I was then in Germany, attracted thither by the wars in that country, which have not yet been brought to a termination; and as I was returning to the army from the coronation of the emperor, the setting in of winter arrested me in a locality where, as I found no society to interest me, and was besides fortunately undisturbed by any cares or passions, I remained the whole day in seclusion, with full opportunity to occupy my attention with my own thoughts. Of these one of the very first that occurred to me was, that there is seldom so much perfection in works composed of many separate parts, upon which different hands had been employed, as in those completed by a single master. Thus it is observable that the buildings which a single architect has planned and executed, are generally more elegant and commodious than those which several have attempted to improve, by making old walls serve for purposes for which they were not originally built. Thus also, those ancient cities which, from being at first only villages, have become, in course of time, large towns, are usually but ill laid out compared with the regularity constructed towns which a professional architect has freely planned on an open plain; so that although the several buildings of the former may often equal or surpass in beauty those of the latter, yet when one observes their indiscriminate juxtaposition, there a large one and here a small, and the consequent crookedness and irregularity of the streets, one is disposed to allege that chance rather than any human will guided by reason must have led to such an arrangement. And if we consider that nevertheless there have been at all times certain officers whose duty it was to see that private buildings contributed to public ornament, the difficulty of reaching high perfection with but the materials of others to operate on, will be readily acknowledged. In the same way I fancied that those nations which, starting from a semi-barbarous state and advancing to civilization by slow degrees, have had their laws successively determined, and, as it were, forced upon them simply by experience of the hurtfulness of particular crimes and disputes, would by this process come to be possessed of less perfect institutions than those which, from the commencement of their association as communities, have followed the appointments of some wise legislator. It is thus quite certain that the constitution of the true religion, the ordinances of which are derived from God, must be incomparably superior to that of every other. And, to speak of human affairs, I believe that the pre-eminence of Sparta was due not to the goodness of each of its laws in particular, for many of these were very strange, and even opposed to good morals, but to the circumstance that, originated by a single individual, they all tended to a single end. In the same way I thought that the sciences contained in books (such of them at least as are made up of probable reasonings, without demonstrations), composed as they are of the opinions of many different individuals massed together, are farther removed from truth than the simple inferences which a man of good sense using his natural and unprejudiced judgment draws respecting the matters of his experience. And because we have all to pass through a state of infancy to manhood, and have been of necessity, for a length of time, governed by our desires and preceptors (whose dictates were frequently conflicting, while neither perhaps always counseled us for the best), I farther concluded that it is almost impossible that our judgments can be so correct or solid as they would have been, had our reason been mature from the moment of our birth, and had we always been guided by it alone.
I was then in Germany, drawn there by the wars that have still not ended. I was returning to the army from the emperor’s coronation when winter forced me to stop in a certain place. There I found no company that interested me. Fortunately, I was also free from worries or strong emotions. So I spent the whole day alone, with plenty of time to consider my own thoughts. One of my first thoughts was about works assembled from many separate parts made by different people. Such works are seldom as perfect as those completed by a single master. Buildings planned and completed by one architect, for example, are generally more elegant and practical than buildings altered by several. Those alterations involve adapting old walls to purposes for which the walls were never built. The same is true of ancient cities that began as villages and grew over time into large towns. Such cities are usually poorly laid out compared with orderly towns freely planned by an architect on an open plain. Although individual buildings in the older cities may often equal or surpass the newer ones in beauty, their arrangement is haphazard. A large building stands here, a small one there, making the streets crooked and irregular. Seeing this arrangement, we are inclined to attribute it to chance rather than to human planning guided by reason. Yet there have always been officials responsible for ensuring that private buildings added to the beauty of public spaces. If we consider their efforts, we readily recognize how difficult perfection is when working only with materials supplied by others. I imagined something similar about nations that began in a partly barbarous state and slowly advanced toward civilization. Their laws developed one after another, forced upon them, so to speak, simply by experiencing the harm of particular crimes and disputes. I thought this process would give them less perfect institutions than nations guided from the beginning by a wise lawmaker’s rules. Thus, the organization of the true religion, whose laws come from God, must certainly be incomparably superior to every other religion’s. Turning to human affairs, I believe Sparta’s superiority did not come from the merits of each individual law. Many of its laws were very strange and even contrary to good morals. Rather, Sparta’s superiority came from having laws created by a single person, all directed toward a single goal. I thought the same about the sciences found in books, at least those based on probable reasoning rather than demonstrations. These sciences consist of the collected opinions of many different people. I thought they were further from the truth than the simple conclusions drawn by a person of good sense. Such a person uses natural, unbiased judgment to consider matters within their own experience. Finally, we must all pass through childhood before reaching adulthood. For a long time, we are necessarily governed by our desires and our teachers. Their instructions often conflict, and perhaps neither our desires nor our teachers always guide us toward what is best. Because of this, I reached a further conclusion about our judgments. They can almost never be as sound or accurate as they would have been under different conditions. That is, if our reason had been mature from birth, and we had always followed reason alone.
