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[Part I]

The Encyclopedia which we are presenting to the public is, as its title declares, the work of a society of men of letters. Were we not of their number, we might venture to affirm that they are all favorably known or worthy of being so. [1] But, without wishing to anticipate a judgment which should be made only by scholars, it is at least incumbent upon us, before all else, to remove the objection that could most easily prejudice the success of such a large undertaking as this. We declare, therefore, that we have not had the temerity to undertake unaided a task so superior to our capabilities, and that our function as editors consists principally in arranging materials which for the most part have been furnished in their entirety by others. We had explicitly made the same declaration in the body of the Prospectus,  [2] but perhaps we should have put it at the beginning of that document. If we had taken that precaution we would doubtless have replied in advance to a large number of gentlemen—and even to some men of letters —who had unquestionably glanced at our Prospectus, as their praises attest, but who, nevertheless, have asked us how two persons could treat all the sciences and all the arts. [3] This being the case, the only way of preventing the reappearance of their objection once and for all is to use the first lines of our work to destroy it, as we are doing here. Our introductory sentences are therefore directed solely to those of our readers who will decide not to go further. To the others we owe a far more detailed description of the execution of the Encyclopedia, which they will find later in this Discourse, together with the names of each of our colleagues. However, a description so important in its nature and substance must be preceded by some philosophical reflections.

The work whose first volume we are presenting today  [4] has two aims. As an Encyclopedia, it is to set forth as well as possible the order and connection of the parts of human knowledge. As a Reasoned Dictionary of the Sciences, Arts, and Trades, it is to contain the general principles that form the basis of each science and each art, liberal or mechanical, and the most essential facts that make up the body and substance of each. [5] These two points of view, the one of an Encyclopedia and the other of a Reasoned Dictionary,  [6] will thus constitute the basis for the outline and division of our Preliminary Discourse → . We are going to introduce them, deal with them one after another, and give an account of the means by which we have tried to satisfy this double object.

If one reflects somewhat upon the connection that discoveries have with one another, it is readily apparent that the sciences and the arts are mutually supporting, and that consequently there is a chain that binds them together. But, if it is often difficult to reduce each particular science or art to a small number of rules or general notions, it is no less difficult to encompass the infinitely varied branches of human knowledge in a truly unified system. [7]

The first step which lies before us in our endeavor is to examine, if we may be permitted to use this term, the genealogy and the filiation of the parts of our knowledge, the causes that brought the various branches of our knowledge into being, and the characteristics that distinguish them. In short, we must go back to the origin and generation of our ideas. [8] Quite aside from the help this examination will give us for the encyclopedic enumeration of the sciences and the arts, it cannot be out of place at the head of a work such as this.

We can divide all our knowledge into direct and reflective knowledge. We receive direct knowledge immediately, without any operation of our will; it is the knowledge which finds all the doors of our souls open, so to speak, and enters without resistance and without effort. The mind acquires reflective knowledge by making use of direct knowledge, unifying and combining it.

All our direct knowledge can be reduced to what we receive through our senses; whence it follows that we owe all our ideas to our sensations. This principle of the first philosophers was for a long time regarded as an axiom by the scholastic philosophers. They respected it merely because it was ancient, and they would have defended “substantial forms” and “occult qualities” with equal vigor. [9] Consequently, during the renaissance of philosophy this true principle received the same treatment as the absurd opinions from which it should have been distinguished: it was proscribed along with them, because nothing is more detrimental to truth, and nothing exposes it more to misinterpretation, than the intermingling or proximity of error. The system of innate ideas, which is attractive in several respects, and the more striking perhaps because it was less familiar, replaced the axiom of the scholastic philosophers [that we owe all our ideas to our sensations]; and after having reigned for a long time, the system of innate ideas still retains some partisans—so great are the difficulties hindering the return of truth, once prejudice or sophism has routed it from its proper place. [10] Of late, however, it has been almost generally agreed that the ancients were right, nor is this the only matter on which we are beginning to draw closer to them.

