xviii The PREFACE.
THUS far, therefore, we fee but little that looks like Activity, even in the Faculty of Reafon. But Reafon has not been yet (hewn in its Height. Tho it have its Origin in phyfical Matters ; and (hew it felf firft in the Efta- blidiment of Caufes, Properties, (St. it reaches much higher, and is feen in its Perfection in Metaphyficks ; where, making its own Productions its Object, it proceeds to examine the Nature and Effence of fucli Caufe, Pro- perty, (Sc. And hence the Doctrine of Quality, Quantity, (St. in the General or Abftract. Nor does the
Matter ftop here ; but the Mind (till proceeds to erect a new and moft magnificent Science of Quantities, Analo- gies, Proportions, (St. hereupon : founded on this Principle, that " fo fir as a thing unknown, agrees or is like " to another tiling known •, fo far is fuch former thing, its Nature, Effects, (St. known :" A Science infinitely extenfive, and productive of infinite Ufes ; as being that whereby Knowledge is applied, or transferr'd from one thing to another : And of infinite Certainty, as being founded on a felf-evident Propofition. It pro- ceeds by Definitions, Axioms, (St. But as the Things themfelves which are its Subject:, are only Abftradts, which are but a kind of Shadows of real and fenfible things -, fo are its Definitions, which cannot be laid to be Definitions in the fame Senfe as thofe of a Concrete, e. g. a Plant, an Inftrument, or the like ; inafmuch as they do not excite any Image or Idea in the Mind. And hence that Difficulty under which the Writers of the Prin- ciples of Mathematicks labour, to give intelligible Definitions of Unity, Multitude, Number, Part, Whole, &c.
ITS Axioms are only Duplicates of fome Propofition, or the fame thing exprefs'd in two manners; the one
direct, the other implicit ; properly call'd Identital Propofitions. Thus that Axiom, " The Whole is equal to its
" Parts ;" eafily refolves into this other, " The Whole has the Nature and Characters of a Whole :" which amounts to this, " A Whole is a Whole."
TO ilhiftrate the Progrefs of the Mind in this new Scene : Suppofe, for inftance, a Ball, or Sphere ; and let it be divided into two Parts.— — Our Senfes do not inform us that the two Segments thereof are equal to the whole one : On the contrary, they reprefent them as very unequal -, and 'tis Reafon alone that finds their Equa- lity. The Caufe hereof, is, that the Figure, (St. of the divided Sphere, which are the things the Eye takes cognizance of, are very different from thofe of the whole one ; and that the Quantity or Subftance, in which alone the Equality confifts, is no Object; of Sight, but only of Reafon ; which informs us that the two Seg- ments are ftill really the whole Sphere, only exiiting with fome variety in refpect of Figure, Place, (St. Hence we find it necefiary, i. e. included in the Nature and Notion of a Whole, that the Sphere be equal to its Parts ; and thus, by analogy, pronounce the fame Ratio univerfally between every Whole and its Parts, and fo make an Axiom which is the Foundation of a new kind of univerfal Knowledge. In effect, to fay that the whole Sphere is equal to its Parts, is no more than to fay, the Quantity or Subftance is not altered by any Alterations made in its Figure, Place, Number, (Sc, which is as much as to fay, that the Subftance is the Subftance, the Sphere, the Sphere.
FROM fuch Axioms it proceeds to Theorems and Problems; every one whereof is refolvable into Thefts and Hypothefis ; each of which may be again refolved into Axioms or identical Propofitions, which is called Demon- ftrating. In fine, all Demonltration fuppofes Identical Propofitions, and turns on 'em; and its Certainty arifes from no other Principle, but the Identity or Samenefs of the Thing implied in fuch Propofitions, with the Thing exprefs'd.
