pared, is that which we call reafoning; and is indeed the chief inftrument by which we push on our discoveries, and enlarge our knowledge. The great art lies in finding out fuch intermediate ideas, as, when compared with the others in the quef tion, will furnish evident and known truths; becaufe, as will afterwards appear, it is only by means of them that we arrive at the knowledge of what is hidden and remote. III. Hence it appears, that every act of reafoning neceffarily includes three diftinct judgments; two wherein the ideas whofe relation we want to difcover are severally compared with the middle idea, and a third wherein they are themselves connected or disjoined, according to the refult of that comparison. Now, as in the fecond part of logic our judgments, when put into words, were called propofitions, fo here in the third part the expreffions of our reafonings are termed fyllogifms. Hence it follows, that as every act of reafoning im plies three feveral judgments, fo every fyllogifm muft include three diftinct propofitions. When a reafoning is thus put into words, and appears in form of a fyllogifm, the intermediate idea made ufe of to discover the agreement or difagreement we fearch for, is called the middle term; and the two ideas themfelves, with which this third is compared, go by the name of the extremes. IV. But as thefe things are beft illuftrated by examples; let us, for instance, set ourselves to inquire whether men are accountable for their actions. As the relation between the ideas of men and accountableness comes not within the immediate view of the mind, our firft care must be to find out fome third idea that will enable us the more eafily to discover and trace it. A very small measure of reflection is fufficient to inform us, that no creature can be accountable for his actions, unless we fuppofe him capable of diftinguishing the good from the bad; that is, unless we fuppofe him poffeffed of reafon. Nor is this alone fufficient. For what would it avail him to know good from bad actions, if he had no freedom of choice, nor could avoid the one and purfue the other? Hence it becomes neceffary to take in both confidera tions in the prefent cafe. It is at the fame time equally apparent, that wherever there is this ability of diftinguishing good from bad actions, and of pursuing the one and avoiding the other, there alfo a creature is accountable. We have then got a third idea, with which accountableness is infepa. rably connected, viz. reason and liberty; which are here to be confidered as making up one complex conception. Let us now take this middle idea, and compare it with the other term in the quef tion, viz. man, and we all know by experience that it may be affirmed of him. Having thus by means of the intermediate idea formed two feveral judgments, viz. that man is possessed of reafon and liberty; and that reafon and liberty imply accountableness; a third obviously and neceffarily follows, viz. that man is accountable for his actions. Here then we have a complete act of reafoning, in which, according to what has been already obferved, there are three diftinct judgments; two that may be ftyled previous, inasmuch as they lead to the other, and arife from comparing the middle idea with the two ideas in the question; the third VOL. XIII. PART 1. is a confequence of thefe previous acts, and flows from combining the extreme ideas between themfelves. If now we put this reafoning into words, it exhibits what logicians term a fyllogifm; and when propofed in due form runs thus:-"Every creature poffeffed of reafon and liberty is accountable for his actions.-Man is a creature poffeffed of reafon and liberty;-Therefore man is accountable for his actions." V. In this fyllogifm we may observe, that there are three feveral propofitions expreffing the three judgments implied in the act of reasoning; and fo difpofed, as to represent diftinctly what paffes within the mind in tracing the more diftant relations of its ideas. The two firft propofitions anfwer the two previous judgments in reafoning, and are called the premises, because they are placed before the other. The third is termed the conclufion, as being gained in confequence of what was alerted in the premises. We are alfo to remember, that the terms expreffing the two ideas whose relations we enquire after, as here man and accountableness, are in general called the extremes; and that the intermediate idea, by means of which the relation is traced, viz. a creature poffeffed of reason and liberty, takes the name of the middle term. Hence it follows, that by the premises of a fyllogifm we are always to understand the two propoitions where the middle term is feverally compared with the extremes; for these conflitute the previ ous judgments, whence the truth we are in quest of is by reasoning deduced. The conclufion is that other propofition, in which the extremes themfelves are joined or feparated agreeably to what appears upon the above comparison. VI. The conclufion is made up of the extreme terms of the fyllogifm: and the extreme, which serves as the predicate of the conclufion, goes by the name of the major term: the other extreme, which makes the fubject in the fame propofition, is called the minor term. From this diftinction of the extremes arifes alfo a diftinction between the premises, where thefe extremes are feverally compared with the middle term. That propofition which compares the greater extreme, or the predicate of the conclufion, with the middle term, is called the major propofition: the other, wherein the fame middle term is compared with the fubject of the conclufion or leffer extreme, is called the minor propofition. All this is obvi ous from the fyllogifm already given, where the conclufion is, Man is accountable for his actions. For here the predicate, accountable for his actions, being connected with the middle