weakening the ground upon which the conclusion rests. The reason is, because the fortites itself may be resolved into as many simple syllogisms as there are middle terms in it; where this is found universally to hold, that when such a resolution is made, and the syllogisms are placed in train, the conclusion of the last in the series is also the conclusion of the fortites. This kind of argument, therefore, as it serves to unite several syllogisms into one, must stand upon the same foundation with the syllogisms of which it consists, and is indeed, properly speaking, no other than a compendious way of reasoning syllogistically.

XIV. What is here laid of plain simple propositions may be as well applied to those that are conditional; that is, any number of them may be so joined together in a series, that the consequent of one shall become continually the antecedent of the next following; in which case, by establishing the antecedent of the first proposition, we establish the consequent of the last, or by removing the last consequent remove also the first antecedent. This way of reasoning is exemplified in the following argument.

"If we love any person, all emotions of hatred towards him cease. "If all emotions of hatred towards a person cease, "we cannot rejoice in his misfortunes. "If we rejoice not in his misfortunes, we certainly "with him no injury: "Therefore, if we love a person, we wish him no "injury."

It is evident that this fortites, as well as the last, may be resolved into a series of distinct syllogisms, with this only difference, that here the syllogisms are all conditional.

XV. We come now to that kind of argument which logicians call induction; in order to the right understanding of which, it will be necessary to observe, that our general ideas are for the most part capable of various subdivisions. Thus the idea of the lowest species may be subdivided into its several individuals, the idea of any genus into the different species it comprehends, and so of the rest. If then we suppose this distribution to be duly made, and so as to take in the whole extent of the idea to which it belongs; then it is plain that all the subdivisions or parts of any idea taken together constitute that whole idea. Thus the several individuals of any species taken together constitute the whole species, and all the various species comprehended under any genus make up the whole genus. This being allowed, it is apparent, that whatever may be affirmed of all the several subdivisions and classes of any idea ought to be affirmed of the whole general idea to which these subdivisions belong. What may be affirmed of all the individuals of any species may be affirmed of the whole species; and what may be affirmed of all the species of any genus may be also affirmed of the whole genus; because all the individuals taken together are the same with the species, and all the species taken together the same with the genus.

XVI. This way of arguing, where we infer universally concerning any idea what we had before affirmed or denied separately of all its several subdivisions and parts, is called reasoning by induction. Thus if we suppose the whole tribe of animals subdivided into men, beasts, birds, insects, and fishes, and then reason concerning them after this manner: "all men have a power of beginning motion; all beasts, birds, and insects, have a power of beginning motion; all fishes have a power of beginning motion; therefore all animals have a power of beginning motion." The argument is an induction. When the subdivisions are just, so as to take in the whole general idea, and the enumeration is perfect, that is, extends to all and every of the inferior classes or parts; there, the induction is complete, and the manner of reasoning by induction is apparently conclusive.

XVII. The last species of syllogism we shall take notice of in this chapter is that commonly distinguished by the name of a dilemma. A dilemma is an argument by which we endeavour to prove the absurdity or falsehood of some assertion. In order to this, we assume a conditional proposition, the antecedent of which is the assertion to be disproved, and the consequent a disjunctive proposition, enumerating all the possible suppositions upon which that assertion can take place. If then it appears, that all these several suppositions ought to be rejected, it is plain, that the antecedent or assertion itself must be so too. When therefore such a proposition as that before mentioned is made the major of any syllogism; if the minor rejects all the suppositions contained in the consequent, it follows necessarily, that the conclusion ought to reject the antecedent, which, as we have said, is the very assertion to be disproved. This particular way of arguing is that which logicians call a dilemma; and from the account here given of it, it appears that we may in the general define it to be a hypothetical syllogism, where the consequent of the major is a disjunctive proposition, which is wholly taken away or removed in the minor. Of this kind is the following:

"If God did not create the world perfect in its kind, it must either proceed from want of inclination, or from want of power. "But it could not proceed either from want of inclination, or from want of power. "Therefore he created the world perfect in its kind." Or, which is the same thing: "It is absurd to say that he did not create the world perfect in its kind."