It is true, however, that it is not customary to pull down all the houses of a town with the single design of rebuilding them differently, and thereby rendering the streets more handsome; but it often happens that a private individual takes down his own with the view of erecting it anew, and that people are even sometimes constrained to this when their houses are in danger of falling from age, or when the foundations are insecure. With this before me by way of example, I was persuaded that it would indeed be preposterous for a private individual to think of reforming a state by fundamentally changing it throughout, and overturning it in order to set it up amended; and the same I thought was true of any similar project for reforming the body of the sciences, or the order of teaching them established in the schools: but as for the opinions which up to that time I had embraced, I thought that I could not do better than resolve at once to sweep them wholly away, that I might afterwards be in a position to admit either others more correct, or even perhaps the same when they had undergone the scrutiny of reason. I firmly believed that in this way I should much better succeed in the conduct of my life, than if I built only upon old foundations, and leaned upon principles which, in my youth, I had taken upon trust. For although I recognized various difficulties in this undertaking, these were not, however, without remedy, nor once to be compared with such as attend the slightest reformation in public affairs. Large bodies, if once overthrown, are with great difficulty set up again, or even kept erect when once seriously shaken, and the fall of such is always disastrous. Then if there are any imperfections in the constitutions of states (and that many such exist the diversity of constitutions is alone sufficient to assure us), custom has without doubt materially smoothed their inconveniences, and has even managed to steer altogether clear of, or insensibly corrected a number which sagacity could not have provided against with equal effect; and, in fine, the defects are almost always more tolerable than the change necessary for their removal; in the same manner that highways which wind among mountains, by being much frequented, become gradually so smooth and commodious, that it is much better to follow them than to seek a straighter path by climbing over the tops of rocks and descending to the bottoms of precipices.
It is true, however, that people do not usually tear down every house in a town just to rebuild differently and improve the streets. But individuals often tear down their own houses to rebuild them. Sometimes they are even forced to rebuild because their houses risk collapsing from age or have unstable foundations. With this example in mind, I became convinced that it would be absurd for an individual to attempt a fundamental reform of a state. Such a person would be overturning the whole state in order to rebuild it in a better form. I thought the same applied to any similar plan to reform the sciences or the established way of teaching them in schools. But I took a different view of the opinions I had accepted up to that time. I thought my best course was to resolve at once to clear them all away. Then I could accept more accurate opinions, or perhaps even the same ones, after examining them through reason. I firmly believed this approach would help me guide my life far better than building only on old foundations. Otherwise, I would be relying on principles I had accepted on trust in my youth. Although I saw various difficulties in this undertaking, those difficulties could be overcome. They could not begin to compare with the difficulties involved in even the smallest reform of public affairs. Once large bodies are overthrown, they are very hard to rebuild. Even keeping them upright is difficult once they have been badly shaken, and their collapse is always disastrous. If states have flaws in their constitutions, custom has undoubtedly done much to soften the resulting problems. The variety of constitutions alone is enough to assure us that many such flaws exist. Custom has even managed to avoid some problems entirely, or gradually correct them, more effectively than foresight could have done. In short, the flaws are almost always easier to bear than the changes needed to remove them. The same is true of roads that wind through mountains. Frequent use gradually makes these roads so smooth and easy to travel that following them is much better than seeking a straighter route. That straighter route would require climbing over rocky peaks and descending to the bottoms of steep drops.
