Reaforing in the righift Exerce of it enly a Concatenation of Syllogifins. IX. WE fee therefore, that in order to infer a Conclufion by a fingle Act of Reafoning, the Premiffes must be intuitive Propofitions. Where they are not, previous Syllogifms are required, in which Cafe Reafoning becomes a complicated Act, taking in a Variety of fucceffive Steps. This frequently happens in tracing the more remote Relation of our Ideas, where many middle Terms being called in, the Conclufion cannot be made out, but in confequence of a Series of Syllogifms following one another in Train. But although in this Concatenation of Propofitions, thofe that form the 'remiffes of the laft Syllogifm, are often confiderably removed from Self-evidence; yet if we trace the Reafoning backwards, we fhall find them the Conclufions of previous Syllogifms, whofe Premiffes approach nearer and nearer to Intuition, in proportion as we advance, and are found at laft to terminate in it. And if, after having thus unravelled a Demonstration, we take it the contrary Way; and obferve how the Mind fetting out with intuitive Perceptions, couples them together to form a Conclufion, how by introducing this Conclufion into another Syllogifm, it ftill advances one Step farther; and fo proceeds, making every new Difcovery fubfervient to its future Progrefs; we fhall then perceive clearly, that Reasoning in the highest Exercife of that Faculty is no more than an orderly Combination of thofe fimple Acts, which we have already fo fully explained. The great Art lies, in fo adjufting our Syllogiíms one to another, that the Propofitious feverally made ufe of as Premiffes, may be manifeft Confequences of what goes before. For as by this Means, every Conclufion is deduced from known and established Truths, the very laft in the Series, how far foever we carry it, will have no lefs Certainty attending it, than the original intuitive Perceptions themselves, in which the whole Chain of Syllogifms takes its Rife. Requires intuitive Cer. tatty in every Step of be Progref fi.n. X. THUS we fee, that Reasoning beginning with firft Principles, rifes gradually from one Judgment to another, and connects them in fuch manner, that every Stage of the Progreffion brings intuitive Certainty along with it. And now at length we may clearly understand the Definition given above of this diftinguishing Faculty of the human Mind. Reafon we have faid is the Ability of deducing unknown Truths, from Principles or Propofitions that are already known. This evidently appears by the foregoing Account, where we fee, that no Propofition is admitted into a Syllogifm, to ferve as one of the previous Judgments on which the Conclufion refts, unless it is itself a known and established Truth, whofe Connection with felf-evident Principles has been already traced Self-evident Turbs, the ultimate Foundation of ail Science and Certain y XI. THERE is yet another Obfervation which naturally offers itself, in confequence of the above Detail; viz. that all the Knowledge acquired by Reafoning, how far foever we carry our Difcoveries, is ftill built upon our intuitive Perceptions. Towards the End of the laft Part we divided Propofitions into felf-evident and demonftrable, and reprefented those of the felf-evident kind, as the Foundation on which the whole Superftructure of human Science refted. This Doctrine is now abundantly confirmed by what has been delivered in the prefent Chapter. We have found that every Difcovery of human Reafon is the Confequence of a Train of Syllogifms, which when traced to their Source, always terminate in fefevident Perceptions. When the Mind arrives at these primitive Truths, it purfues not its Enquiries farther, as well knowing, that no Evidence can exceed that which flows from an • immediate View of the Agreement or Difagreement between its Ideas. And hence it is, that in unravelling any Part of Knowledge, in order to come at the Foundation on which it ftands; intuitive Truths are always the laft Refort of the Understanding, beyond which it aims not to advance, but poffeffes its Notions in perfect Security, as having now reached the very Spring and Fountain of all Science and Certainty. CHA P. II. Of the feveral Kinds of Reasoning, and first of that by which we determiue the Genera and Species of Things. I. W old." TE have endeavoured in the foregoing Reaf,ring Chapter to give as diftinct a Notion as poffible of Reafoning, and of the Manner in which it is conducted. Let us now enquire a little into the Dif coveries made by this Faculty, and what thofe Ends are, which we have principally in view in the Exercife of it. All the Aims of human Keaton may in the general be reduced to these two: 1. To rank Things under thofe univerfal Ideas to which they truly belong; and, 2. To afcribe to them their feveral Attributes and Properties in confequence of that Diftribution, II. FIRST The firft Kind II. FIRST then I fay, that one great Aim of human Reafon is, to determine the Genera and Species of Things. We have feen in the first Part of this Treatife, how the Mind proceeds in framing general Ideas. We have alfo feen in the fe cond Part, how by means of these general Ideas, we come by univerfal Propofitions. Now as in thefe univerfal Propofitions, we affirm fomie Property of a Genus or Species, it is plain that we cannot apply this Property to particular Objects, till we have firft determined, whether they are comprehended under that general Idea, of which the Property is. affirmed. Thus there are certain Properties belonging to all even Numbers, which nevertheless cannot be applied to any particular Number, until we have firft difcovered it to be of the Species expreffed by that natural Name. Hence Reafoning begins with referring Things to their feveral Divifions and Claffes in the Scale of our Ideas; and as thefe Divisions are all diftinguished by particular Names, we hereby learn to apply the Terms expreffing general Conceptions, to fuch particular Objects, as come under our immediate Confideration. The Steps by subich we ar rive at Con clufions of this Sort. III. Now in order to arrive at thefe Conclufions, by which the feveral Objects of Perception are brought under general Names, two Things are manifeftly neceffary. Firft, that we take a View of the Idea itself denoted by that general Name, and carefully attend to the diftinguishing