XVIII. The nature then of a dilemma is universally this. The major is a conditional proposition, whose consequent contains all the several suppositions upon which the antecedent can take place. As therefore these suppositions are wholly removed in the minor, it is evident that the antecedent must be so too; inasmuch that we here always argue from the removal of the consequent to the removal of the antecedent. That is, a dilemma is an argument in the modus tollens of hypothetical syllogisms, as logicians love to speak. Hence it is plain, that if the antecedent of the major is an affirmative proposition, the conclusion of the dilemma will be negative; but if it is a negative proposition, the conclusion will be affirmative.

CHAP. V. Of Demonstration.

I. Having dispatched what seemed necessary to be said with regard to the forms of syllogisms, we now proceed proceed to explain their use and application in reasoning. We have seen, that in all the different appearances they put on, we still arrive at a just and legitimate conclusion; now it often happens, that the conclusion of one syllogism becomes a previous proposition in another; by which means great numbers of them are sometimes linked together in a series, and truths are made to follow one another in train. And as in such a concatenation of syllogisms all the various ways of reasoning that are truly conclusive may be with safety introduced; hence it is plain, that in deducing any truth from its first principles, especially where it lies at a considerable distance from them, we are at liberty to combine all the several kinds of arguments above explained, according as they are found best to suit the end and purpose of our inquiries.

When a proposition is thus by means of syllogisms collected from others more evident and known, it is said to be proved; so that we may in the general define the proof of a proposition to be a syllogism, or series of syllogisms, collecting that proposition from known and evident truths. But more particularly, if the syllogisms of which the proofs consist admit of no premises but definitions, self-evident truths, and propositions already established, then is the argument so constituted called a demonstration; whereby it appears that demonstrations are ultimately founded on definitions and self-evident propositions.

II. All syllogisms whatsoever, whether compound, multiform, or defective, are reducible to plain simple syllogisms in some one of the four figures. But this is not all. Syllogisms of the first figure, in particular, admit of all possible conclusions; that is, any propositions whatsoever, whether an universal affirmative or universal negative, a particular affirmative or particular negative, which fourfold division embraces all their varieties; any one of these may be inferred by virtue of some syllogism in the first figure. By this means it happens that the syllogisms of all the other figures are reducible also to syllogisms of the first figure, and may be considered as standing on the same foundation with them. We cannot here demonstrate and explain the manner of this reduction, because it would too much swell the bulk of this treatise. It is enough to take notice that the thing is universally known and allowed among logicians, to whose writings we refer such as desire farther satisfaction in this matter. This then being laid down, it is plain that any demonstration whatsoever may be considered as composed of a series of syllogisms, all in the first figure. For, since all the syllogisms that enter the demonstration are reducible to syllogisms of some one of the four figures; and since the syllogisms of all the other figures are farther reducible to syllogisms of the first figure, it is evident, that the whole demonstration may be resolved into a series of these last syllogisms. Let us now, if possible, discover the ground upon which the conclusion rests in syllogisms of the first figure; because, by so doing, we shall come at an universal principle of certainty, whence the evidence of all demonstrations in all their parts may be ultimately derived.

III. The rules then of the first figure are briefly these. The middle term is the subject of the major proposition, and the predicate of the minor. The major is always an universal proposition, and the minor always affirmative. Let us now see what effect these rules will have in reasoning. The major is an universal proposition, of which the middle term is the subject, and the predicate of the conclusion the predicate. Hence it appears, that in the major the predicate of the conclusion is always affirmed or denied universally of the middle term. Again, the minor is an affirmative proposition, whereof the subject of the conclusion is the subject, and the middle term the predicate. Here then the middle term is affirmed of the subject of the conclusion; that is, the subject of the conclusion is affirmed to be comprehended under, or to make a part of, the middle term. Thus then we see what is done in the premises of a syllogism of the first figure. The predicate of the conclusion is universally affirmed or denied of some idea. The subject of the conclusion is affirmed to be or to make a part of that idea. Hence it naturally and unavoidably follows, that the predicate of the conclusion ought to be affirmed or denied of the subject. To illustrate this by an example, we shall resume one of the syllogisms of the first chapter.