Hence it is that I cannot in any degree approve of those restless and busy meddlers who, called neither by birth nor fortune to take part in the management of public affairs, are yet always projecting reforms; and if I thought that this tract contained aught which might justify the suspicion that I was a victim of such folly, I would by no means permit its publication. I have never contemplated anything higher than the reformation of my own opinions, and basing them on a foundation wholly my own. And although my own satisfaction with my work has led me to present here a draft of it, I do not by any means therefore recommend to every one else to make a similar attempt. Those whom God has endowed with a larger measure of genius will entertain, perhaps, designs still more exalted; but for the many I am much afraid lest even the present undertaking be more than they can safely venture to imitate. The single design to strip one’s self of all past beliefs is one that ought not to be taken by every one. The majority of men is composed of two classes, for neither of which would this be at all a befitting resolution: in the first place, of those who with more than a due confidence in their own powers, are precipitate in their judgments and want the patience requisite for orderly and circumspect thinking; whence it happens, that if men of this class once take the liberty to doubt of their accustomed opinions, and quit the beaten highway, they will never be able to thread the byway that would lead them by a shorter course, and will lose themselves and continue to wander for life; in the second place, of those who, possessed of sufficient sense or modesty to determine that there are others who excel them in the power of discriminating between truth and error, and by whom they may be instructed, ought rather to content themselves with the opinions of such than trust for more correct to their own reason.
For this reason, I cannot approve at all of those restless, meddlesome people who are always planning reforms. Neither their birth nor their circumstances call them to take part in public affairs. If I thought anything in this work justified suspecting me of such foolishness, I would never allow its publication. My aim has never gone beyond reforming my own opinions and building them on a foundation entirely my own. Although my satisfaction with my work has led me to offer an outline here, I do not recommend that everyone try the same thing. Those whom God has given greater intelligence may perhaps pursue still higher aims. But I greatly fear that most people could not safely attempt even what I have undertaken. The very decision to abandon all past beliefs is not one everyone should make. Most people fall into two groups, and this decision would be unsuitable for either. First are those who have too much confidence in their own abilities. They rush to judgment and lack the patience needed to think carefully and methodically. If such people once allow themselves to doubt their familiar opinions and leave the well-traveled road, they will lose their way. They will never manage to follow the side path that would take them to their destination more quickly. Instead, they will wander for the rest of their lives. Second are those with enough sense or modesty to recognize that others are better at distinguishing truth from error. Since they can learn from those people, they should be content with their teachers’ opinions. They should not trust their own reason to arrive at more accurate ones.
For my own part, I should doubtless have belonged to the latter class, had I received instruction from but one master, or had I never known the diversities of opinion that from time immemorial have prevailed among men of the greatest learning. But I had become aware, even so early as during my college life, that no opinion, however absurd and incredible, can be imagined, which has not been maintained by some on of the philosophers; and afterwards in the course of my travels I remarked that all those whose opinions are decidedly repugnant to ours are not in that account barbarians and savages, but on the contrary that many of these nations make an equally good, if not better, use of their reason than we do. I took into account also the very different character which a person brought up from infancy in France or Germany exhibits, from that which, with the same mind originally, this individual would have possessed had he lived always among the Chinese or with savages, and the circumstance that in dress itself the fashion which pleased us ten years ago, and which may again, perhaps, be received into favor before ten years have gone, appears to us at this moment extravagant and ridiculous. I was thus led to infer that the ground of our opinions is far more custom and example than any certain knowledge. And, finally, although such be the ground of our opinions, I remarked that a plurality of suffrages is no guarantee of truth where it is at all of difficult discovery, as in such cases it is much more likely that it will be found by one than by many. I could, however, select from the crowd no one whose opinions seemed worthy of preference, and thus I found myself constrained, as it were, to use my own reason in the conduct of my life.