Marks which ferve to characterize it. Secondly, that we compare this Idea with the Object under Confideration, obferving diligently wherein they agree or differ. If the Idea is found to correfpond with the particular Object, we then without Hefitation apply the general Name; but if no fuch Correspondence intervenes, the Conclufion must neceffarily take a contrary Turn. Let us for inftance take the Number Eight, and confider by what Steps we are led to pronounce it an even Number. First then we call to mind the Idea fignified by the Expreffion an even Number, viz. that it is a Number divisible into equal Parts. then compare this Idea with the Number Eight, and finding them manifeftly to agree, fee at once the Neceffity of admitting the Conclufion. Thefe feveral Judgments therefore, tranfferred into Language, and reduced to the Form of a Syllogifm, appear thus: We Every Number that may be divided into two equal Parts is an EVEN Number. The Number EIGHT may be divided into two equal Parts. Thefe Steps always fol lowed, is in familiar Cafes we do not alrays attend to them. IV. I HAVE made choice of this Example, not fo much for the Sake of the Conclufion, which is obvious enough, and might have been obtained without all that Parade of Words; but chiefly because it is of eafy Comprehenfion, and ferves at the fame time diftinctly to exhibit the Form of Reafoning, by which the Understanding conducts itfelf in all Inftances of this kind. And here it may be obferved, that where the general Idea, to which particular Objects are referred, is very familiar to the Mind, and frequently in view; this Reference, and the Application of the general Name, seem to be made without any Apparatus of Reafoning. When we fee a Horfe in the Fields, or a Dog in the Street, we readily apply the Name of the Species; Habit, and a familiar Acquaintance with the general Idea, fuggefting it inftantaneously to the Mind. We are not however to imagine on this Account, that the Understanding departs from the ufual Rules of juft Thinking. A frequent Repetition of Acts begets a Habit; and Habits are attended with a certain Promptnefs of Execution, that prevents our obferving the feveral Steps and Gradations, by which any Courfe of Action is accomplished. But in other Inftances, where we judge not by pre-contracted Habits, as when the general Idea is very complex, or lefs familiar to the Mind; we always proceed according to the Form of Reasoning eftablished above. A Goldfmith for inftance, who is in doubt as to any Piece of Metal, whether it be of the Species called Gold; firft examines its Properties, and then comparing them with the general Idea fignified by that Name, if he finds a perfect Correfpondence, no longer hefitates under what Clafs of Metals to rank it. Now what is this, but following Step by Step thofe Rules of Reafoning, which we have before laid down as the Standards, by which to regulate our Thoughts in all Conclufions of this kind? The great Im portance oftis Branch of Reajoning. V. NOR let be imagined, that our Refearches here, because in Appearance bounded to the impofing of general Names upon particular Objects, are therefore trivial and of little Confequence. Some of the moft confiderable Debates among Mankind, and fuch too as nearly regard their Lives, Intereft, and Happiness, turn wholly upon this Article. Is it not the chief Employment of our feveral Courts of Judicature, to determine in particular Inftances, what is Law, Juftice, and Equity? Of what Importance is it in many Cafes, to decide aright, whether an Action fhall be termed Murder or Manflaughter? We fee then, that no less than the Lives and Fortunes of Men, depend often VOL. II. I upon upon these Decifions. The Reafon is plain. Actions when once referred to a general Idea, draw after them all that may be affirmed of that Idea; infomuch that the determining the Species of Actions, is all one with determining what Proportion of Praife or Difpraife, Commendation or Blame, &c. ought to follow them. For as it is allowed that Murder deferves Death, by bringing any particular Action under the Head of Murder, we of courfe decide the Punishment due to it. And the xa& Obfer. vance of it practifed by Mathemati cians, VI. BUT the great Importance of this Branch of Reafoning, and the Neceffity of Care and Circumfpection, in referring particular Objects to general Ideas, is ftill farther evident from the Practice of the Mathematicians. Every one who has read Euclid knows, that he frequently requires us to draw Lines thro' certain Points, and according to fuch and fuch Directions. The Figures thence refulting are often Squares, Parallelograms, or Rectangles. Yet Euclid never fuppofes this from their bare Appearance, but always demonftrates it upon the ftricteft Principles of Geometry. Nor is the Method he takes in any thing different from that described above. Thus for inftance, having defined a Square to be a Figure bounded by four equal Sides, joined together at right Angles; when fuch a Figure arifes in any Conftruction previous to the Demonftration of a Propofition, yet he never calls it by that Name, until he has fhewn that its Sides are equal, and all its Angles right ones. Now this is apparently the fame Form of Reasoning we have before exhibited, in proving Eight to be an even Number; as will be evident to any one who reduces it into a regular Syllogifm. I fhall only add, that when Euclid has thus determined the Species of any Figure, he is then and not before at liberty to afcribe to it all the Properties already demonftrated of that Figure, and thereby render it fubfervient to the future Courfe of his Reasoning. Fixed and in variable feady Appli cation of Names, renders this Part VII. HAVING thus fufficiently explained the Rules, by which we are to conduct ourselves, in ranking particular Objects under general Ideas, and fhewn their Conformity to the Practice and Manner of the Mathematicians; it remains only to obferve, that the true Way of rendering this Part of Knowledge both eafy and certain, is; by habituating ourselves to clear and determinate Ideas, and keeping them fteadily annexed to their refpective Names. For as all our Aim is, to apply general Words aright; if thefe Words ftand for invariable Ideas, that are perfectly known to the Mind, and can be readily diftinguished of Knowledge both cafy and certain upon |