"Every creature possessed of reason and liberty is accountable for his actions."

"Man is a creature possessed of reason and liberty: Therefore man is accountable for his actions."

Here, in the first proposition, the predicate of the conclusion accountability is affirmed of all creatures that have reason and liberty. Again, in the second proposition, man, the subject of the conclusion, is affirmed to be or to make a part of this class of creatures. Hence the conclusion necessarily and unavoidably follows, viz., that man is accountable for his actions; because, if reason and liberty be that which constitutes a creature accountable, and man has reason and liberty, it is plain he has that which constitutes him accountable. In like manner, where the major is a negative proposition, or denies the predicate of the conclusion universally of the middle term, as the minor always affirms the subject of the conclusion, to be or make a part of that middle term, it is no less evident that the predicate of the conclusion ought in this case to be denied of the subject. So that the ground of reasoning, in all syllogisms of the first figure, is manifestly this: "Whatever may be affirmed universally of any idea, may be affirmed of every or any number of particulars comprehended under that idea." And again: "Whatever may be denied universally of any idea, may be in like manner denied of every or any number of its individuals." These two propositions are called by logicians the dictum de omni, and dictum de nullo; and are indeed the great principles of syllogistic reasoning, inasmuch as all conclusions whatsoever either rest immediately upon them, or upon propositions deduced from them. But what adds greatly to their value is, that they are really self-evident truths, and such as we cannot gainsay without running into an express contradiction. To affirm, for instance, that no man is perfect, and yet argue that some men are perfect; or to say that all men are mortal, and yet that some men are not mortal, is to assert a thing to be and not to be at the same time. IV. And now we may affirm, that, in all syllogisms of the first figure, if the premises are true, the conclusion must needs be true. If it be true that the predicate of the conclusion, whether affirmative or negative, agrees universally to some idea; and if it be also true that the subject of the conclusion is a part of or comprehended under that idea; then it necessarily follows, that the predicate of the conclusion agrees also to the subject. Far to assert the contrary, would be to run counter to some one of the two principles before established; that is, it would be to maintain an evident contradiction. And thus we are come at last to the point we have been all along endeavouring to establish; namely, that every proposition which can be demonstrated is necessarily true. For as every demonstration may be resolved into a series of syllogisms all in the first figure; and as in any one of these syllogisms, if the premises are true, the conclusion must needs be so too; it evidently follows, that if all the several premises are true, all the several conclusions are so, and consequently the conclusion also of the last syllogism, which is always the proposition to be demonstrated. Now that all the premises of a demonstration are true, will easily appear from the very nature and definition of that form of reasoning. A demonstration, as we have said, is a series of syllogisms, all whose premises are either definitions, self-evident truths, or propositions already established. Definitions are identical propositions, wherein we connect the description of an idea with the name by which we choose to have that idea called, and therefore as to their truth there can be no dispute. Self-evident propositions appear true of themselves, and leave no doubt or uncertainty in the mind. Propositions, before established, are no other than conclusions gained by one or more steps from definitions and self-evident principles; that is, from true premises, and therefore must needs be true. Whence all the previous propositions of a demonstration being, we see, manifestly true; the last conclusion, or proposition to be demonstrated, must be so too. So that demonstration not only leads to certain truth, but we have here also a clear view of the ground and foundation of that certainty. For as, in demonstrating, we may be said to do nothing more than combine a series of syllogisms together, all resting on the same bottom; it is plain that one uniform ground of certainty runs through the whole, and that the conclusions are everywhere built upon some one of the two principles before established, as the foundation of all our reasoning. These two principles are easily reduced into one, and may be expressed thus: "Whatever predicate, whether affirmative or negative, agrees universally to any idea;" "the same must needs agree to every or any number of individuals comprehended under that idea." And thus at length we have, according to our first design, reduced the certainty of demonstration to one simple and universal principle; which carries its own evidence along with it, and which is indeed the ultimate foundation of all syllogistic reasoning.

