have place but where we make use of terms standing for fuch complex ideas. But our complex ideas, being nothing more than different combinations of fimple ideas, we then know and comprehend them perfectly, when we know the feveral fimple ideas of which they confift, and can fo put them together in our minds, as may be neceffary towards the framing of that peculiar connection, which gives every idea its diftinct and proper appearance,

VII. Two things are therefore required in every definition: firft, That all the original ideas, out of which the complex one is formed, be diftinctly enumerated; and, 2dly, That the order and manner of combining them into, one conception be clearly explained. Where a definition has thefe requifites, nothing is wanting to its perfection; becaufe every one who reads it and understands the terms, feeing at once what ideas he is to join together, and alfo in what manner, can at pleasure form in his own mind the complex conception anfwering to the term defined. Let us, for inftance, fuppofe the word fquare to stand for that idea by which we reprefent to ourselves a figure whofe fides fubtend quadrants of a circumfcribed circle. The parts of this idea are the fides bounding the figure. These must be 4 iu number, and all equal among themselves, because they are each to fub tend a 4th part of the fame circle. But, befides thefe component parts, we muft alfo take notice of the manner of putting them together, if we would exhibit the precife idea for which the word Square here fands. For 4 equal right lines, any. how joined, will not fubtend quadrants of a circumfcribed circle, A figure with this property muft have its fides ftanding alfo at right angles. Taking in therefore this laft confideration refpect. ing the manner of combining the parts, the idea is fully defcribed, and the definition thereby rendered complete. For a figure bounded by 4 equal fides, joined together at right angles, has the pro, perty required; and is moreover the only rightlined figure to which that property belongs.

deed that to which alone we can have recourse, where any doubt or difficulty arifes, It is not, however, neceffary that we mould practise it in every cafe. Many of our ideas are extremely complicated, infomuch that to enumerate all the fimple perceptions out of which they are formed, would be a very troublesome and tedious work. For this reafon logicians have established certain compendious rules of defining, of which we shall give fome account. But for the better underftanding of what follows, it is neceffary to obferve, that there is a certain gradation in the compofition of our ideas. The mind of man is very limited in its views, and cannot take in a great number of objects at once. We must therefore proceed by fteps, and make our firft advances fubfervient to thofe which follow, Thus, in forming our complex notions, we begin at firft with but a few fimple ideas, fuch as we can manage with ease, and unite them together into one conception. When we are provided with a fufficient flock of these, and have by habit and use rendered them familiar to our minds, they become the component parts of other ideas ftill more complicated, and form what we may call a fecond order of compound notions. This procefs may be continued to any degree of compofition we please, mounting from one ftage to another, and enlar ging the number of combinations.

II. But in a series of this kind, whoever would acquaint himself perfectly with the laft and higheft order of ideas, finds it the most expedient method to proceed gradually through all the intermediate fteps. For, were he to take any very compound idea to pieces, and, without regard to the feveral claffes of fimple perceptions that have already been formed into diftinct combinations, break it at once into its original principles, the number would be fo great as perfectly to confound the imagination, and overcome the utmost reach and capacity of the mind. When we fee a prodigious multitude of men jumbled together in crowds, without order or any regular pofition, we find it impoffible to arrive at an exact knowledge of their number. But if they are formed into feparate battalions, and so stationed as to fall within the leifure furvey of the eye; by viewing them fucceffively and in order, we come to an çafy and certain determination. It is the fame in our complex ideas. When the original perceptions, out of which they are framed, are very numerous, it is not enough that we take a view of them in loofe and fcattered bodies; we must form them into diftinct claffes, and unite these claffes in a juft and orderly manner, before we can arrive at a true knowledge of the compound notices, resulting from them.