term in the first of the two premifes, every creature possessed of reafon and liberty is accountable for his actions, gives what we call the major propofition. In the fecond of the premises, man is a creature possessed of reafon and liberty, we find the leffer extreme, or fubject of the conclufion, viz. man, connected with the fame middle term, whence it is known to be the minor propofition. When a fyllogifm is propofed in due form, the major propofition is always placed firft, the minor next, "and the conclufion laft. VII.These things premised, we may, in the general, define reafoning to be an act or operation of the mind, deducing fome unknown proposition from Xx other other previous ones that are evident and known. Thefe previous propofitions, in a fimple act of reafoning, are only two in number; and it is always required that they be of themfelves apparent to the understanding, infomuch that we affent to and perceive the truth of them as foon as propofed. In the fyllogism given above, the premises are fuppofed to be felf-evident truths; otherwife the conclufion could not be inferred by a single act of reasoning., If, for inftance, in the major, every creature poffeffed of reafon and liberty is accountable for his actions," the connection between the subject and predicate could not be perceived by a bare attention to the ideas themfelves; it is evident that this propofition would no lefs require a proof than the conclufion deduced from 66 it. In this cafe a new middle term must be fought for, to trace the connection here supposed; and this of courfe furnishes another fyllogifm, by which haying established the propofition in queftion, we are then, and not before, at liberty to ufe it in any fucceeding train of reafoning. And fhould it fo happen, that in this ad effay there was still fome previous propofition whofe truth did not appear at first, fight, we muft then have recourfe to a third logifm, to lay open that truth to the mind: because fo long as the premifes remain uncertain, the conclufion built upon them must be fo too. When, by conducting our thoughts in this manner, we at laft arrive at fome fyllogifm where the previous propofitions are intuitive truths; the mind then refts in full fecurity; as perceiving that the feveral conclufions it has paffed through, ftand upon the immoveable foundations of felf-evidence, and when traced to their fource terminate in it. VIII. We fee, therefore, that, to infer a conelufion by a fingle act of reafoning, the premises must be intuitive propofitions. Where they are not, previous fyllogifms are required; in which cafe reafoning becomes a complicated act, taking in a variety of fucceffive fteps. 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 fyllogifms following one another in train. But although in this concatenation of propofitions, thofe that form the premifes of the laft fyllogifm are often confiderably removed from felf-evidence; yet if we trace the reasoning backwards, we hall find them the conlufions of previous fyllogifms, whofe premifes approach nearer and nearer to intuition in proportion as we advance, and are found at last to terminate in it. And if, after having thus unravel led 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 fyllogifm, it ftill advances one ftep farther; and fo proceeds, making every new difcovery fubfervient to its future progrefs; we fhall then perceive clearly, that reafoning, in the highest fenfe of that faculty, is no more than an orderly combination of thofe fimple acts which we have already so fully explained. IX. Thus we fee, that reasoning, beginning with first principles, rifes gradually from one judgment to another, and connects them in such manner, that every ftage 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 see that no propofition is admitted into a fyllogifm, to ferve as one of the previous judgments on which the conclufion refts, unless it is itself a known and eftablished truth, whofe connection with self-evident principles has been already traced. SECT. II. Of the SEVERAL KINDS of REASONING; and FIRST of THAT by which we DETERMINE the GENERA and SPECIES of THINGS. I. ALL the aims of human reafon may in general be reduced to thefe 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. One great aim of human reason is to determine the genera and fpecies of things. We have feen, in the 1ft part of this Treatife, how the mind proceeds in framing general ideas. We have alfo feen, in the IId Part, how, by means of these general ideas, we come by univerfal propofitions. Now as in thefe univerfal propofitions we affirm fome property of a genus or fpecies, 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 discovered it to be of the fpecies expreffed by that natural name. Hence reafoning begins with referring things to their feveral divifions and claffes in the fcale of our ideas; and as thefe divifions are all diftinguifhed by particular names, we hereby learn to apply the terms expreffing general conceptions to fuch particular objects as come under our immediate obfervation. III. Now, to arrive at thefe conclufions, by which the feveral objects of perception are brought under general names, two things are manifeftly neceffary. First, that we take a view of the idea itself denoted by that general name, and carefully attend to the diftinguishing marks which serve to characterise it. 2dly, That we compare this idea with the object under confideration, obferving di ligently wherein they agree or differ. If the idea is found to correfpond with the particular object, we then without hefitation apply to the general name; but if no fuch correfpondence intervenes, the conclufion muft neceffarily take a contrary turn. Let us, for inftance, take the number eight, and confider by what fteps we are led to pronounce it an even number. Firft, then, we call to mind the idea fignified by the