For my part, I would certainly have belonged to the latter group if I had learned from only one teacher. The same would have been true if I had never encountered the long-standing disagreements among the most learned people. But even in college, I had learned that no opinion is so absurd or unbelievable that no philosopher has defended it. Later, during my travels, I noticed that people whose opinions strongly conflict with ours are not therefore barbarians or savages. On the contrary, many of these nations use their reason as well as we do, if not better. I also considered how differently someone develops when raised from infancy in France or Germany. That same person, starting with the same mind, would have developed very differently among the Chinese or among savages. Even in clothing, fashions we liked ten years ago now seem extravagant and ridiculous. Yet those fashions may perhaps return to favor within another ten years. So I concluded that our opinions rest far more on habit and example than on certain knowledge. Finally, although our opinions rest on these foundations, I noticed that a majority vote does not guarantee truth in difficult questions. In such cases, one person is much more likely to discover the truth than many people are. Yet I could find no one among the crowd whose opinions seemed preferable to the others. So I found myself, as it were, forced to use my own reason to guide my life.
But like one walking alone and in the dark, I resolved to proceed so slowly and with such circumspection, that if I did not advance far, I would at least guard against falling. I did not even choose to dismiss summarily any of the opinions that had crept into my belief without having been introduced by reason, but first of all took sufficient time carefully to satisfy myself of the general nature of the task I was setting myself, and ascertain the true method by which to arrive at the knowledge of whatever lay within the compass of my powers.
But like someone walking alone in the dark, I decided to move slowly and with great care. Even if I made little progress, I would at least avoid falling. I did not even choose to reject outright any opinions I had come to hold without reason. Instead, I first took enough time to understand carefully the overall task I was setting myself. I also sought the right method for gaining knowledge of whatever was within my powers to understand.
Among the branches of philosophy, I had, at an earlier period, given some attention to logic, and among those of the mathematics to geometrical analysis and algebra,--three arts or sciences which ought, as I conceived, to contribute something to my design. But, on examination, I found that, as for logic, its syllogisms and the majority of its other precepts are of avail--rather in the communication of what we already know, or even as the art of Lully, in speaking without judgment of things of which we are ignorant, than in the investigation of the unknown; and although this science contains indeed a number of correct and very excellent precepts, there are, nevertheless, so many others, and these either injurious or superfluous, mingled with the former, that it is almost quite as difficult to effect a severance of the true from the false as it is to extract a Diana or a Minerva from a rough block of marble. Then as to the analysis of the ancients and the algebra of the moderns, besides that they embrace only matters highly abstract, and, to appearance, of no use, the former is so exclusively restricted to the consideration of figures, that it can exercise the understanding only on condition of greatly fatiguing the imagination; and, in the latter, there is so complete a subjection to certain rules and formulas, that there results an art full of confusion and obscurity calculated to embarrass, instead of a science fitted to cultivate the mind. By these considerations I was induced to seek some other method which would comprise the advantages of the three and be exempt from their defects. And as a multitude of laws often only hampers justice, so that a state is best governed when, with few laws, these are rigidly administered; in like manner, instead of the great number of precepts of which logic is composed, I believed that the four following would prove perfectly sufficient for me, provided I took the firm and unwavering resolution never in a single instance to fail in observing them.
Earlier, I had given some attention to logic among the branches of philosophy, and to geometrical analysis and algebra in mathematics. I thought these three arts or sciences ought to contribute something to my purpose. But when I examined logic, I found that its syllogisms and most of its other rules were more useful for communicating what we already know than for discovering the unknown. Or, like the art of Lully, they helped us speak without judgment about things we know nothing about. Logic does contain a number of sound and excellent rules. Yet so many harmful or unnecessary rules are mixed in with the good ones that separating them is nearly as difficult as carving a Diana or a Minerva from a rough block of marble. Then I considered the analysis of the ancients and the algebra of the moderns. Both deal only with highly abstract matters that seem to have no use. Ancient analysis focuses so exclusively on figures that it can exercise the understanding only by greatly tiring the imagination. Modern algebra, meanwhile, is so bound by certain rules and formulas that it becomes a confusing and obscure art. Rather than a science suited to developing the mind, it is an art likely to leave the mind confused. These considerations led me to seek another method that would combine the advantages of all three without their faults. A great many laws often only obstruct justice. A state is therefore best governed when it has few laws and strictly enforces them. In the same way, I believed the following four rules would be entirely sufficient for me, instead of logic’s many rules. But I would have to resolve firmly and unwaveringly never to fail to follow them, even once.