VIII. It will now be obvious to every one, in what manner we ought to proceed, in order to arrive at juft and adequate definitions. First, we are to take an exact view of the idea to be defcribed, trace it to its original principles, and mark the feveral fimple perceptions that enter into the compofition of it. 2dly, We are to confider the particular manner in which thefe elementary ideas are combined, in order to form that precife conception for which the term we make ufe of ftands. When this is done, and the idea wholly unravelled, we have only to tranfcribe the appearance it makes to our own minds. Such a defcription, by diftinctly exhibiting the order and number of our primitive conceptions, cannot fail. III. This gradual progrefs of the mind to its to excite at the fame time, in the mind of every compound. notions, through a variety of intermeone that reads it, the complex idea refulting from diate fteps, plainly points out the manner of con them; and therefore attains the true and proper ducting the definitions by which thefe notions are end of a definition. conveyed into the minds of others. For as the and advances through a fucceffion of different orferies begins with fimple and eafy combinations, ders, rifing one above another in the degree of compofition, it is evident, that, in a train of definitions expreffing these ideas, a like gradation is to be obferved. Thus the complex ideas of the

SECT. III. Of the COMPOSITION and RESOLU-
TIONS of our IDEAS, and the RULES of DEFI-
NITION thence arifing.

I. THE rule laid down in the laft fection is general, extending to all poffible 'cafes; and is in

loweft

lowest order can no otherwise be defcribed than by enumerating the fimple ideas out of which they are made, and explaining the manner of their union. But then, in the fecond or any other fucceeding order, as they are formed out of thofe gradual combinations, and conftitute the inferior claffes, it is not neceffary, in defcribing them, to mention one by one all the fimple ideas of which they confift. They may be more diftinctly and briefly unfolded, by enumerating the compound ideas of a lower order, from whofe union they refult, and which are all fuppofed to be already known in confequence of previous definitions. Here then it is, that the logical method of defining takes place; which, that it may be the better understood, we fhall explain fomewhat more particularly the several steps and gradations of the mind in compounding its ideas, and thence de duce that peculiar form of a definition which logicians have thought fit to establish.

rywhere bounded. But if we defcend farther, and confider the boundaries of this space, as that they may be either lines or furface, we fall into the feveral fpecies of figure. For where the space is bounded by one or more furfaces, we give it the name of a folid figure; but where the boun. daries are lines, it is called a plain figure.

VI. In this view of things it is evident, that the fpecies is formed by fuperadding a new idea to the genus. Here, for inftance, the genus is circumfcribed fpace. If now to this we fuperadd the idea of a circumfcription by lines, we frame the notion of that species of figures which are called plain; but if we conceive the circumfcription to be by surfaces, we have the fpecies of folid figures. This fuperadded idea is called the specifie difference, not only as it ferves to divide the fpecies from the genus, but because, being different in all the several fubdivifions, we thereby alfo diftinguish the species one from another. And as it is likeIV. All the ideas we receive from the feveral wife that conception, which, by being joined to objects of nature that furround us, reprefent dif- the general idea, completes the notion of the fpetinct individuals. Thefe individuals, when com- cies; hence it is plain, that the genus and specific pared together, are found in certain particulars to difference are to be confidered as the proper and refemble each other. Hence, by collecting the re- constituent parts of the fpecies. If we trace the fembling particulars into one conception, we form progrefs of the mind still farther, and obferve it the notion of a fpecies. And here let it be obfer advancing through the inferior fpecies, we fhall ved, that this laft idea is lefs complicated than find its manner of proceeding to be always the that by which we reprefent any of the particular fame. For every lower fpecies is formed by fuobjects contained under it. For the idea of the peradding fome new idea to the fpecies next fpecies excludes the pecularities of the feveral in- above it; infomuch that in this descending scale of dividuals, and retains only fuch properties as are our perceptions, the understanding paffes through common to them all. Again, by comparing feve different orders of complex notions, which beral fpecies together, and obferving their refem- come more and more complicated at every step it blance, we form the idea of a genus; where, in takes. Let us refume here, for instance, the fpethe fame manner as before, the compofition is lef- cies of plain figures. They imply no more than fened, because we leave out what is particular to space bounded by lines. But if we take in an adthe several species compared, and retain only the ditional confideration of the nature of thefe lines, particulars wherein they agree. It is eafy to con- as whether they are right or curves, we fall into ceive the mind proceeding thus from one ftep to the fubdivifions of plain figure, diftinguished by another, and advancing through its feveral claffes the names of rectilinear, curvilinear, and mixtili of general notions, until at laft it comes to the near. higheft genus of all, denoted by the word being, where the bare idea of existence is only concerned. V. In this procedure we fee the mind unravelling a complex idea, and tracing it in the afcend ing fcale, from greater or lefs degrees of compo. fition, until it terminates in one fimple percep. tion. If now we take the feries the contrary way, and, beginning with the laft or higheft genus, carry our view downwards, through all the inferior genera and fpecies, quite to the individuals, we fhall thereby arrive at a diftinct apprehenfion of the conduct of the understanding in compound ing its ideas. For, in the feveral claffes of our perceptions, the higheft in the scale is for the moft part made up of but a few fimple ideas, fuch as the mind can take in and furvey with eafe. This firft general notion, when branched out into the different fubdivifions contained under it, has in every one of them fomething peculiar, by which they are diftinguifhed among themselves; info. much that, in defcending from the genus to the fpecies, we always fuperadd fome new idea, and thereby increase the degree of compofition. Thus the idea denoted by the word figure is of a very general nature, and compofed of but few fimple perceptions, as implying no more than space eve