expreffion an even number, viz. that it is a number divifible into two equal parts. We then compare this idea with the number eight, and, finding them to agree, see at once the neceffity of admitting the conclufion. Thefe Thefe feveral judgments, therefore, transferred into language, and reduced into the form of a fyllogifm, appear thus:-" Every number that may be divided into two equal parts is an even num ber: The number EIGHT may be divided into two equal parts;-Therefore the number eight is an even number.' IV. Here it may be observed, 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, feem 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 fpecies; habit, and a familiar acquaintance with the general idea, fuggefting it infrantaneously 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 promptness 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 precontracted habits, as when the general idea is very complex, or lefs familiar to the mind, we always proceed according to the form of reafoning eftablished above. A goldsmith, for inftance, who is in doubt as to any piece of metal, whether it be of the fpecies 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. V. Nor let it be imagined that our researches here, because in appearance bounded to the impofing of general names upon particular objects, are therefore trivial and of little, confequence. Some of the most 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 several 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 manslaughter? We fee then that no lefs than the lives and fortunes of men often depend upon these decisions. The reason 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 fpecies of ac tions is all one with determining what proportion of praise or difpraise, 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. VI. But the great importance of this branch of reasoning, and the neceflity of care and circumspection in 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 through certain points, and according to fuch and fuch directions. The figures thence re fulting are often fquares, parallelograms, or rec tangles. Yet Euclid never supposes this from their bare appearance, but always demonstrates it upon the ftricteft principles of geometry. Nor is the method he takes in any thing different from that defcribed above. Thus, for instance, having defined a square to be a figure bounded by four equal fides joined together at right angles; when fuch a figure arifes in any conftruction previous to the demonftration of a proposition, yet he never calls it by that name until he has shown that its fides are equal, and all its angles right ones. Now this is apparently the fame form of reafoning we have before exhibited in proving eight to be an even number. VII. Having thus explained the rules by which we are to conduct ourselves in ranking particular objects under general ideas, and shown 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 respective names. For as all our aim is to apply general words aright, if these words ftand for invariable ideas that are perfectly known to the mind, and can be readi ly diftinguished upon occafion, there will be lit tle danger of mistake or error in our reafonings. Let us fuppofe that, by examining any object, and carrying our attention fucceflively from one part to another, we have acquainted ourselves with the feveral particulars obfervable in it If among thefe we find fuch as conftitute fome general idea, framed and settled before-hand by the understanding, and diftinguished by a particular name, the refemblance thus known and perceived neceffarily determines the fpecies of the object, and thereby gives it a right to the name by which that fpecies is called. Thus four equal fides, joined together at right angles, make up the notion of a Square. As this is a fixed and invariable idea, without which the general name cannot be applied; we never call any particular figure a square until it appears to have thefe feveral conditions; and contrarily, wherever a figure is found with thefe conditions, it neceffarily takes the name of a fquare, The fame will be found to hold in all our other reafonings of this kind, where nothing can create any difficulty but the want of fettled ideas. If, for inftance, we have not determined within ourselves the precife notion denoted by the word manflaughter, it will be impoffible for us to decide whether any particular action ought to bear that name: because, however nicely we examine the action itself, yet, being ftrangers to the gene ral idea with which it is to be compared, we are utterly unable to judge of their agreement or difagreement. But if we take care to remove this obstacle, and diftinetly trace the two ideas under confideration, all difficulties vanish, and the refolution becomes both eafy and certain. VIII. Thus we fee of what importance it is to wards the improvement and certainty of human knowledge, that we accuftom ourselves to clear and determinate ideas, and a steady application of words. Xx 2 SECT I. WE now come to the ad great end which men have in view in their reafonings: namely, the difcovering and afcribing to things their feveral attributes and properties. And here it will be neceflary to diftinguish between reafoning, as it regards the fciences, and as it concerns common life. In the fciences, our reafon is employed chiefly about univerfal truths, it being by them alone that the bounds of human knowledge are enlarged. Hence the divifion of things into various claffes, called otherwife genera and fpecies. For thefe univerfal ideas being fet up as the reprefentatives of many particular things, whatever is affirmed of them may be alfo affirmed of all the individuals to which they belong. Murder, for inftance, is a general idea, reprefenting a certain fpecies of human actions. Reafon tells us that the punishment due to