V. Demonstration therefore serving as an infallible guide to truth, and standing on so sure and unalterable a basis, we may now venture to assert, that the rules of logic furnish a sufficient criterion for the distinguishing between truth and falsehood. For since every proposition that can be demonstrated is necessarily true, he is able to distinguish truth from falsehood who can with certainty judge when a proposition is truly demonstrated. Now a demonstration is, as we have said, nothing more than a concatenation of syllogisms, all whose premises are definitions, self-evident truths, or propositions previously established. To judge therefore of the validity of a demonstration, we must be able to distinguish whether the definitions that enter it are genuine, and truly descriptive of the ideas they are meant to exhibit: whether the propositions affirmed without proofs as intuitive truths have really that self-evidence to which they lay claim: whether the syllogisms are drawn up in due form, and agreeable to the laws of argumentation: in fine, whether they are combined together in a just and orderly manner, so that no demonstrable propositions serve anywhere as premises unless they are conclusions of previous syllogisms. Now it is the business of logic, in explaining the several operations of the mind, fully to instruct us in all these points. It teaches the nature and end of definitions, and lays down the rules by which they ought to be framed. It unfolds the several species of propositions, and distinguishes the self-evident from the demonstrable. It delineates also the different forms of syllogisms, and explains the laws of argumentation proper to each. In fine, it describes the manner of combining syllogisms, so that they may form a train of reasoning, and lead to the effective discovery of truth. The precepts of logic therefore, as they enable us to judge with certainty when a proposition is duly demonstrated, furnish a sure criterion for the distinguishing between truth and falsehood.

VI. Perhaps it may be objected, that demonstration is a thing very rare and uncommon, as being the prerogative of but a few sciences, and therefore where a criterion here given can be of no great use. But certain wherever, by the bare contemplation of our ideas, knowledge truth is discoverable, there also demonstration may be attained. Now that is an abundantly sufficient criterion which enables us to judge with certainty in all cases where the knowledge of truth comes within our reach; for with discoveries, that lie beyond the limits of the human mind, we have, properly, no business or concernment. When a proposition is demonstrated, we are certain of its truth. When, on the contrary, our ideas are such as have no visible connection or repugnance, and therefore furnish not the proper means of tracing their agreement or disagreement, there we are sure that scientific knowledge is not attainable. But where there is some foundation of reasoning, which yet amounts not to the full evidence of demonstration, there the precepts of logic, by teaching us to determine aright of the degree of proof, and of what is still wanting to render it full and complete, enable us to make a due estimate of the measures of probability, and to proportion our assent to the grounds on which the proposition stands. And this is all we can possibly arrive at, or even so much as hope for, in the exercise of faculties so imperfect and limited as ours.

VII. Before we conclude this chapter, it may not be improper to take notice of the distinction of it into direct and indirect. Part III.

A direct demonstration is, when, beginning with definitions, self-evident propositions, or known and allowed truths, we form a train of syllogisms, and combine them in an orderly manner, continuing the series through a variety of successive steps, until at last we arrive at a syllogism whose conclusion is the proposition to be demonstrated. Proofs of this kind leave no doubt or uncertainty behind them; because, all the several premises being true, the conclusions must be so too, and of course the very last conclusion or proposition to be proved. The other species of demonstration is the indirect, or, as it is sometimes called, the apagogical. The manner of proceeding here is, by assuming a proposition which directly contradicts that we mean to demonstrate; and thence, by a continued train of reasoning, in the way of a direct demonstration, deducing some absurdity or manifest untruth. For hereupon we conclude, that the proposition assumed was false; and thence again, by an immediate consequence, that the proposition to be demonstrated is true. Thus Euclid, in his third book, being to demonstrate that circles which touch one another inwardly have not the same centre, assumes the direct contrary to this, viz. that they have the same centre; and thence, by an evident train of reasoning, proves that a part is equal to the whole. The supposition therefore leading to this absurdity he concludes to be false, viz. that circles touching one another inwardly have the same centre; and thence again immediately infers, that they have not the same centre.