VII. And here we must observe, that though plain figures, when confidered as one of thofe branches that come under the notion of figure in general, take the name of a fpecies; yet, compared with the claffes of curvilinear, rectilinear, and mixtilinear, into which they themselves may be divided, they really become a genus of which the before mentioned fubdivifions conftitute the feveral fpecies. These fpecies, in the fame manner as in the cafe of plain and folid figures, confift of the genus and specific difference as their conftituent parts. For in the curvilinear kind, the curvity of the lines bounding the figure makes what is called the specific difference; to which if we join the genus, which here is a plain figure or space circumfcribed by lines, we have all that is necessary towards completing the notion of this fpecies. We are only to take notice, that this laft fubdivifion, having two genera above it, viz. plain figure, and figure in general; the genus joined with the fpecific difference, in order to conftitute the fpecies of curvilinears, is that which lies neareft to the faid fpecies. It is the notion of plain figure, and not of figure in general, that, joined with the idea of curvity, makes up the complex conception of curve-lined figures. For in this defcending scale

of

ledge of this kind respects only our ideas, and the relations between them; and therefore can serve only as a foundation to such reasonings as are employed in investigating those relations. Now it fo happens, that many of our judgments are converfant about facts, and the real existence of things, which cannot be traced by the bare contemplation of our ideas. It does not follow, because I have the idea of a circle in my mind, that therefore a figure answering to that idea has a real exiftence in nature. I can form to myfelf the notion of a centaur or golden mountain, but never imagine on that account that either of them exifts. What then are the grounds of our judgment in relation to facts? EXPERIENCE and TESTIMONY. By experience we are informed of the existence of the feveral objects which furround us, and operate upon our fentes. Teftimony is of a wider extent, and reaches not only to objects beyond the present fphere of our obfervation, but also to facts and tranfactions, which being now paft, and having no longer any exiftence, could not without this conveyance have fallen under our cognizance.

