Of still some previous proposition whose truth did not appear at first sight, we must then have recourse to a Reasoning. third syllogism, in order to lay open that truth to the mind: because so long as the premises remain uncertain, the conclusion built upon them must be so too. When, by conducting our thoughts in this manner, we at last arrive at some syllogism where the previous propositions are intuitive truths; the mind then rests in full security, as perceiving that the several conclusions it. has passed through stand upon the immoveable foundation of self-evidence, and when traced to their source terminate in it. of that the terms expressing the two ideas whose relaReasoning, tions we inquire 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 possessed of reason and liberty, takes the name of the middle term. Hence it follows, that by the premises of a syllogism we are always to understand the two propositions where the middle term is severally compared with the extremes; for these constitute the previous judgments, whence the truth we are in quest of is by reasoning deduced. The conclusion is that other proposition, in which the extremes themselves are joined or separated agreeably to what appears upon the above comparison. 64 Major and VI. The conclusion is made up of the extreme terms minor term, of the syllogism: and the extreme, which serves as the major and predicate of the conclusion, goes by the name of the minor proposition. major term: the other extreme, which makes the subject in the same proposition, is called the minor term. From this distinction of the extremes arises also a distinction between the premises, where these extremes are severally compared with the middle term. That proposition which compares the greater extreme, or the predicate of the conclusion, with the middle term, is called the major proposition: the other, wherein the same middle term is compared with the subject of the conclusion or lesser extreme, is called the minor proposition. All this is obvious from the syllogism already given, where the conclusion 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 premises, every creature possessed of reason and liberty is accountable for his actions, gives what we call the major proposition. In the second of the premises, man is a creature possessed of reason and liberty, we find the lesser extreme, or subject of the conclusion, viz. man, connected with the same middle term, whence it is known to be the minor proposition. When a syllogism is proposed in due form, the major proposition is always placed first, the minor next, and the conclusion last. 65 tuitive truths. In a single VII. These things premised, we may in the geneact of rea- ral define reasoning to be an act or operation of the soning the premises mind, deducing some unknown proposition from other must be in- previous ones that are evident and known. These previous propositions, in a simple act of reasoning, are only two in number; and it is always required that they be of themselves apparent to the understanding, insomuch that we assent to and perceive the truth of them as soon as proposed. In the syllogism given above, the premises are supposed to be self-evident truths; otherwise the conclusion could not be inferred by a single act of reasoning. If, for instance, in the major, every creature possessed of reason and liberty is accountable for his actions, the connexion between the subject and predicate could not be perceived by a bare attention to the ideas themselves; it is evident that this proposition would no less require a proof than the conclusion deduced from it. In this case a new middle term must be sought for, to trace the connexion here supposed; and this of course furnishes another syllogism, by which having established the proposition in question, we are then, and not before, at liberty to use it in any succeeding train of reasoning. And should it so happen, that in this second essay there was 66 VIII. We see, therefore, that in order to infer a Reasoning, in the highconclusion by a single act of reasoning, the premises est exercise must be intuitive propositions. Where they are not, of it, only a previous syllogisms are required; in which case rea-concatenasoning becomes a complicated act, taking in a variety tion of syllogisms. of successive steps. This frequently happens in tracing the more remote relation of our ideas; where, many middle terms being called in, the conclusion cannot be made out but in consequence of a series of syllogisms following one another in train. But although in this concatenation of propositions, those that form the premises of the last syllogism are often considerably removed from self-evidence; yet if we trace the reasoning backwards, we shall find them the conclusions of previous syllogisms, whose premises 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 unravelled a demonstration, we take it the contrary way; and observe how the mind, setting out with intuitive perceptions, couples them together to form a conclusion: how, by introducing this conclusion into another syllogism, it still advances one step father; and so proceeds, making every new discovery subservient to its future progress; we shall then perceive clearly, that reasoning, in the highest sense of that faculty, is no more than an orderly combination of those simple acts which we have already so fully explained. 