Part IV, Chapter 2: Of the Two Kinds of Method, Analysis and Synthesis
METHOD may be called, in general, the art of disposing well a series of many thoughts, either for the discovering truth when we are ignorant of it, or for proving it to others when it is already known.
Thus there are two kinds of method, one for discovering truth, which is called analysis, or the method of resolution, and which may also be called the method of invention; and the other for explaining it to others when we have found it, which is called synthesis, or the method of composition, and which may be also called the method of doctrine. We do not commonly treat of the entire body of a science by analysis, but employ it only to resolve some question. All questions are either of words or things. By questions of words we here mean, not those in which we inquire into words, but those in which, through the words, we inquire into things, as those in which we engage to find the sense of an enigma, or to explain, from obscure or ambiguous words, what is the true meaning of an author. Questions of things may be reduced to four principal kinds: the first is, when we seek causes through effects. We know, for example, the different effects of the loadstone—we inquire into the cause of these; we know the different effects which are commonly attributed to the abhorrence of a vacuum—we inquire whether that is the true cause, and we have found that it is not; we know the ebb and flow of the sea—we ask what can be the cause of a motion so great and so regular.
The second is, when we seek effects through causes. It was always, for example, known that wind and water possessed great power over the movements of bodies; but the ancients, not having sufficiently examined what effects might flow from these causes, did not apply them as they have since been applied, by means of mills, to a great number of purposes very useful to society, which wonderfully lessen the labour of men, which ought to be the result of true physics: so that we may say that the first kind of questions in which we seek causes through effects, constitute the speculative part of physics; and the second kind, in which we seek effects by causes, the practical.
The third kind of questions is, when through the parts we seek the whole: as when, having many numbers, we seek their sum by adding them together; or when, having two, we seek their product by multiplying them together.
Author’s note: The greater part of what is here said of questions is taken from a MS. of the late M. Descartes, which M. Clercelier had the goodness to lend me.
The fourth is, when, having the whole and some part, we seek another part; as when, having one number and another which is to be subtracted from it, we seek what remains; or when, having a number, we seek what such a part of it will be.
But it must be remarked that, in order to extend further the two last kinds of questions, and in order that we may comprehend what cannot be properly brought under the two first, it is necessary to take the word part in its most general signification for all which a thing comprises—its modes, its extremities, its accidents, its properties, and, in general, all its attributes, so that, for example, we shall seek the whole by its parts when we seek to find the area of a triangle from its height and base, and we shall, on the contrary, seek a part by the whole, and another part when we seek to find the side of a rectangle from knowing its area and one of its sides.
Now, whatever may be the nature of the question which we propose to resolve, the first thing which we must do is to conceive, accurately and distinctly, precisely what it is we are seeking, that is, what is the precise point of the question. For we must avoid what happens to some, who, by a precipitation of mind, engage in the resolution of what is proposed to them before having sufficiently considered by what signs or marks they might recognise what they seek for if they met with it, as a valet, who, when commanded by his master to fetch one of his friends, should hurry away before having learnt more particularly from his master who that friend was.
Now, although in every question there is something unknown, otherwise there would be nothing to seek, it is, nevertheless, necessary that even that which is unknown should be marked out and designated by certain conditions which may determine us to seek one thing rather than another, and which may enable us to judge, when we have found it, that it is the thing of which we were in search. And these conditions ought to be well considered beforehand, that we may not add anything which is not contained in that which is proposed, and that we may not omit anything which it does contain, for we may sin in both these ways.
We should sin in the first way, if when, for example, we were asked what animal that is which goes in the morning on four feet, at mid-day on two, and in the evening on three, we believed ourselves obliged to take all these words, feet, morning, middle-day, evening, in their strict and literal meaning; for he who proposes this enigma has not laid it down as a condition that we must take them in this way, but it is sufficient that these words may, by metaphor, be referred to other things, and thus that question is properly resolved when we say that animal is man.
