Rule XIII
If we perfectly understand a problem we must abstract it from every superfluous conception, reduce it to its simplest terms and, by means of an enumeration, divide it up into the smallest possible parts.
Rule XIV
The problem should be re-expressed in terms of the real extension of bodies and should be pictured in our imagination entirely by means of bare figures. Thus it will be perceived much more distinctly by our intellect.
Rule XV
It is generally helpful if we draw these figures and display them before our external senses. In this way it will be easier for us to keep our mind alert.
Rule XVI
As for things which do not require the immediate attention of the mind, however necessary they may be for the conclusion, it is better to represent them by very concise symbols rather than by complete figures. It will thus be impossible for our memory to go wrong, and our mind will not be distracted by having to retain these while it is taken up with deducing other matters.
Rule XVII
We should make a direct survey of the problem to be solved, disregarding the fact that some of its terms are known and others unknown, and intuiting, through a train of sound reasoning, the dependence of one term on another.
Rule XVIII
For this purpose only four operations are required: addition, subtraction, multiplication and division. The latter two operations should seldom be employed here, for they may lead to needless complication, and they can be carried out more easily later.
Rule XIX
Using this method of reasoning, we must try to find as many magnitudes, expressed in two different ways, as there are unknown terms, which we treat as known in order to work out the problem in the direct way. That will give us as many comparisons between two equal terms.
Rule XX
Once we have found the equations, we must carry out the operations which we have left aside, never using multiplication when division is in order.
Rule XXI
If there are many equations of this sort, they should all be reduced to a single one, viz. to the equation whose terms occupy fewer places in the series of magnitudes which are in continued proportion, i.e. the series in which the order of the terms is to be arranged.
THE SEARCH FOR TRUTH
Translated by Elizabeth S. Haldane and G. R. T. Ross
CONTENTS
PREFATORY NOTE TO ‘THE SEARCH AFTER TRUTH.’
THE SEARCH AFTER TRUTH BY THE LIGHT OF NATURE.
PREFATORY NOTE TO ‘THE SEARCH AFTER TRUTH.’
This unfinished Dialogue, Descartes’ biographer Baillet tells us, was intended to form two volumes written in French. A Latin translation appeared in an edition of 1701 published at Amsterdam. Leibniz was known to have ‘a Dialogue in French’ amongst the unpublished papers of Descartes, and this French text was sought for in vain by MM. Adam and Tannery at the Royal Library of Hanover where it was likely to be found. A young student named Jules Sire was, however, fortunate enough to discover, not Leibniz’s original copy but another. Leibniz was in Paris with Tschirnhaus, and he took Tschirnhaus to see Clerselier, who had what remained of Descartes’ papers. Tschirnhaus copied ‘The Search after Truth’ and sent it to Leibniz, and this was the copy discovered by Sire. We do not know whether Clerselier’s copy was incomplete, or Tschirnhaus’ transcription of it, but it does not give more than half of the Latin version of 1701. Leibniz himself added at the end, ‘I have the rest elsewhere.’ MM. Adam and Tannery thus published Tschirnhaus’s copy of the original in French, completing it from the Latin, and this is the edition here used. The date of the work is unknown.
E. S. H.
THE SEARCH AFTER TRUTH BY THE LIGHT OF NATURE.
The Search after Truth by means of the Light of Nature which alone, and without the assistance of Religion or Philosophy, determines what are the opinions which a good man should hold on all matters which may occupy his thoughts, and which penetrate into the secrets of the most curious of the sciences.
A good man has no need to have read every book, nor to have carefully learned all that which is taught in the Schools; it would even be a defect in his education were he to have devoted too much of his time to the study of letters. There are many other things to do in life, and he has to direct that life in such a manner that the greater part of it shall remain to him for the performance of good actions which his own reason ought to teach him, even supposing that he were to receive his lessons from it alone. But he comes into the world in ignorance, and as the knowledge of his earliest years rests only on the weakness of the senses and the authority of masters, he can scarcely avoid his imagination being filled with an infinite number of false ideas, before his reason has the power of taking his conduct into its own hands; in consequence he requires to have good natural endowments or else instruction from a wise man, both in order to rid himself of the false doctrines with which his mind is filled, and for building the first foundations of a solid knowledge, and discovering all the means by which he may carry his knowledge to the highest point to which it can possibly attain.