67 IX. Thus we see, that reasoning, beginning with Requires first principles, rises gradually from one judgment to another, and connects them in such manner, that certainty in every every step stage of the progression brings intuitive certainty along of the prewith it. And now at length we may clearly under-gression. stand the definition given above of this distinguishing faculty of the human mind. Reason, we have said, is the ability of deducing unknown truths from principles or propositions that are already known. This evidently appears by the foregoing account, where we see that no proposition is admitted into a syllogism, to serve as one of the previous judgments on which the conclusion rests, unless it is itself a known and established truth, whose connexion with self-evident principles has been already traced. CHAP. II. Of the several kinds of Reasoning: and first, of that by which we determine the Genera and Species of Things. Of 69 The first kind regards the II. One great aim of human reason is to determine Reasoning the genera and species of things. We have seen in the First Part of this treatise, how the mjnd proceeds in framing general ideas. We have also seen in the Second Part, how by means of these general ideas we come by universal propositions. Now as in these unigenera and versal propositions we affirm some property of a genus species of or species, it is plain that we cannot apply this properthings. *See Foot ty to particular objects till we have first determined Note, 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 first discovered it to be of the species expressed by that natural name. Hence reasoning begins with referring things to their several divisions and classes in the scale of our ideas; and as these divisions are all distinguished by particular names, we hereby learn to apply the terms expressing general conceptions to such particular objects as come under our immediate observation. p. 136. 70 The steps by which we arrive sions of this sort. III. Now, in order to arrive at these conclusions, by which the several objects of perception are brought unat conclu der general names, two things are manifestly necessary. First, That we take a view of the idea itself denoted by that general name, and carefully attend to the distinguishing marks which serve to characterize it. Secondly, That we compare this idea with the object under consideration, observing diligently wherein they agree or differ. If the idea is found to correspond with the particular object, we then without hesitation apply the general name; but if no such correspondence intervenes, the conclusion must necessarily take a contrary turn. attend to them. Let us, for instance, take the number eight, and consider by what steps we are led to pronounce it an even number. First then, we call to mind the idea signified by the expression an even number, viz. that it is a number divisible into two equal parts. We then compare this idea with the number eight, and finding them manifestly to agree, see at once the necessity of admitting the conclusion. These several judgments therefore transferred into language, and reduced to the form of a syllogism, appear thus: 66 Every number that may be divided into two equal "parts is an even number: “The number eight may be divided into two equal 66 parts; "Therefore the number eight is an even number.” 71 Those steps IV. Here it may be observed, that where the gealways neral idea, to which particular objects are referred, is followed, very familiar to the mind, and frequently in view; though in this reference, and the application of the general familiar cases we do name, seem to be made without any apparatus of reanot always soning. When we see a horse 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, suggesting it instantaneously to the mind. We are not however to imagine on this account that the understanding departs from the usual rules of just thinking. A frequent repetition of acts begets a habit; and habits are attended with a certain promptness of execution, that prevents our observing the several steps and gradations by which any course of action is accomplished. But in other instances, where we judge not by precontracted habits, as when the Of general idea is very complex, or less familiar to the Reasoning mind, we always procced according to the form of reasoning established above. A goldsmith, for instance, who is in doubt as to any piece of metal, whether it be of the species called gold, first examines its properties, and then comparing them with the general idea signified by that name, if he finds a perfect correspondence, no longer hesitates under what class of metals to rank it. 72 branch of V. Nor let it be imagined that our researches here, The great because in appearance bounded to the imposing of ge- importance neral names upon particular objects, are therefore tri- of this vial and of little consequence. Some of the most con- reasoning; siderable debates among mankind, and such too as nearly regard their lives, interest, and happiness, turn wholly upon this article. Is it not the chief employment of our several courts of judicature to determine in particular instances, what is law, justice, and equity? Of what importance is it in many cases to decide aright whether an action shall be termed murder or manslaughter? We see then that no less than the lives and fortunes of men depend often 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; insomuch that the determining the species of actions is all one with determining what proportion of praise or dispraise, commendation or blame, &c. ought to follow them. For as it is allowed that murder deserves death; by bringing any particular action under the head of murder, we of course decide the punishment due to it. 73 vance of it VI. But the great importance of this branch of rea- and the exsoning, and the necessity of care and circumspection act obserin referring particular objects to general ideas, is still practised farther evident from the practice of the mathemati- by mathecians. Every one who has read Euclid, knows, that maticians. he frequently requires us to draw lines through certain points, and according to such and such directions. The figures thence resulting are often squares, parallelograms, or rectangles. Yet Euclid never supposes this from their bare appearance, but always demonstrates it upon the strictest principles of geometry. that described above. Thus, for instance, having deNor is the method he takes in any thing different from sides joined together at right angles; when such a fifined a square to be a figure bounded by four equal gure arises in any construction previous to the demonstration of a proposition, yet he never calls it by that name until he has shown that its sides are equal, and all its angles right ones. Now this is apparently the same form of reasoning we have before exhibited in proving eight to be an even number. 