IT appears then, that the whole Procefs confifts in abftracting, or fetting afide the fenfible Idea that gave the firft Occafion, and confidering the Relations thereof by themfelves, as if they had diftinct, independent Exiftences. By thus excluding the Confideration of the phyfical Ens, Senfation and Imagination are of courfe ex- cluded, with all the Action and Infpiration annex'd to 'em ; and thus is Reafon left in full play, without any
thing to fuperfede, or divert it.- Thus we may be faid to make a new World, and furnifti it with a new Set
of Creatures ; and a new Doctrine, which is, as it were, the Shadow of the former. Metaphyficks, and Mathe- maticks, in effect:, are the Science of Enlia humana, or rationis, as Phyfics of Entia natures, or fen/us.
BUT fuch Abftracts, e. g. Quantity, Meafure, Weight, (St. tho no immediate Objects of Senfe, have yet a Connexion with things which have, whereby they become of the utmoft import in the World. There is that Relation eftablifhed between the Faculties of Senfe and Reafon, that tho the Objects of the one be not cogniza- ble by the other, yet the Communication between 'em is by the all-wife Creator made very near and intimate : Such Dimenfions, Weight, (St. are combined by him with fuch Effects, Motions, Refinances, (St. and prove the Occafion of fuch and fuch Effects : which is the great Principle of all human Action, and all truly artificial production in the World.
BY means of this Communication, the firft Impulfe is brought back again from the higheft pitch of abftracted Mathematicks, to the firft Objects of Senfe ; from F'luxions and Differences, the fartheft Parts of the Pais a" infini Reafon has ever travell'd to, to the grofieft and moft palpable Objects that ftrike every Senfe. And thus are Action and Paffion, Senfation and Reafon, Art and Science, found to reciprocate, and produce each other.
HAVING thus difcufs'd the Nature, and Characters of Art and Sciente ; it remains to fettle the Notion of
a TERM cf Art ; a Diction as little underftood as any thing in Language. Art and Science, we have ob-
ferved, are Denominations of Knowledge under this or that Habitude ; and Words are Reprefentatives of the feveral Parts thereof. The whole Compafs of Words, in all their Cafes, is fuppos'd equivalent to the whole Syftem of pofiible Science ; tho 'tis only a fmall Part thereof that is actual, i. e. only a few of the portable Combinations are, or ever will be, made.
THE Bufinefs of Knowledge, then, is canton'd out among the Body of Words: but they don't bear equal Shares thereof. Being Creatures of our own, we have dealt with 'em accordingly ; and made fome more, others lefs fignificant, at pleafure : fome (land for large Tracts, or Provinces ; others for little Spots, or petty Diftricts thereof. In effect, the Order wherein we attain our Knowledge, has occafion'd us to make a kind of Sortment and Package, if I may ufe the Word, in the Matter thereof. Tho the Mind only fees and perceives Individuals, which alone are the proper Objects thereof ; yet it has a Power of combining and complicating thefe together, for its own conveniency : And hence its progrefs from Particulars to Generals ; from Simple,
to Complex. Hence we come to have Words of all Orders, and Degrees ; from the Simplicity of an Atom,
to the Complexnefs of the Univerfe. 'Tis pleafant to trace the Mind bundling up its Ideas, and giving Names to the feveral Parcels ; to obferve, for inftance, how it proceeds from the fimple Idea, Thinking, to the more complex one, Knowledge, thence to the more complex, a Stiente, thence farther to Scientijical, &c.
INDEED 'tis very few of our Words that exprefs fingle, or fimple Ideas. The Reafon is, that obferving certain Relations to obtain between the feveral Ideas ; as, of Caufe and Effect, Subject and Attribute, (Sc. we don't fo much confider them abfblutely and independently, as under fuch Circumftances and Relations to each other. The great Readinefs and Propenfity of the Mind to combine, and bundle up its Ideas, and thus pay, or receive 'em in Parcels, has left us very few fimple ones ; I mean, very few Names which denote only one Idea. The Words Atom, or Mathematital Point, ufually imply feveral Ideas ; in regard we are led to take their Attributes, and Relations, into the Confideration of the Subject : Thus we confider the Atom as hard, heavy, and invifible ; as the Principle of phyfical Magnitude ; as contributing to the Conftitution of Bodies, (St. Even the primary Qualities themfelves, as hardnefs, heaviness, &c. fimple as they are in their own
Nature ;