The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.
The first rule was never to accept anything as true unless I clearly knew it to be true. That meant carefully avoiding hasty judgments and prejudice. It also meant judging only on what appeared to my mind so clearly and distinctly that no doubt was possible.
The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
Second, divide each problem being examined into as many parts as possible and as needed to solve it properly.
The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
The third rule was to organize my thoughts, starting with the simplest things and those easiest to understand. This would allow me to advance gradually, as if step by step, toward understanding more complex things. I would give things an order in my thoughts, even when they had no natural order of coming before or after one another.
And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.
And the last was to make complete lists and comprehensive reviews in every case. I would do so to be sure I had left nothing out.
The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another. And I had little difficulty in determining the objects with which it was necessary to commence, for I was already persuaded that it must be with the simplest and easiest to know, and, considering that of all those who have hitherto sought truth in the sciences, the mathematicians alone have been able to find any demonstrations, that is, any certain and evident reasons, I did not doubt but that such must have been the rule of their investigations. I resolved to commence, therefore, with the examination of the simplest objects, not anticipating, however, from this any other advantage than that to be found in accustoming my mind to the love and nourishment of truth, and to a distaste for all such reasonings as were unsound. But I had no intention on that account of attempting to master all the particular sciences commonly denominated mathematics: but observing that, however different their objects, they all agree in considering only the various relations or proportions subsisting among those objects, I thought it best for my purpose to consider these proportions in the most general form possible, without referring them to any objects in particular, except such as would most facilitate the knowledge of them, and without by any means restricting them to these, that afterwards I might thus be the better able to apply them to every other class of objects to which they are legitimately applicable. Perceiving further, that in order to understand these relations I should sometimes have to consider them one by one and sometimes only to bear them in mind, or embrace them in the aggregate, I thought that, in order the better to consider them individually, I should view them as subsisting between straight lines, than which I could find no objects more simple, or capable of being more distinctly represented to my imagination and senses; and on the other hand, that in order to retain them in the memory or embrace an aggregate of many, I should express them by certain characters the briefest possible. In this way I believed that I could borrow all that was best both in geometrical analysis and in algebra, and correct all the defects of the one by help of the other.
Geometers use long chains of simple, easy reasoning to reach the conclusions of their most difficult proofs. This led me to imagine that all things within human understanding are connected in the same way. Nothing would be so distant as to lie beyond our reach, or so hidden that we could not discover it. We would only need to avoid accepting falsehood as truth and keep our thoughts in the proper order. That order would allow us to deduce one truth from another. I had little difficulty deciding where to begin. I was already convinced that I must start with the simplest things, those easiest to understand. Among all who had so far sought truth in the sciences, mathematicians alone had found proofs. By proofs, I mean certain and clear reasons. I therefore had no doubt that mathematicians must have followed this rule in their investigations. So I decided to begin by examining the simplest things. I expected no benefit beyond training my mind to love truth, draw nourishment from it, and reject unsound reasoning. But I did not intend to master all the individual sciences commonly called mathematics. I noticed that, however different their objects, these sciences all consider only the various relations or proportions between those objects. So I thought it best to study these proportions in the most general way possible. I would connect them with particular objects only when those objects would make the proportions easiest to understand. Even then, I would not limit the proportions to those objects. That way, I could later apply the proportions more easily to every other class of objects where they legitimately applied. I also saw that understanding these relations would sometimes require examining them one by one. At other times, I would only need to keep the relations in mind or grasp them as a whole. To examine the relations individually more easily, I thought I should picture them as relations between straight lines. I could find no objects simpler or easier to represent clearly to my imagination and senses. On the other hand, to remember the relations or grasp many together, I should express them using the shortest possible symbols. In this way, I believed I could draw on the best of both geometrical analysis and algebra. I could also use each to correct all the defects of the other.