VIII. Now, because this manner of demonstration is accounted by some not altogether so clear and satisfactory; we shall therefore endeavour to shew, that it equally with the other leads to truth and certainty. Two propositions are said to be contradictory one of another, when that which is asserted to be in the one is asserted not to be in the other. Thus the propositions, Circles that touch one another inwardly have the same centre, and Circles that touch one another inwardly have not the same centre, are contradictory; because the second affirms the direct contrary of what is affirmed in the first. Now, in all contradictory propositions, this holds universally, That one of them is necessarily true, and the other necessarily false. For if it be true, that circles which touch one another inwardly have not the same centre; it is unavoidably false, that they have the same centre. On the other hand, if it be false that they have the same centre, it is necessarily true that they have not the same centre. Since therefore it is impossible for them to be both true or both false at the same time; it unavoidably follows, that one is necessarily true, and the other necessarily false. This then being allowed, which is indeed self-evident, if any two contradictory propositions are assumed, and one of them can by a clear train of reasoning be demonstrated to be false; it necessarily follows, that the other is true. For as the one is necessarily true, and the other necessarily false; when we come to discover which is the false proposition, we thereby also know the other to be true.

IX. Now this is precisely the manner of an indirect demonstration, as is evident from the account given of it above. For there we assume a proposition which directly contradicts that we mean to demonstrate; and, having by a continued series of proofs shewn it to be false, thence infer, that its contradictory, or the proposition to be demonstrated, is true. As therefore this last conclusion is certain and unavoidable; let us next inquire after what manner we come to be satisfied of the falsehood of the assumed proposition, that so no possible doubt may remain as to the force and validity of demonstrations of this kind. The manner then is plainly this: Beginning with the assumed proposition, we, by the help of definitions, self-evident truths, or propositions already established, continue a series of reasoning, in the way of a direct demonstration, until at length we arrive at some absurdity or known falsehood. Thus Euclid, in the example before-mentioned, from the supposition that circles touching one another inwardly have the same centre, deduces, that a part is equal to the whole. Since therefore, by a due and orderly process of reasoning, we come at last to a false conclusion; it is manifest, that all the premises cannot be true; for, were all the premises true, the last conclusion must be so too, by what has been before demonstrated. Now, as to all the other premises made use of in the course of reasoning, they are manifest and known truths by supposition, as being either definitions, self-evident propositions, or truths previously established. The assumed proposition is that only as to which any doubt or uncertainty remains. That alone therefore can be false; and indeed, from what has been already shewn, must unavoidably be so. And thus we see, that in indirect demonstrations, two contradictory propositions being laid down, one of which is demonstrated to be false, the other, which is always the proposition to be proved, must necessarily be true; so that here, as well as in the direct way of proof, we arrive at a clear and satisfactory knowledge of truth.

X. This is universally the method of reasoning in all apagogical or indirect demonstrations. But if any proposition is assumed, from which, in a direct train of reasoning, we can deduce its contradictory; the proposition so assumed is false, and the contradictory one true. For if we suppose the assumed proposition to be true, then, since all the other premises that enter the demonstration are also true, we shall have a series of reasoning consisting wholly of true premises; whence the last conclusion or contradictory of the assumed proposition must be true likewise: so that by this means we should have two contradictory propositions both true at the same time, which is manifestly impossible. The assumed proposition therefore, whence this absurdity flows, must necessarily be false; and consequently its contradictory, which is here the proposition deduced from it, must be true. If then any proposition is proposed to be demonstrated, and we assume the contradictory of that proposition, and thence directly infer the proposition to be demonstrated; by this very means we know that the proposition so inferred is true. For since from an assumed proposition we have deduced its contradictory, we are thereby certain that the assumed proposition is false; and if so, then its contradictory, or that deduced from it, which in this case is the same with the proposition to be demonstrated, must be true.