74 VII. Having thus explained the rules by which we Fixed and are to conduct ourselves in ranking particular objects invariable ideas, with under general ideas, and shown their conformity to a steady the practice and manner of the mathematicians: it re- application mains only to observe, that the true way of rendering of names, this part of knowledge both easy and certain is, by renders this habituating ourselves to clear and determinate ideas, part of knowledge and keeping them steadily annexed to their respective both easy For as all our aim is to apply general words and ceraright, if these words stand for invariable ideas that tain. are perfectly known to the mind, and can be readily distinguished upon occasion, there will be little danger names. Of of mistake or error in our reasonings. Let us suppose Reasoning that, by examining any object, and carrying our attention successively from one part to another, we have acquainted ourselves with the several particulars observable in it. If among these we find such as constitute some general idea, framed and settled beforehand by the understanding, and distinguished by a particular name, the resemblance thus known and perceived necessarily determines the species of the object, and thereby gives it a right to the name by which that species is called. Thus four equal sides, 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 these several conditions; and contrarily, wherever a figure is found with these conditions, it necessarily takes the name of a square. The same will be found to hold in all our other reasonings of this kind, where nothing can create any difficulty but the want of settled ideas. If, for instance, we have not determined within ourselves the precise notion denoted by the word manslaughter, it will be impossible for us to decide whether any particular action ought to bear that name because, however nicely we examine the action itself, yet, being strangers to the general idea with which it is to be compared, we are utterly unable to judge of their agreement or disagreement. But if we take care to remove this obstacle, and distinctly trace the two ideas under consideration, all difficulties vanish, and the resolution becomes both easy and certain. 75 The dis as it regards the sciences, and as it concerns common life. VIII. Thus we see of what importance it is towards CHAP. III. Of Reasoning, as it regards the Powers Of their characters and behaviour, the constitution of the 76 in the rea II. Hence it appears that reasoning, as it regards The steps "Every virtuous man is worthy of esteem. 77 I. WE now come to the second great end which tinction of men have in view in their reasonings; namely, the reasoning, discovering and ascribing to things their several attributes and properties. And here it will be necessary to distinguish between reasoning, as it regards the sciences, and as it concerns common life. In the sci- III. By this syllogism it appears, that before we af- The conences, our reason is employed chiefly about univer- firm any thing of a particular object, that object must nexion and dependence sal truths, it being by them alone that the bounds of be referred to some general idea. Sempronius is pro- of the two. human knowledge are enlarged. Hence the division nounced worthy of esteem only in consequence of his grand of things into various classes, called otherwise genera being a virtuous man, or coming under that general branches of and species. For these universal ideas being set up as notion. Hence we see the necessary connexion of the reasoning the representatives of many particular things, whatever various parts of reasoning, and the dependence they one upon another is affirmed of them may be also affirmed of all the in- have one upon another. The determining the genera dividuals to which they belong. Murder, for instance, and species of things is, as we have said, one exercise is a general idea, representing a certain species of hu- of human reason; and here we find that this exercise man actions. Reason tells us that the punishment due is the first in order, and previous to the other, which to it is death. Hence every particular action, coming consists in ascribing to them their powers, properties,. under the notion of murder, has the punishment of and relations. But when we have taken this previous death allotted to it. Here then we apply the general step, and brought particular objects under general. truth to some obvious instance; and this is what pro- names; as the properties we ascribe to them are no perly constitutes the reasoning of common life. For other than those of the general idea, it is plain that, men, in their ordinary transactions and intercourse in order to a successful progress in this part of knowone with another, have, for the most part, to do on-ledge, we must thoroughly acquaint ourselves with the by with particular objects. Our friends and relations, several relations and attributes of these our general 4 ideas, Of ideas. When this is done, the other part will be easy, Reasoning and requires scarce any labour or thought, as being no more than an application of the general form of reasoning represented in the foregoing syllogism. Now, as we have already sufficiently shown how we are to proceed in determining the genera and species of things, which, as we have said, is the previous step to this second branch of human knowledge; all that is farther wanting towards a due explanation of it is, to offer some considerations as to the manner of investigating 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 universal truths; insomuch that our deductions in this way constitute that particular species of reasoning which we have before said regards principally the sciences. 