Nothing is more indisputable than the existence of our sensations. Thus, in order to prove that they are the principle of all our knowledge, it suffices to show that they can be; for in a well-constructed philosophy, any deduction which is based on facts or recognized truths is preferable to one which is supported only by hypotheses, however ingenious. Why suppose that we have purely intellectual notions at the outset [innate ideas], if all we need do in order to form them is to reflect upon our sensations? The discussion which follows will demonstrate that these notions, in fact, have no other origin. [11]

The fact of our existence is the first thing taught us by our sensations and, indeed, is inseparable from them. [12] From this it follows that our first reflective ideas must be concerned with ourselves, that is to say, must concern that thinking principle which constitutes our nature and which is in no way distinct from ourselves. The second thing taught us by our sensations is the existence of external objects, among which we must include our own bodies, since they are, so to speak, external to us even before we have defined the nature of the thinking principle within us. These innumerable external objects produce a powerful and continued effect upon us which binds us to them so forcefully that, after an instant when our reflective ideas turn our consciousness inward, we are forced outside again by the sensations that besiege us on all sides. They tear us from the solitude that would otherwise be our lot. The multiplicity of these sensations, the consistency that we note in their evidence, the degrees of difference we observe in them, and the involuntary reactions that they cause us to experience —as compared with that voluntary determination we have over our reflective ideas, which is operative only upon our sensations themselves [13]—all of these things produce an irresistible impulse in us to affirm that the objects we relate to these sensations, and which appear to us to be their cause, actually exist. This impulse has been considered by many philosophers to be the work of a Superior Being and the most convincing argument for the existence of these objects. And indeed, since there is no connection between each sensation and the object that occasions it, or at least the object to which we relate it, it does not seem that any possible passage from one to the other can be found through reasoning. Only a kind of instinct, surer than reason itself, can compel us to leap so great a gap. This instinct is so strong in us that even if one were to suppose for a moment that it subsisted while all external objects were destroyed, the reconstitution of those objects could not add to its strength. [14] Therefore, let us believe without wavering that in fact our sensations have the cause outside ourselves which we suppose them to have; because the effect which can result from the real existence of that cause could not differ in any way from the effect we experience. Let us not imitate those philosophers of whom Montaigne speaks, who, when asked about the principle of men’s actions, were still trying to find out whether there are men. [15] Far from wishing to cast shadows on a truth recognized even by the skeptics when they are not debating, let us leave the trouble of working out its principle to the enlightened metaphysicians. It is for them to determine, if that be possible, what gradation our soul observes when it takes that first step outside itself, impelled, so to speak, and held back at the same time by a crowd of perceptions, [16] which, on the one hand, draw it toward external objects, and on the other hand (since these perceptions belong properly only to the soul itself) seem to circumscribe it in a narrow space from which they do not permit it to withdraw.

Of all the objects that affect us by their presence, the existence of our body strikes us most vividly because it belongs to us most intimately. But hardly do we become aware of the existence of our body before we become aware of the attention it demands of us in warding off the dangers that surround it. Subject to endless needs, extremely sensitive to the action of external bodies, it would soon be destroyed were it not for the care we take in preserving it. Not that all external bodies give us disagreeable sensations; some seem to compensate us by the pleasure which their action brings to us. But such is the misfortune of the human condition that pain is our most lively sentiment; pleasure affects us less than pain and hardly ever suffices to make up to us for it. In vain did some philosophers assert, while suppressing their groans in the midst of sufferings, that pain was not an evil at all. [17] In vain did others place supreme happiness in sensuality—of which they nevertheless deprived themselves through fear of its consequences. All of them would have known our nature better if they had been content to limit their definition of the sovereign good of the present life to the exemption from pain, and to agree that, without hoping to arrive at this sovereign good, we are allowed only to approach it more or less, in proportion to our vigilance and the precautions we take. Reflections as natural as these will inevitably strike any man who is left alone and free of the prejudices of education or study. They will be the consequence of the first impression he receives from external objects, and they can be placed among the number of those first exertions of the soul which are deemed most valuable and worthy of observation by those who are truly wise, but which are neglected or rejected by ordinary philosophy, whose first principles are almost always contradicted by them. [18]