XI. We have a curious instance of this in the twelfth proposition of the ninth book of the Elements. Euclid there proposes to demonstrate, that in any series...

Part III.

A due knowledge of numbers, rising from unity in geometrical progression, all the prime numbers that measure the last term of the series will also measure the next after unity. In order to this, he assumes the contradictory of the proposition to be demonstrated; namely, that some prime number measuring the last term in the series does not measure the next after unity; and thence, by a continued train of reasoning, proves that it actually does measure it. Hereupon he concludes the assumed proposition to be false; and that which is deduced from it, or its contradictory, which is the very proposition he proposed to demonstrate, to be true. Now that this is a just and conclusive way of reasoning, is abundantly manifest from what we have so clearly established above.

XI. Having thus sufficiently evinced the certainty of demonstration in all its branches, and shown the rules by which we ought to proceed, in order to arrive at a just conclusion, according to the various ways of arguing made use of; it is needless to enter upon a particular consideration of those several species of false reasoning. And of which logicians distinguish by the name of sophism, it is sufficient to He that thoroughly understands the form and structure of a good argument, will of himself readily discern error even the slightest deviation from it. And although sophisms and fallacies have been divided into many classes, which are all called by sounding names, that therefore carry in them much appearance of learning; yet are the errors themselves so very palpable and obvious, that it would be lost labour to write for a man capable of being misled by them. Here therefore we choose to conclude this part of logic; and shall in the next give some account of Method: which, though inseparable from reasoning, is nevertheless always considered by logicians as a distinct operation of the mind; because its influence is not confined to the mere exercise of the reasoning faculty, but extends in some degree to all the transactions of the understanding.

PART IV.

OF METHOD.

We have now done with the three first operations of the mind, whose office it is to search after truth, and enlarge the bounds of human knowledge. There is yet a fourth, which regards the disposure and arrangement of our thoughts, when we endeavour to put them together as that their mutual connection and dependence may be clearly seen. This is what logicians call Method, and place always the last in order in explaining the powers of the understanding; because it necessarily supposes a previous exercise of our other faculties, and some progress made in knowledge, before we can exert it in any extensive degree.

II. In this view, it is plain that we must be beforehand well acquainted with the truths we are to combine together; otherwise, how could we discern their several connections and relations, or dispose of them as their mutual dependence may require? But it often happens, that the understanding is employed, not in the arrangement and composition of known truths, but in the search and discovery of such as are unknown. And here the manner of proceeding is very different. We assemble at once our whole stock of knowledge relating to any subject, and, after a general survey of things, begin with examining them separately and by parts. Hence it comes to pass, that whereas, at our first setting out, we were acquainted only with some of the grand strokes and outlines of truth; by thus pursuing her through her several windings and recesses, we gradually discover those more inward and finer touches whence she derives all her strength, symmetry, and beauty. And here it is, that when, by a narrow scrutiny into things, we have unravelled any part of knowledge, and traced it to its first and original principles, inasmuch that the whole frame and contexture of it lies open to the view of the mind; here it is, that, taking it the contrary way, and beginning with these principles, we can so adjust and put together the parts as the order and method of science requires.

III. But as these things are best understood when illustrated by examples; let us suppose any machine, for instance a watch, presented to us, whose structure and composition we are as yet unacquainted with, but illustrate want, if possible, to discover. The manner of proceeding, in this case, is, by taking the whole to pieces, watch, and examining the parts separately, one after another. When, by such a scrutiny, we have thoroughly informed ourselves of the frame and contexture of each, we then compare them together, in order to judge of their mutual action and influence. By this means we gradually trace out the inward make and composition of the whole, and come at length to discern how parts of such a form, and to put together as we found in unravelling and taking them asunder, constitute that particular machine called a watch, and contribute to all the several motions and phenomena observable in it. This discovery being made, we can take things the contrary way, and, beginning with the parts, to dispose and connect them as their several uses and structures require, until at length we arrive at the whole itself, from the unravelling of which these parts resulted.