78 Two things IV. But that we may conduct our thoughts with required to some order and method, we shall begin with observmake a ing, that the relations of our general ideas are of two good rea- kinds: either such as immediately discover themselves, soner. 79 First, An extensive upon comparing the ideas one with another; or such as, being more remote and distant, require art and contrivance to bring them into view. The relations of the first kind furnish us with intuitive and self-evident truths: those of the second are traced by reasoning, and a due application of intermediate ideas. It is of this last kind that we are to speak here, having despatched what was necessary with regard to the other in the Second Part. As, therefore, in tracing the more distant relations of things, we must always have recourse to intervening ideas, and are more or less successful in our researches according to our acquaintance with these ideas, and ability of applying them; and it is evident, that to make a good reasoner, two things are principally required. First, An extensive knowledge of those intermediate ideas, by means of which things may be compared one with another. Secondly, The skill and talent of applying them happily in all particular instances that come under consideration. V. In order to our successful progress in reasoning, we must have an extensive knowledge of those interknowledge mediate ideas by means of which things may be com diate ideas. pared one with another. For as it is not every idea of interme that will answer the purpose of our inquiries, but such only as are peculiarly related to the objects about which we reason, so as, by a comparison 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 some among them that will help us to the truths here required. And, indeed, it is found to hold in experience, that in proportion as we enlarge our views of things, and grow acquainted with a multitude of different objects, the reasoning faculty gathers strength: for, by extending our sphere of knowledge, the mind acquires a certain force and penetration, as being ac customed to examine the several appearances of its ideas, and observe what light they cast one upon another. VI. This is the reason why, in order to excel remarkably in any one branch of learning, it is necessary to have at least a general acquaintance with the whole circle of arts and sciences. The truth of it is, 80 we must be all the various divisions of human knowledge are very Of nearly related among themselves, and, in innumerable Reasoning. instances, serve to illustrate and set off each other. And although it is not to be denied that, by an ob- To excel in stinate application to one branch of study, a man may any one make considerable progress, and acquire some degree branch of of eminence in it; yet his views will be always nar-learning row and contracted, and he will want that masterly in general discernment which not only enables us to pursue our acquainted discoveries with case, but also, in laying them open with the to others, to spread a certain brightness around them. whole cirBut when our reasoning regards a particular science, cle of arts it is farther necessary that we more nearly acquaint ourselves with whatever relates to that science. 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 questions of any science, we are by no means qualified to reason with advantage until we have perfectly mastered the science to which they belong. and scien ces. 81 The skill of termediate stances. VII. We come now to the second thing requir- Secondly, ed, in order to a successful progress in reasoning; namely, the skill and talent of applying intermediate applying inideas happily in all particular instances that come un-ideas hapder consideration. And here, rules and precepts are pily in par of little service. Use and experience are the best ticular ininstructors. For, whatever logicians may boast ofst being able to form perfect reasoners by book and rule, we find by experience, that the study of their precepts does not always add any great degree of strength to the understanding. In short, it is the habit alone of reasoning that makes a reasoner. And therefore the true way to acquire this talent is, by being much conversant in those sciences where the art of reasoning is allowed to reign in the greatest perfection. Hence it was that the ancients, who so well understood the manner of forming the mind, always began with mathematics, as the foundation of their philosophical studies. Here the understanding is by degrecs habituated to truth, contracts insensibly a certain fondness for it, and learns never to yield its assent to any proposition but where the evidence is sufficient to produce full conviction. For this reason Plato has called mathematical demonstrations the cathartics or purgatives of the soul, as being the proper means to cleanse it from error, and restore that natural exercise of its faculties in which just thinking consists. 82 monstra VIII. If therefore we would form our minds to a The study habit of reasoning closely and in train, we cannot take of matheany more certain method than the exercising ourselves matical dein mathematical demonstrations, so as to contract a kind tions of of familiarity with them. Not that we look upon it as great avail necessary that all men should be deep mathematicians; in this rebut that, having got the way of reasoning which that spect. study necessarily brings the mind to, they may be As also of able to transfer it to other parts of knowledge, as they such aushall have occasion. 