The necessity of protecting our own bodies from pain and destruction causes us to examine which among the external objects can be useful or harmful to us, in order to seek out some and shun others. But hardly have we begun to survey these objects when we discover among them a large number of beings who seem entirely similar to ourselves, that is, whose forms are entirely like ours and who seem to have the same perceptions as we do, so far as we can judge at first glance. All this causes us to think that they also have the same needs that we experience and consequently the same interest in satisfying them. Whence we conclude that we should find it advantageous to join with them in finding out what can be beneficial to us and what can be detrimental to us in Nature. The communication of ideas is the principle and support of this union, and necessarily requires the invention of signs—such is the source of the formation of societies, with which must have come the birth of languages. [19]

This interchange which so many powerful motives cause us to form with other men soon increases the scope of our ideas and gives birth to entirely new ones in us, by all appearances far removed from those we would have had by ourselves without such aid. It is for the philosopher to decide whether this reciprocal communication, together with the resemblance we note between our sensations and those of our kind, does not contribute much to strengthen our irresistible inclination to assume the existence of all the objects which strike our attention. In order to keep within my subject, I will note simply that the pleasure and the advantage we find in such an interchange, whether in sharing our ideas with other men or in combining their ideas with ours, ought to lead us to strengthen more and more the bonds of the society thus established and to make it as useful for us as possible. But, since each member of society tries to increase for himself the usefulness that he draws from it and must compete with each of the other members, whose eagerness to do the same is equally strong, all cannot have a like share of the advantages, although all have the same right to them. Such a legitimate right is, therefore, soon transgressed by that barbarian right of inequality called the law of the strongest, which we find so difficult not to abuse, though the practice of it likens us to animals. Thus the strength with which nature endows certain men, and which they should doubtless use only to aid and protect the weak, is on the contrary the origin of the latter’s oppression. But the more violent the oppression the less patiently the weak suffer it, because they feel that nothing reasonable could have caused their subjection. Such is the origin of the concept of the unjust, and consequently of moral good and evil, of which so many philosophers have tried to find the principle and which the cry of Nature, resounding in all men, makes understood among even the most savage people. Such is the origin also of that natural law which we find within us, the source of the first laws which men must of necessity have created. [20] Even without the help of these laws, that natural law is sometimes strong enough, if not to abolish oppression, at least to hold it within certain limits. Thus the evil we experience through the vices of our own species produces in us the reflective knowledge of the virtues opposed to these vices, a precious knowledge of which we might perhaps have been deprived if a perfect union and equality had prevailed among men. [21]

By the acquired idea of the just and the unjust (and consequently the idea of the moral nature of actions), we are naturally led to consider what principle it is within us that acts, or, which amounts to the same thing, the substance that wills and conceives. It is not necessary to probe deeply into the nature of our body and the idea we have of it to recognize that it could not be that substance, because the properties we observe in matter have nothing in common with the faculty of willing and thinking. Consequently, this being called Us is made up of two principles of a different nature [body and soul], so closely united that we could neither suspend nor alter the correspondence which prevails between the movements of the one and the reactions of the other, and subjects each to the other. This mutual slavery [of soul and body] which is so independent of us, together with the reflections we are impelled to make on the nature of the two principles and on their imperfection, lifts us to the contemplation of an all-powerful Intelligence who is the source of what we are and who consequently requires our worship. [22] Our inner conviction alone would suffice to make us recognize the existence of such a being, even if the universal testimonies of other men and of all Nature were not joined with it.

It is therefore evident that the purely intellectual concepts of vice and virtue, the principle and the necessity of laws, the spiritual nature of the soul, the existence of God and of our obligations toward him—in a word, the truths for which we have the most immediate and indispensable need—are the fruits of the first reflective ideas that our sensations occasion.

However interesting these first truths may be for the most noble part of ourselves, soon the body, to which the soul is joined, turns our attention to itself, because of the necessity of providing for its endlessly multiplying needs. The care for its preservation must be directed either toward preventing the evils that threaten it or toward remedying those that have attacked it. We try to satisfy these needs by two means: by our own discoveries and by the investigations of other men, which our social intercourse puts us in a position to enjoy. Whence must have come the birth of agriculture and medicine first, and then all the most absolutely necessary arts. They were at the same time both our most primitive knowledge and the source of all other knowledge, even of that which by its nature seems most remote from them. We must develop this point in further detail.