Suppose, again, that we were asked by what artifice the figure of a Tantalus could have been made, which, lying on a column in the midst of a vase in the posture of a man who bent down to drink, was never able to do so, because the water, though able to rise very well in the vase up to his mouth, as soon as it reached his lips all flowed away, until none was left in the vase. We should sin by adding conditions which would not at all contribute towards the solution of this question, if we were to busy ourselves in seeking after some secret wonder in the figure of this Tantalus, which caused the water to flow away as soon as it had touched his lips—for this is not involved in the question—and if we would conceive it aright, we ought to reduce it to these terms:—To make a vase which would hold water so long as it was filled to a certain height, and which would let it all flow away again if it were filled beyond. And this is very easy, for we need only hide in the column a syphon which has one small opening below, through which the water enters, and the longer leg of which has an opening below the foot of the vase; so long as the water which we put in the vase does not reach the height of the syphon it will remain there, but when it reaches it, it will all flow away through the longer leg of the syphon, which is hidden below the foot of the vase.
It is asked, again, What could be the secret of that water drinker who exhibited himself at Paris twenty years ago, and how it could be that in throwing out water from his mouth he filled, at the same time, five or six different glasses with water of different colours? If we imagine that these waters of different colours were in his stomach, and he separated them in throwing them up, one into one glass and another into another, we should inquire after a secret which we could never find, since it is not possible; whereas we ought to inquire only how water coming at the same time from the same mouth appeared of different colours in each of these glasses, and it is very likely that this would be from some tincture that he had placed at the bottom of each of these glasses.
It is also an artifice of those who propose questions which they do not wish should be easily resolved, to surround that which is to be found with so many conditions which are useless, and which do not contribute anything to its discovery, that we cannot easily detect the true point of the question, and that we thus lose time, and uselessly weary the mind in keeping its attention fixed on things which do not at all contribute to resolve it.
The other way in which we sin in the examination of the conditions of what we seek, is, when we omit some things which are essential to the question proposed. It is proposed, for example, to find, by art, perpetual motion; for we know well that there are some which are perpetual in nature, such as the movements of fountains, of rivers, of seas. There are some who, having imagined that the earth turns on its centre, and that it is only a great magnet, of which the loadstone has all the properties, have also believed that we might dispose a magnet so that it would always turn circularly; but even if this were so, we should not then solve the problem of finding, by art, perpetual motion, since that motion would be as natural as that of a wheel exposed to the current of a river.
When, therefore, we have well examined the conditions which designate and mark out what is unknown in the question, we must then examine what is known, since it is through this that we must arrive at the knowledge of what is unknown; for we need not imagine that we shall find a new kind of being, inasmuch as our intelligence can go no further than the recognition that what we seek participates in such and such a way in the nature of things already known. If, for example, a man were blind from birth, it would be in vain to seek after arguments and proofs to convey to him the true idea of colours such as we possess through sense; and so, if the magnet about which we interrogate nature, were a new kind of being, the like of which our mind had never conceived, we could never attain to the knowledge of it by reasoning, for we should need for this a different mind from our own. And so we ought to believe that we have found all that can be found by the human mind, if we can distinctly conceive such a mixture of the beings and natures which are known to us as may produce all the effects which we see in the magnet.
Now it is in the attention we give to that which is known in the question we wish to resolve, that analysis mainly consists, the whole art being to derive, from this examination, many truths which may conduct us to the knowledge of what we seek.