In this work I propose to show what these means are, and to bring to light the true riches of our souls, by opening to each one the road by which he can find in himself, and without borrowing from any, the whole knowledge which is essential to him in the direction of his life, and then by his study succeed in acquiring the most curious forms of knowledge that the human reason is capable of possessing.
R. H.
But in order that the greatness of my scheme may not to begin with seize your minds with an astonishment so great that confidence in my words can no longer find therein a place, I warn you that what I undertake is not as difficult as might be imagined. Those branches of knowledge which do not extend beyond the capacities of the human mind are, as a matter of fact, united by a bond so marvellous, they are capable of being deduced from one another by sequences so necessary, that it is not essential to possess much art or address in order to discover them, provided that by commencing with those that are most simple we learn gradually to raise ourselves to the most sublime. That is what I shall try to show you here by a system of reasoning so clear and yet so simple, that every one will be able to judge for himself that if he has not observed the same things, it is solely because he has not cast his eyes in the right direction, nor fixed his thoughts on the same considerations as I, and that no more glory is due to me for having discovered them, than is due to a casual passer-by for having accidentally discovered under his feet a rich treasure which had for long successfully eluded the searches of many.
And certainly I am surprised that amongst so many distinguished minds which in a matter of this description should have succeeded much better than I, none have had the patience to find their way out of their difficulties; and that nearly all have followed in the footsteps of these travellers who, abandoning the main route in favour of a cross-road, find themselves lost amongst briars and precipices.
But I do not desire to examine into what others have known or have been ignorant of. It will suffice for me to note that even if all the knowledge which we can desire is to be found in books, that which they contain of good is mingled with so many futilities, and confusedly dispersed in such a mass of great volumes, that, in order to read them, more time would be requisite than human life can supply us with, and more talent in discovering the useful than would be required in ascertaining it for ourselves.
That is what makes me hope that the reader will not be vexed by here finding an easier path, and that the facts which I shall advance will not be the less well received, even although I do not borrow them from Plato or Aristotle, but show that they have current value in the world, just as has money which is in nowise of less value when it proceeds from the purse of a peasant than when it comes from the treasury. I have even made it my business to make them equally useful to all men; and I have not been able to discover a style better adapted to this end than that of genuine conversation, wherein ea
ch one familiarly explains to his friends the best of his thoughts. And under the names Eudoxus, Polyander, and Epistemon, I assume that a man endowed with ordinary mental gifts, but whose judgment is not spoiled by any false ideas, and who is in possession of his whole reason in all the purity of its nature, receives as his guests in the country house which he inhabits, two men the most distinguished and interesting of their time, one of whom has studied not at all, while the other is well acquainted with all that can be learnt in the Schools. And there (in the midst of other discourse which each one can imagine for himself, as well as the local conditions and particular surroundings from which I shall frequently cause them to take examples in order to make their conceptions more clear), they thus introduce the subject of which they will afterwards treat to the end of these two books.
Polyander, Epistemon, Eudoxus.
Polyander. I consider you are so fortunate in having discovered all these wonderful things in the Greek and Latin books, that it seems to me that if I had studied as much as you, I should be as different from what I now am, as angels are from you. And I cannot excuse the folly of my parents who, being persuaded that the study of letters would enfeeble the mind, sent me to the court and camps at so early an age, that I should all my life have had to bewail my ignorance, had I not learned something from my association with you.
Epistemon. The best thing that you could be taught on this subject is that the desire for knowledge, which is common to all men, is an evil which cannot be cured, for curiosity increases with knowledge; and as the deficiencies that are present in our soul only trouble us in so far as we recognise them, you have a certain advantage over us, in that you do not see as we do, that many things are lacking to you.
Eudoxus. Can it be, Epistemon, that you who are so well instructed, can believe that there is in nature any evil so universal that there is no remedy to be applied to it? As for me, I consider that just as there are in each country sufficient fruits and rivers to appease the hunger and thirst of all men, so there are truths that can be known in every matter sufficient to satisfy fully the curiosity of healthy minds; and I think that the body of a dropsical patient is not further removed from its normal condition than the mind of those who are perpetually worked upon by an insatiable curiosity.