it is death. Hence every particular action, coming under the notion of murder, has the punishment of death allotted to it. Here then we apply the general truth to some obvious inftance; and this is what properly conftitutes the reafening of common life. For men, in their ordinary tranfactions and intercourse one with another, have, for the moft part, to do only with particular objects. Our friends and relations, their characters and behaviour, the conftitution of the feveral bodies that furround us, and the ufes to which they may be applied, are what chiefly engage our attention. In all thefe, we reafon about particular things; and the whole refult of our reafoning is, the applying the general truths of the fciences in the ordinary tranfactions of human life. When we fee a viper, we avoid it. Wherever we have occafion for the forcible action of water to move a body that makes confiderable refiftance, we take care to convey it in fuch a manner that it fhall fall upon the object with impetuofity. Now all this happens in confequence of our familiar and ready application of thefe two general truths. "The bite of a viper is mortal." "Water falling upon a body with impetuofity, acts very forcibly towards fetting it in motion." In like manner, if we fet ourselves to confider any particular character, in order to determine the share of praise or dispraise that belongs to it, our great concern is to afcertain exactly the proportion of virtue and vice, The reafon is obvious. A juft determination, in all cafes of this kind, depends entirely upon an application of thefe general maxims of morality; Firtuous actions deferve praise; vicious actions dejerve blame. II. Hence it appears, that reasoning, as it regards common life, is no more than the afcribing the general properties of things to thofe feveral objects with which we are more immediately concerned, according as they are found to be of that particular divifion or class to which the properties belong. The steps then by which we proceed are manifeftly thefe. First, we refer the object under confideration to fome general idea or class of things. We then recollect the feveral attributes of that general idea. And, laftly, afcribe all thofe attributes to the prefent object. Thus, find it to be of the kind called virtuous, when we, in confidering the character of Sempronius, if we at the fame time, reflect that a virtuous character is deferving of esteem, it naturally and obviously follows that Sempronius is fo too. These thoughts, put into a fyllogifm, in order to exhibit the form of reafoning here required, run thus:-"Every virtuous man is worthy of efteem.-Sempronius is a virtuous man :-Therefore Sempronius is worthy of esteem." III. By this fyllogifm it appears, that before we affirm any thing of a particular object, that object must be referred to fome general idea. Sempronius is pronounced worthy of efteem only in confequence of his being a virtuous man, or coming under that general notion. Hence we fee the neceffary connection of the various parts of reasoning, and the dependence they have one upon another. The determining the genera and species of things is one exercife of human reafon; and here we find that this exercise is the firft in order, and previous to the other, which confifts in afcribing to them their powers, properties, and relations. But when we have taken this previous ftep, and brought particular objects under general names; as the properties we afcribe to them are other than thofe of the general idea, it is plain that, in order to a fuccefsful progrefs in this part of knowledge, we must thoroughly acquaint ourfelves with the feveral relations and attributes of these our general ideas. When this is done, the other part will be eafy, and requires fcarce any labour or thought, as being no more than an application of the general form of reafoning reprefented in the foregoing fyllogifin. Now, as we have already fufficiently shown how we are to proceed in determining the genera and fpecies of things, which, as we have faid, is the previous ftep to this fecond branch of human knowledge; all that is farther wanting towards a due explanation of it is, to offer fome confiderations as to the manner of inveftigating the general relations of our ideas. This is the highest exercise of the powers of the understanding, and that by means whereof we arrive at the discovery of univerfal truths; infomuch that our deductions in this way conftitute that particular fpecies of reasoning which regards principally the sciences. IV. But that we may conduct our thoughts with fome order and method, we shall begin with obferving, that the relations of our general ideas are of two kinds: either fuch as immediately dif cover themselves, upon comparing the ideas one with another; or fuch as, being more remote and diftant, require art and contrivance to bring them into view. The relations of the first kind furnish us with intuitive and felf-evident truths: those of the second are traced by reafoning, and due application of intermediate ideas. It is of this laft kind that we are to speak here, having difcuffed the other in the ad part. As, therefore, in tracing the more distant relations of things, we must always have recourfe to intervening ideas, and are more or lefs fuccessful in our researches according to our acquaintance with these ideas, and ability of applying them; it is evident that, to make a good reafoner, two things are princi pally pally required. ift, An extenfive knowledge of thofe intermediate ideas, by means of which things may be compared one with another. 