Working separately or together and assisting one another in their intellectual endeavors, the first men were perhaps not long in discovering a part of the uses to which they could put material bodies. Being eager above all for useful knowledge, they must at first have put aside all idle speculations, and, rapidly surveying the different beings observable in Nature, combined them materially, so to speak, according to their most striking and palpable properties. After this first combining must have come a more sophisticated one, which, although still related to their needs, was chiefly concerned with a deeper study of some of the less evident properties, with the alteration and decomposition of bodies, and with the use which could be derived from them. [23]

Stimulated as they were by so engrossing an aim as self-preservation, these men of whom we speak and their successors were able, no doubt, to make some progress along the path of knowledge. Nevertheless, it was not long before their experience and observations in this vast universe brought them to obstacles which proved insurmountable to their greatest efforts. It was then that their intellects, which had become accustomed to meditation and were eager to draw profit from it, must have made the uniquely interesting discovery of the properties of physical bodies, a discovery that knows no limits and which served as a valuable expedient in these circumstances. And indeed, if an abundance of pleasurable knowledge could console us for our lack of useful truth, we might say that the study of Nature lavishly serves our pleasures at least, even though it withholds from us the necessities of life. It is, so to speak, a kind of superfluity that compensates, although most imperfectly, for the things we lack. Moreover, in the hierarchy of our needs and of the objects of our passions, pleasure holds one of the highest places, and curiosity is a need for anyone who knows how to think, especially when this restless desire is enlivened with a sort of vexation at not being able to satisfy itself entirely. Thus, we owe much of our purely enjoyable knowledge to the fact that we are unfortunately incapable of acquiring the more necessary kind. Another motive serves to keep us at such work: utility, which, though it may not be the true aim, can at least serve as a pretext. The mere fact that we have occasionally found concrete advantages in certain fragments of knowledge, when they were hitherto unsuspected, authorizes us to regard all investigations begun out of pure curiosity as being potentially useful to us. Such was the origin and the cause of progress of the vast science generally called Physics, or the study of Nature, which includes so many different parts. Agriculture and medicine, which were the principal cause of its birth, are nowadays only branches of it, and although they are the most essential and the earliest branches of all, they have been honored more or less in proportion to the degree to which they have been stifled and overshadowed by the others.

In our study of Nature, which we make partly by necessity and partly for amusement, we note that bodies have a large number of properties. [24] However, in most cases they are so closely united in the same subject that, in order to study each of them more thoroughly, we are obliged to consider them separately. Through this operation of our intelligence we soon discover properties which seem to belong to all bodies, such as the faculty of movement or of remaining at rest, and the faculty of communicating movement, which are the sources of the principal changes we observe in Nature. By examining these properties—above all the last one—with the aid of our own senses, we soon discover another property upon which all of these depend: impenetrability, which is to say, that specific force by virtue of which each body excludes all others from the place it occupies, so that when two bodies are put together as closely as possible, they can never occupy a space smaller than the one they filled separately. Impenetrability is the principal property by which we make a distinction between the bodies themselves and the indefinite portions of space in which we conceive them as being placed—at least the evidence of our senses tells us such is the case. Even if they are deceptive on this point, it is an error so metaphysical that our existence and the preservation of our lives have nothing to fear from it, and it continually crops up in our mind almost involuntarily, as part of our ordinary way of thinking. Everything induces us to conceive of space as the place (if not real, at least supposed) occupied by bodies. And indeed, it is by conceiving of sections of that space as being penetrable and immobile that our idea of movement achieves the greatest clarity it can have for us. We are therefore almost naturally impelled to differentiate, at least mentally, between two sorts of extension, one being impenetrable and the other constituting the place occupied by bodies. [25] And thus, although impenetrability belongs of necessity to our conception of the parts of matter, nevertheless, since it is a relative property (that is, we get an idea of it only by examining two bodies together), we soon accustom ourselves to thinking of it as distinct from extension and to considering the latter separately from it.