As, suppose it be asked whether the soul of man is immortal, and that, in order to discover this, we apply ourselves to consider the nature of the soul, we remark, in the first place, respecting it, that it is the property of the soul to think, and that it may doubt of everything else without being able to doubt whether it thinks, since doubt itself is a thought. We then inquire what it is to think, and finding that nothing is contained in the idea of thought which belongs to the idea of substance extended, which we call body, and that we may even deny of thought everything which belongs to body (such as being long, short, deep, having diversity of parts, and being of such or such a figure, being divisible, &c.), without destroying, on that account, the idea which we have of thought, we conclude from this that thought is not a mode of substance extended, since, according to the nature of a mode, it cannot be conceived to exist when that of which it was the mode is denied. Whence, we infer again, that thought not being a mode of substance extended, must be the attribute of another substance, and that thus the substance which thinks and the substance extended are two substances really distinct; from which it follows that the destruction of the one does not involve the destruction of the other, since even the substance extended is not properly destroyed, but that all which happens in what we call destruction is nothing more than the change or dissolution of some parts of matter which always remain in nature, as we know well enough that in breaking all the wheels of a clock none of its substance is destroyed, although we say that the clock is destroyed; which proves that the soul, not being divisible, and not being composed of any parts, cannot perish, and is, therefore, immortal.
This is what is called analysis or resolution, on which it may be remarked: —
1st, That we ought to observe in it, as well as in the method, which is called that of composition, always to pass from that which is more known to that which is less; for there is not any true method which can dispense with this rule.
2d, But it differs from that of composition in this—that we take those truths known in the particular examination from the thing which we are supposed to know, and not from things more general, as we do in the method of doctrine. Thus, in the example which we have given, we did not begin by the establishment of these general maxims:—That no substance perishes, properly speaking; that what is called destruction is only a dissolution of parts; that thus that which has no parts cannot be destroyed, &c. But we ascended by degrees to these general knowledges.
3°. We propose clear and evident maxims only in proportion as we need them, whereas, in the other, we establish them at first, as will be shown hereafter.
4°. Finally, these two methods differ only as the road by which we ascend from a valley to a mountain from that by which we descend from the mountain into the valley, which is no difference of road, but only a difference in the going; or, as the two ways differ, which we may employ to prove that a person is descended from St Louis, of which the one is to show that this person had such a one for his father, who was the son of such a one, and he of another, and so on to St Louis; and the other, that of commencing with St Louis, and showing that he had such children, and that from these children others descended down to the person in question. And this example is the more suitable on this occasion, since it is certain, that, in order to find an unknown genealogy, we must remount from the son to the father, whereas, in explaining it after it has been found, the most common method is to commence with the stock, in order to show the descendants from it, which is also what is commonly done in the sciences, where, after having used analysis to find some truth, we employ the other method for explaining what is found.
We may hence understand that this is the analysis of the geometers; for it proceeds as follows:—A question having been proposed to them, in relation to which they are ignorant—if it be a theorem, of its truth or falsehood; if a problem, of its possibility or impossibility—they assume that it is as it is proposed; and examining what follows from this, if they arrive, in that examination, at some clear truth from which what is proposed to them is a necessary consequence, they conclude from this that what is proposed to them is true; and, returning then through the way they had come, they demonstrate it by another method which is called composition. But if they fall, as a necessary consequence from what is proposed to them, into some absurdity or impossibility, they conclude from this, that what is proposed to them is false and impossible.
This is what may be said generally touching analysis, which consists more in judgment and sagacity of mind than in particular rules. The four following, nevertheless, which M. Descartes proposes in his method, may be useful for preserving us from error, when seeking after the truth in human sciences, although, indeed, they apply generally to all kinds of method, and not specially to analysis alone.
The first is, Never to accept anything as true which we do not clearly know to be so, that is to say, to avoid carefully precipitation and prejudice, and to comprise nothing more in our judgments than what is presented so clearly to the mind that we have no room to doubt it.
The second, To divide each of the difficulties we examine into as many parts as possible, and as may be necessary for resolving it.
A third, To conduct our thoughts in order, by commencing with objects the most simple and the most easily known, in order to ascend by degrees to the knowledge of the most complex, supposing even, from the order between them, that they do not naturally precede each other.
The fourth, to make, in relation to everything, enumerations so complete that we may be assured of having omitted nothing.
It is true that there is much difficulty in observing these rules, but it is always advantageous to have them in the mind, and to observe them as much as possible when we try to discover the truth by means of reason, and as far as our mind is capable of knowing it.