle or circle, only as they are in idea in his own mind; for it is poffible he never found either of them existing mathematically, i. e. precifely 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 exifting; because real things are no farther concerned, nor intended to be meant by any fuch propofitions, 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 alfo of a triangle, wherever it really exifts. Whatever other figure exifts, that is not exactly anfwerable to that idea of a triangle in his mind, is not at all concerned in that propofition; and therefore he is certain all his knowledge concerning fuch ideas, is real knowledge; because intending things no farther than they agree with thofe his ideas, he is fure what he knows concerning thofe figures, when they have barely an ideal exiftence in his mind, will hold true of them also, when they have a real existence in matter; his confideration being barely of thofe figures, which are the fame, wherever or however they exift. $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 difagreement of our ideas, and demonftration nothing but the perception of fuch agreement, by the intervention of other ideas or mediums, our moral ideas, as well as mathematical, being archetypes themfelves, and fo adequate and complete ideas, all the agreement or difagreement which we shall find in them, will produce real knowledge, as well as in mathematical figures. $ 8. Existence not required to make it real. FOR the attaining of knowledge and certainty, it is requifite that we have determined ideas; and to make our knowledge real, it is requifite that the ideas anfwer their archetypes. Nor let it be wondered, that I place the certainty of our knowledge in the confideration of our ideas, with fo little care and regard (as it may feem) to the real exiftence of things; fince moft of thofe difcourfes, which take up the thoughts, and engage the difputes of thofe who pretend to make it their business to inquire after truth and certainty, will, I prefume, upon examination, be found to be general propofitions and notions in which exiftence is not at all concerned. All the difcourfes of the mathematicians about the fquaring of a circle, conic fections, or any other part of mathematics, concern not the exiflence of any of thofe figures; but their demonftrations, which depend on their ideas, are the fame, whether there be any fquare or circle exifting in the world or no. In the fame manner, the truth and certainty of moral difcourfes abftracts from the lives of men, and the existence of those virtues in the world whereof they treat. Nor are Tully's Offices lefs 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 exifted no where, when he writ, but in idea. If it be true in fpeculation, i. e. in idea, that murder deferves death, it will also be true in reality of any action that ifts conformable to that idea of murder. As for other actions, the truth of that propofition concerns them not. And thus it is of all other fpecies of things, which have no other effence but thofe ideas which are in the minds of men. 9. Nor will it be lefs true or certain, because mo ral Ideas are of our own making and naming. But it will here be faid, that if moral knowledge be placed in the contemplation of our own moral ideas, and thofe, as other modes, be of our own making, what strange notions will there be of justice and temperance? What confufion of virtues and vices, if every one may make what ideas of them he pleases? No confufion nor diforder in the things themfelves, nor the reasonings about them; no more than (in mathematics) there would be a disturbance in the demonftration, or a change in the properties of figures, and their relations one to another, if a man should make a triangle with four corners, or a trapezium with four right angles; that is, in plain English, change the names of the figures, and call that by one name, which mathematicians call ordinarily by another. For let a man make to himself the idea of a figure with three angles, whereof one is a right one, and call it, if he pleafe, equilaterum or trapezium, or any thing elfe, the properties of, and demonftrations about that idea will be the fame, as if he called it a rectangular triangle. I confefs, the change of the name, by the impropriety of fpeech, will at firft disturb him, who knows not what idea it lands for; but as foon as the figure is drawn, the confequences and demonftration are plain and clear. Juft the fame is it in moral knowledge, let a man have the idea of taking from others, without their confent, what their honeft induftry has poffeffed them of, and eall this juftice, if he please. He that takes the name here without the idea put to it will be mistaken, by joining another idea of his own to that name; but ftrip the idea of that name, or take it fuch as it is in the speaker's mind, and the fame things will agree to it, as if you called it injuftice. Indeed wrong names in moral discourses breed ufually more disorder, because they are not fo eafily rectified as in mathematics, where the figure once drawn and feen, makes the name useless and of no force; for what need of a fign, when the thing fignified is present and in view? But in moral names, that cannot be so easily and fhortly done, because of the many decompofitions that go to the making up the complex ideas of those modes. But yet for all this, mifcalling of any of thofe ideas, contrary to the ufual fignification of the words of that language, hinders not but that we may have certain. and demonftrative knowledge of their feveral agreements and difagreements, if we will carefully, as in mathematics, keep to the fame precife ideas, and trace them in their feveral relations one to another, without being led away by their names. If we but feparate the idea under confideration from the fign that ftands for it, our knowledge goes equally on in the difcovery of real truth and certainty, whatever founds we make use of. § 10. Mifnaming disturbs not the Certainty of the Knowledge. ONE thing more we are to take notice of, that where God, or any other law-maker hath defined any moral names, there they have made the effence of that species to which that name belongs; and there it is not fafe to apply or use them otherwife; but in other cafes, it is bare impropriety of fpeech to apply them contrary to the common ufage of the country. But yet even this too disturbs not the certainty of that knowledge, which is ftill to be had by a due contemplation, and comparing of those even nick-named ideas. VOL. III. C 11. Ideas of Subftances have their Archetypes without us. THIRDLY, There is another fort of complex ideas, which being referred to archetypes without us, may differ from them, and fo our knowledge about them may come short of being real. Such are our ideas of fubftances, which confifting of a collection of fimple ideas, fuppofed taken from the works of nature, may yet vary from them by having more or different ideas united in them, than are to be found united in things themselves; from whence it comes to pafs, that they may, and often do fail of being exactly conformable to things themselves. 12. So far as they agree with those, fo far our Knowledge concerning them is real. I SAY then, that to have ideas of fubftances, which, by being conformable to things, may afford us real knowledge, it is not enough, as in modes, to put together fuch ideas as have no inconfiftence, though they did never before fo exift; v. g. the ideas of facrilege or perjury, &c. were as real and true ideas before, as after the existence of any fuch fact. But our ideas of fubftances being fuppofed copies, and referred to archetypes without us, muft till be taken from fomething that does or has exifted; they must not confift of ideas put together at the pleasure of our thoughts, without any real pattern they were taken from, though we can perceive no inconfiftence in fuch a combination. The reafon whereof is, becaufe we, knowing not what real conftitution it is of fubftances whereon our fimple ideas depend, and which really is the caufe of the ftrict union of fome of them one with another, and the exclufion of others; there are very few of them that we can be fure are or are not inconfiftent in nature, any farther than experience and fenfible obfervation reach. Herein therefore is founded the reality of our knowledge concerning fubftances, that all our complex ideas of them must be fuch, and fuch only, as are made up of fuch fimple ones as have been difcovered to coexist in nature. And our ideas being thus true, |