2d. The fkill and talent of applying them happily in all particular inftances that come under confidera tion. V. In order to our fuccefsful progrefs in reafoning, we must have an extenfive knowledge of thofe intermediate ideas by means of which things may be compared one with another. For as it is not every idea that will answer the purpose of our inquiries, but fuch only as are peculiarly related to the objects about which we reafon, fo as, by a comparifon with them, to furnish evident and known truths; nothing is more apparent than that the greater variety of conceptions we can call into view, the more likely we are to find fome among them that will help us to the truths here required. And, indeed, it holds in experience, that in proportion as we enlarge our views of things, and grow acquainted with a multitude of different objects, the reafoning faculty gathers ftrength: for by extending our sphere of know ledge, the mind acquires a certain force and pene tration, as being accustomed to examine the feveral appearances of its ideas, and obferve what light they caft one upon another. VI. This is the reafon why, in order to excel remarkably in any one branch of learning, it is neceffary to have at least a general acquaintance with the whole circle of arts and sciences. All the various divifions of human knowledge are very nearly related among themselves, and, in innumerable inftances, ferve to illuftrate and fet off each other. And although it is not to be denied that, by an obftinate application to one branch of ftu, dy, a man may make confiderable progrefs, and acquire fome degree of eminence in it; yet his views will be always narrow and contracted, and he will want that masterly discernment which not only enables us to pursue our difcoveries with eafe, but also, in laying them open to others, to spread a certain brightnefs around them. But when our reasoning regards a particular science, it is farther neceffary that we more nearly acquaint ourselves with whatever relates to that fcience. A general knowledge is a good preparation, and enables us to proceed with ease and expedition in whatever branch of learning we apply to. But then, in the minute and intricate queftions of any science, we are by no means qualified to reafon with advantage until we have perfectly mastered the fcience to which they belong. VII. We come now to the fecond thing required, in order to a fuccefsful progrefs in reafon ing; namely, the skill and talent of applying intermediate ideas happily in all particular inftan ces that come under confideration. And here rules and precepts are of little fervice. Ufe and experience are the beft inftructors. For, what ever logicians may boaft of being able to form perfect reafoners by book and rule, we find by experience, that the ftudy of their precepts does not always add any great degree of ftrength to the understanding. In fhort, it is the habit alone of reasoning that makes a reafoner. And therefore the true way to acquire this talent is, by being much converfant in those sciences where the art of reafoning is allowed to reign in the greatest perfection. Hence it was that the ancients, who fo well understood the manner of forming the mind, always began with MATHEMATICS, as the foundation of their philofophical ftudies. Here the understanding is by degrees habituated to truth, contracts infenfibly a certain fondness for it, and learns never to yield its affent to any propofition, but where the evidence is fafficient to produce full conviction. For this reafon PLATT has called mathematical demonftrations the cathartics or purgatives of the foul, as being the proper means to cleanse it from error, and restore that natural exercise of its faculties in which juft thinking confifts. VIII. If therefore we would form our minds to a habit of reafoning closely and in train, we cannot take any more certain method than the exercifing ourselves in mathematical demonftrations, fo as to contract a kind of familiarity with them. Not that we look upon it as neceffary that all men should be deep mathematicians; but that, having got the way of reafoning which that study neceffarily brings the mind to, they may be able to transfer it to other parts of knowledge, as they fhall have occafion. IX. But although the study of mathematics be of all others the most useful to form the mind and give it an early relith of truth, yet ought not other parts of philofophy to be neglected. For there also we meet with many opportunities of exercifing the powers of the understanding; and the variety of fubjects naturally leads us to obferve all thofe different turns of thinking that are peculiarly adapted to the feveral ideas we examine, and the truth we fearch after. A mind thus trained acquires a certain mastery over its own thoughts, infomuch that it can range and model them at pleasure, and call fuch into view as best fuit its prefent defigns. Now in this the whole art of reafoning confifts; from among a great variety of different ideas to fingle out those that are most proper for the bufinefs in hand, and to lay them together in fuch order, that from plain and eafy beginnings, by gentle degrees, and a continued train of evident truths, we may be infenfibly led on to fuch discoveries as at our first fetting out appeared beyond the reach of human underftanding. For this purpose, befides the study of mathematics before recommended, we ought to apply ourselves diligently to the reading of fuch authors as have diftinguished themselves for ftrength of reasoning, and a juft and accurate manner of thinking. For it is obfervable, that a mind exercised and seasoned to truth, feldom refts fatisfied in a bare contemplation of the arguments offered by others; but will be frequently affaying its own ftrength, and pursuing its difcoveries upon the plan it is moft accustomed to. Thus we infenfibly contract a habit of tracing truth from one stage to another, and of investigating those general relations and properties which we afterwards afcribe to particular things, according as we find them comprehended under the abftract ideas to which the properties belong. SECT. IV. Of the FORMS of SYLLOGISMS. gifm s |