on obfervation, afcribing to bodies fuch qualities as are answerable to the perceptions they excite in us. Not that we ever fuppofe the qualities of bodies to be things of the fame nature with our perceptions; for there is nothing in fire fimilar to our fenfation of heat, or in a sword fimilar to pain: but that when different bodies excite in our minds fimilar perceptions, we neceffarily ascribe to these bodies not only an exiftence independent of us, but likewife fimilar qualities, of which it is the nature to produce fimilar perceptions in the human mind. But this is not the only advantage derived from experience; for to that too we are indebted for all our knowledge regarding the coexiftence of fenfible qualities in objects, and the operations of bodies one upon another. Ivory, for inftance, is hard and elaftic; this we know by experience, and indeed by that alone. For, being altogether strangers to the true nature both of elafticity and hardness, we cannot by the bare contemplation of our ideas determine how far the one neceffarily implies the other, or whether there may not be a repugnance between them. But III. Here we have three foundations of human when we observe them to exift both in the fame judgment, from which the whole fyftem of our object, we are then affured from experience that knowledge may with eafe and advantage be deria they are not incompatible; and when we also ved. First, intuition, which refpects our ideas find, that a ftone is bard and not elastic, and that themselves, and their relations; and is the foun- air though elaftic is not hard, we also conclude upon dation of that species of reasoning which we call the fame foundation, that the ideas are not necefDEMONSTRATION. For whatever is deduced from farily conjoined, but may exift feparately in diffeour intuitive perceptions, by a clear and connect- rent objects. In like manner, with regard to the ed feries of proofs, is faid to be demonftrated, operations of bodies one upon another, it is eviand produces abfolute certainty in the mind. dent, that our knowledge this way is all derived Hence the knowledge obtained in this manner is from obfervation. AQUA REGIA diffolves gold, what we properly term SCIENCE; because in eve- as has been found by frequent trial, nor is there ry step of the procedure it carries its own evidence any other way of arriving at the difcovery. Naalong with it, and leaves no room for doubt or he- turalifts may tell us, if they please, that the parts fitation. And it is highly worthy of notice, that of aqua regia are of a texture apt to infinuate beas the truths of this class express the relation between the corpuscles of gold, and thereby loofen tween our ideas, and the fame relations must ever and invariably fubfift, between the fame ideas, our deductions in the way of fcience conftitute what we call ETERNAL, NECESSARY, and IMMUTABLE TRUTHS. If it be true that the whole is equal to all its parts, it must be fo unchangeably; because the relation of equality being attached to the ideas themfelves, muft ever intervene where the fame ideas are compared. Of this nature are all the truths of natural religion, morality and mathematics, and in general whatever may be gathered from the bare view and confideration of our ideas. IV. The 2d ground of human judgment is ExPERIENCE; from which we infer the existence of thofe objects which furround us, and fall under the immediate notice of our fenfes. When we fee the fun, or caft our eyes towards a building, we not only have perceptions of thefe objects within ourfelves, but afcribe to them a real existence out of the mind. It is alfo by the information of the fenfes that we judge of the qualities of bodies; as when we fay that SNOW is white, FIRE bot, STEEL hard. For, as we are wholly unacquainted with the internal ftructure and conftitution of the bodies that produce these sensations in us, nay, are unable to trace any connection between that ftructure and the fenfations themfelves, it is evident, that we build our judgments altogether up.

and shake them afunder. If this is a true account of the matter, it will notwithstanding be allowed, that our conjecture in regard to the conformation of thefe bodies is deduced from the experiment, and not the experiment from the conjecture. It was not from any previous knowledge of the intimate ftructure of aqua regia and gold, and the aptnefs of their parts to act or be acted upon, that we came by the conclufion abovementioned. The internal conftitution of bodies is in a manner wholly unknown to us; and could we even furmount this difficulty, yet as the feparation of the parts of gold implies fomething like an active force in the menftruum, and we are unable to conceive how it comes to be poffeffed of this activity, the effect must be owned to be altogether beyond our comprehenfion. But when repeated trials had once confirmed it, infomuch that it was admitted as an established truth in natural knowledge, it was then eafy for men to spin out theories of their own invention, and contrive fuch a ftructure of parts, both for gold and aqua regia, as would best serve to explain the phenomenon upon the principles of that fyftem of philofophy they had adopted.

V. From what has been said, it is evident, that as intuition is the foundation of what we call fcientifical knowledge, fo is experience of natural. For this laft being wholly taken up with objects of

fenfe,