83 thors on Of rally leads us to observe all those different turns of Reasoning, thinking that are peculiarly adapted to the several ideas we examine, and the truth we search after. A mind thus trained acquires a certain mastery over its own thoughts, insomuch that it can range and model them at pleasure, and call such into view as best suit its present designs. Now in this the whole art of reasoning consists; from among a great variety of different ideas to single out those that are most proper for the business in hand, and to lay them together in such order, that from plain and easy beginnings, by gentle degrees, and a continued train of evident truths, we may be insensibly led on to such discoveries, as at our first setting out appeared beyond the reach of human understanding. For this purpose, besides the study of mathematics before recommended, we ought to apply ourselves diligently to the reading of such authors as have distinguished themselves for strength of reasoning, and a just and accurate manner of thinking. For it is observable, that a mind exercised and seasoned to truth, seldom rests satisfied in a bare contemplation of the arguments offered by others; but will be frequently assaying its own strength, and pursuing its discoveries upon the plan it is most accustomed to. insensibly contract a habit of tracing truth from one stage to another, and of investigating those general relations and properties which we afterwards ascribe to particular things, according as we find them comprehended under the abstract ideas to which the properties belong. 84 CHAP IV. Of the Forms of Syllogisms. Thus we The figures J. HITHERTO we have contented ourselves with a of syllo- general notion of syllogisms, and of the parts of which gisms. they consist. It is now time to enter a little more particularly into the subject, to examine their various forms, and lay open the rules of argumentation proper to each. In the syllogisms mentioned in the foregoing chapters, we may observe, that the middle term is the subject of the major proposition, and the predicate of the minor. This disposition, though the most natural and obvious, is not however necessary; it frequently happening, that the middle term is the subject in both the premises, or the predicate in both; and sometimes directly contrary to its disposition in the foregoing chapters, the predicate in the major, and the subject in the minor. Hence the distinction of syllogisms into various kinds, called figures by logicians. For figure, according to their use of the word, is nothing else but the order and disposition of the middle term in any syllogism. And as this disposition is, we see, fourfold, so the figures of syllogisms thence arising are four in number. When the middle term is the subject of the major proposition, and the predicate of the minor, we have what is called the first figure; As, "No work of God is bad: "The natural passions and appetites of men are "the work of God: "Therefore none of them is bad." If, on the other hand, it is the predicate of both the premises, the syllogism is said to be the second figure: As, "The only Being who ought to be worshipped is "the Creator and Governor of the world: "The Creator aud Governor of the world is "God: "Therefore God is the only Being who ought to "be worshipped.” 35 II. But, besides this fourfold distinction of syllo- The moods gisms, there is also a farther subdivision of them in of sylloevery figure, arising from the quantity and quality, as gisms. they are called, of the propositions. By quantity we mean the consideration of propositions, as universal or particular; by quality, as affirmative or negative. Now as, in all the several dispositions of the middle term, the propositions of which a syllogism consists may be either universal or particular, affirmative or negative; the due determination of these, and so puting them together as the laws of argumentation require, constitute what logicians call the moods of syllogisms. Of these moods there is a determinate number to every figure, including all the possible ways in which propositions differing in quantity or quality can be combined, according to any disposition of the middle term, in order to arrive at a just conclusion. The first figure has only four legitimate moods. The major proposition in this figure must be universal, and the minor affirmative; and it has this property, that it yields conclusions of all kinds, affirmative and negative, universal and particular. The second figure has also four legitimate moods. Its major proposition must be universal, and one of the premises must be negative. It yields conclusions both universal and particular, but all negative. The third figure has six legitimate moods. Its minor must always be affirmative; and it yields conclusions both affirmative and negative, but all particular. These are all the figures which were admitted by the inventor of syllogisms, and of which, so far as we know, the number of legitimate moods has been ascertained, and severally demonstrated. In every figure it will be found upon trial, that there are sixty-four different moods of syllogism; and he who thinks it worth while to construct so many in the fourth figure, always remembering that the middle term in each must be the predicate of the major and the subject of the minor proposition, will easily discern what number of these moods are legitimate, and give true conclusions. Besides the rules that are proper to each figure, Aristotle has given some that are common to all, by which the legitimacy of syllogisms may be tried. 3 These |