Epistemon. I have, it is true, heard in former times that our desires could not extend naturally to things that seemed to us impossible, and that it ought not to do so to those that are vicious or useless; but so many things can be known which appear possible to us, and which are not only good and agreeable, but also very necessary in the conduct of life, that I cannot believe that anyone ever knew enough of them not to have legitimate reasons always to desire to know more.
Eudoxus. What, then, would you say of me, if I tell you that I no longer feel any desire to learn anything at all, and that I am as happy with my small knowledge as Diogenes used to be with his tub, and all this without my having any need of his philosophy? For the knowledge of my neighbours is not the limit of my own, as are their fields which here surround the small piece of ground that I possess; and my mind at its own will disposing of all the truths which it comes across, does not dream that there are others to discover. For it enjoys the same repose that the king of an isolated country would have were he so separated from all others as to imagine that beyond his frontiers there was nothing but unfertile deserts and uninhabitable mountains.
Epistemon. If any other but you spoke to me thus, I should regard him as one whose mind was either very vain or else too little given to curiosity; but the retreat which you have chosen in this solitude, and the small amount of pains that you take to become known, removes from you the charge of vanity; and the time you have hitherto consecrated to journeyings, visiting learned men, and examining everything that is most difficult in each science, suffices to assure us that you are not lacking in curiosity. I can hence say nothing but that I consider you very happy and that I am convinced that you must be in the possession of a knowledge much more perfect than that of others.
Eudoxus. I thank you for the good opinion in which you hold me, but I do not desire to abuse your courtesy to the point of desiring that you should believe what I have just said, solely on the faith of my words. We must not advance opinions so far removed from vulgar beliefs, without at the same time being able to demonstrate certain effects from so doing; that is why I beg you both to be good enough to spend this delightful season here, so that I may have the opportunity of openly showing you some part of the things that I know. For I venture to flatter myself that not alone will you recognise that I have some reason for being happy in this knowledge, but, in addition, that you yourselves will have much happiness from the things that you will have learned.
Epistemon. I would not wish to refuse a favour that already I so ardently desired of you.
Polyander. And I shall have great pleasure in being present at this discussion, not that I believe myself capable of deriving any good from it.
Eudoxus. On the contrary, Polyander, believe me it will be you who will derive advantage from it, because you are quite unprejudiced, and it will be easier for me to guide aright any one with an open mind than Epistemon, whom we shall often find in opposition to us. But in order to make you more easily understand the nature of the knowledge of which I am going to treat, I beg you to observe a difference which exists between the sciences and those simple forms of knowledge which can be acquired without the aid of reasoning, such as languages, history, geography, &c., or to speak generally, everything that depends on experience alone. I am ready to grant that the life of a man would not suffice to acquire a knowledge of all that the world contains; but I am also persuaded that it would be folly to desire that it should be so, and that it is no longer the duty of an ordinary well-disposed man to know Greek and Latin any more than it is to know the languages of Switzerland or Brittany; or that the history of the Empire should be known any more than that of the smallest state in Europe. And I consider that such a one should consecrate his leisure to good and useful things alone, and occupy his memory only with those that are most necessary. As to those sciences which are nothing but the judgments which we base on some knowledge previously acquired, some are deduced from common objects of which every one is cognisant, and others from rare and well thought out experiments. And I confess likewise that it would be impossible for us to treat in detail each one of these last; for we should first of all have to examine all the herbs and stones brought to us from the Indies; we should have to have beheld the phoenix, and in a word to be ignorant of none of the marvellous secrets of nature. But I shall believe myself to have sufficiently fulfilled my promise if, in explaining to you the truths which may be deduced from common things known to each one of us, I make you capable of discovering all the others when it pleases you to take the trouble to seek them.
Polyander. - For my part I believe that this is likewise all that it is possible to desire, and I would have been satisfied if you had merely taught me a certain number of propositions which are so celebrated that no one can be ignorant of them, such as those that concern the Deity, the rational soul, the virtues, their reward, &c., propositions which I compare with those ancient families which every one recognises as the most illustrious, although the titles of their nobility are concealed under the ruins of antiquity. For I do not really doubt that those who first of all induced the human race to believe in all these things had excellent reasons for proving them; but their arguments have been so rarely repeated since, that no one knows them any longer: and yet they are truths so important, that the dictates of prudence tell us that we should believe them blindly at the risk of being deceived, rather than that we should await a future life in order to be further instructed in them.