IV. And as it is in tracing and examining the works Ground of art; so is it, in a great measure, in unfolding any part and synthesis of human knowledge: for the relations and mutual methods-habitudes of things do not always immediately appear upon comparing them one with another. Hence we have recourse to intermediate ideas; and, by means of them, are furnished with those previous propositions that lead to the conclusion we are in quest of. And if it happen that the previous propositions themselves are not sufficiently evident, we endeavour, by new middle terms, to ascertain their truth; still tracing things backward, in a continual series, until at length we arrive at some syllogism where the premises are first and self-evident principles. This done, we become perfectly satisfied as to the truth of all the conclusions we have passed through, inasmuch as they are now seen to stand upon the firm and immovable foundation of our intuitive perceptions. And as we arrived at this certainty by tracing things backward to the original principles whence they flow; so may we we at any time renew it by a direct contrary process, if, beginning with these principles, we carry the train of our thoughts forward until they lead us, by a connected chain of proofs, to the very last conclusion of the series.

V. Hence it appears, that, in disposing and putting together our thoughts, either for our own use, that the discoveries we have made may at all times lie open to the review of the mind, or where we mean to communicate and unfold the discoveries to others, there are two ways of proceeding equally within our choice: for we may propose the truths relating to any part of knowledge, as they presented themselves to the mind in the manner of investigation; carrying on the series of proofs, in a reverse order, until they at last terminate in first principles: or, beginning with these principles, we may take the contrary way, and from them deduce, by a direct train of reasoning, all the several propositions we want to establish. This diversity in the manner of arranging our thoughts gives rise to the twofold division of method established among logicians: for method, according to their use of the word, is nothing else but the order and disposition of our thoughts relating to any subject. When truths are so proposed and put together as they were or might have been discovered, this is called the analytic method, or the method of resolution; insomuch as it traces things backward to their source, and resolves knowledge into its first and original principles. When, on the other hand, they are deduced from these principles, and connected according to their mutual dependence, insomuch that the truths first in order tend always to the demonstration of those that follow; this constitutes what we call the synthetic method, or method of composition. For here we proceed by gathering together the several scattered parts of knowledge, and combining them into one whole or system, in such manner that the understanding is enabled distinctly to follow truth through all her different stages and gradations.

VI. There is this farther to be taken notice of, in relation to these two species of method; that the first has also obtained the name of the method of invention, because it observes the order in which our thoughts succeed one another in the invention or discovery of truth. The other, again, is often denominated the method of doctrine or instruction; insomuch as, in laying our thoughts before others, we generally choose to proceed in the synthetic manner, deducing them from their first principles. For we are to observe, that although there is great pleasure in pursuing truth in the method of investigation, because it places us in the condition of the inventor, and shews the particular train and process of thinking by which he arrived at his discoveries; yet is it not so well accommodated to the purposes of evidence and conviction. For, at our first setting out, we are commonly unable to divine where the analysis will lead us; insomuch that our researches are for some time little better than a mere groping in the dark. And even after light begins to break in upon us, we are still obliged to many reviews, and a frequent comparison of the several steps of the investigation among themselves. Nay, when we have unravelled the whole, and reached the very foundation on which our discoveries stand, all our certainty, in regard to their truth, will be found in a great measure to arise from that connection we are now able to discern between them and first principles, taken in the order of composition. But in the synthetic manner of disposing our thoughts, the case is quite different: for as we here begin with the intuitive truths, and advance by regular deductions from them, every step of the procedure brings evidence and conviction along with it; so that, in our progress from one part of knowledge to another, we have always a clear perception of the ground on which our assent rests. In communicating therefore our discoveries to others, this method is apparently to be chosen, as it wonderfully improves and enlightens the understanding, and leads to an immediate perception of truth.