And, in point of fact, the accurate observance of these few precepts gave me, I take the liberty of saying, such ease in unraveling all the questions embraced in these two sciences, that in the two or three months I devoted to their examination, not only did I reach solutions of questions I had formerly deemed exceedingly difficult but even as regards questions of the solution of which I continued ignorant, I was enabled, as it appeared to me, to determine the means whereby, and the extent to which a solution was possible; results attributable to the circumstance that I commenced with the simplest and most general truths, and that thus each truth discovered was a rule available in the discovery of subsequent ones Nor in this perhaps shall I appear too vain, if it be considered that, as the truth on any particular point is one whoever apprehends the truth, knows all that on that point can be known. The child, for example, who has been instructed in the elements of arithmetic, and has made a particular addition, according to rule, may be assured that he has found, with respect to the sum of the numbers before him, and that in this instance is within the reach of human genius. Now, in conclusion, the method which teaches adherence to the true order, and an exact enumeration of all the conditions of the thing sought includes all that gives certitude to the rules of arithmetic.
In fact, carefully following these few rules made it easy for me to work through all the questions in these two sciences. I take the liberty of saying so. I spent two or three months examining these questions. During that time, I solved problems I had once thought extremely difficult. Even when I still did not know a solution, I seemed able to determine how far a solution was possible. I also seemed able to determine the means of finding it. These results came from starting with the simplest and most general truths. Each truth I discovered then became a rule for discovering further truths. Perhaps I will not seem too vain if we consider that there is only one truth about any particular point. Whoever grasps that truth knows all that can be known about that point. For example, take a child who has learned basic arithmetic and correctly added some numbers according to the rules. The child can be certain of having found the sum as fully as any human mind could. In conclusion, the method teaches us to follow the right order and list exactly all the conditions of the problem. Such a method includes everything that makes the rules of arithmetic certain.
But the chief ground of my satisfaction with thus method, was the assurance I had of thereby exercising my reason in all matters, if not with absolute perfection, at least with the greatest attainable by me: besides, I was conscious that by its use my mind was becoming gradually habituated to clearer and more distinct conceptions of its objects; and I hoped also, from not having restricted this method to any particular matter, to apply it to the difficulties of the other sciences, with not less success than to those of algebra. I should not, however, on this account have ventured at once on the examination of all the difficulties of the sciences which presented themselves to me, for this would have been contrary to the order prescribed in the method, but observing that the knowledge of such is dependent on principles borrowed from philosophy, in which I found nothing certain, I thought it necessary first of all to endeavor to establish its principles. And because I observed, besides, that an inquiry of this kind was of all others of the greatest moment, and one in which precipitancy and anticipation in judgment were most to be dreaded, I thought that I ought not to approach it till I had reached a more mature age (being at that time but twenty-three), and had first of all employed much of my time in preparation for the work, as well by eradicating from my mind all the erroneous opinions I had up to that moment accepted, as by amassing variety of experience to afford materials for my reasonings, and by continually exercising myself in my chosen method with a view to increased skill in its application.
But my main reason for being satisfied with this method was the confidence that it let me reason about everything. If I could not reason with absolute perfection, I could at least reason as well as I possibly could. Besides, I could tell that using the method was gradually training my mind to understand its subjects more clearly and distinctly. And because I had not limited the method to any particular subject, I hoped to apply it to other sciences. I hoped it would help solve their difficulties just as successfully as those of algebra. Yet I would not have dared to examine all the scientific difficulties I encountered at once. Doing so would have gone against the order prescribed by the method. But I saw that knowledge in these sciences depended on principles drawn from philosophy, where I found nothing certain. So I thought I first needed to try to establish the principles of philosophy. I also saw that no other inquiry was more important, or gave greater reason to fear haste and premature judgment. So I thought I should wait until I was older before approaching this inquiry. I was only twenty-three at the time. Before beginning, I also thought I should spend much time preparing for the work. I needed to rid my mind of all the mistaken opinions I had accepted up to then. I also needed to gather a wide range of experience to provide material for my reasoning. And I needed to keep practicing my chosen method to become more skilled at applying it.