Through this new consideration we now see bodies only as shaped and extended parts of space, this being the most general and most abstract point of view from which we can envisage them. For extension in which we did not distinguish shaped parts would be only a distant and obscure vision where everything would elude us because we would be unable to discern anything clearly. Color and shape—properties which are always attached to bodies although they vary for each one— help us in some way to detach bodies from the background of space. Even one of these properties is sufficient in this respect, and for the purpose of considering bodies in their most intellectual form, we prefer shape to color. This may be because shape is the most familiar  [26] to us, being known both by sight and touch; or because it is easier to conceive of shape without color in a body than color without shape; or finally it may be because shape serves to fix the parts of space more easily and in a less vague way.

Hence we are led to ascertain the properties of extension simply as to shape. This is the object of Geometry, which facilitates its task by considering extension limited first by a single dimension, then by two, and finally by the three dimensions constituting the essence of an intelligible body (that is to say, of a portion of space terminated in every direction by intellectual boundaries).

Thus, by a few successive operations and abstractions of our minds we divest matter of almost all its sensible properties, in order to envisage in a sense only its phantom. One should recognize first of all that the discoveries to which this investigation brings us will certainly be very useful in all cases in which there is no need to consider the impenetrability of bodies, as for example, when it is a question of studying their movement, considering them as shaped, mobile parts of space, distant from one another.

Since our examination of shaped extension presents us with a large number of possible combinations, it is necessary to invent some means of achieving those combinations more easily; and since they consist chiefly in calculating and relating the different parts of which we conceive the geometric bodies to be formed, this investigation soon brings us to Arithmetic or the science of numbers. This [science] is simply the art of finding a short way of expressing a unique relationship [a number] which results from the comparison of several others. [27] The different ways of comparing these relationships [numbers] give the different rules of Arithmetic [addition, subtraction, etc.].

Moreover, if we reflect upon these rules we almost inevitably perceive certain principles or general properties of the relationships, by means of which we can, expressing these relationships [numbers] in a universal way, discover the different combinations that can be made of them. The result of these combinations reduced to a general form will in fact simply be arithmetical calculations, indicated and represented by the simplest and shortest expression consistent with their generality. [28] The science or the art of thus denoting relationships [numbers] is called Algebra. Thus, although no calculation proper is possible except by numbers, nor any magnitude measurable except by extension (for without space we could not measure time exactly), we arrive through the continual generalization of our ideas at that principal part of mathematics, and of all the natural sciences, called the Science of Magnitudes in general. It is the foundation of all possible discoveries concerning quantity, that is to say, concerning everything that is susceptible to augmentation or diminution.

This science is the farthest outpost to which the contemplation of the properties of matter can lead us, and we would not be able to go further without leaving the material universe altogether. But such is the progress of the mind in its investigations that after having generalized its perceptions to the point where it can no longer break them up further into their constituent elements, it retraces its steps, reconstitutes anew its perceptions themselves, and, little by little and by degrees, produces from them the concrete beings that are the immediate and direct objects of our sensations. These beings, which are immediately relative to our needs, are also those which it is most important for us to study. Mathematical abstractions help us in gaining this knowledge, but they are useful only insofar as we do not limit ourselves to them.

That is why, having so to speak exhausted the properties of shaped extension through geometric speculations, we begin by restoring to it impenetrability, which constitutes physical body and was the last sensible quality of which we had divested it. The restoration of impenetrability brings with it the consideration of the action of bodies on one another, for bodies act only insofar as they are impenetrable. It is thence that the laws of equilibrium and movement, which are the object of Mechanics, are deduced. We extend our investigations even to the movement of bodies animated by unknown driving forces or causes, provided the law whereby these causes act is known or supposed to be known. [29]

Having at last made a complete return to the corporeal world, we soon perceive the use we can make of Geometry and Mechanics for acquiring the most varied and profound knowledge about the properties of bodies. It is approximately in this way that all the so-called physico-mathematical sciences were born. We can put at their head Astronomy, the study of which, next to the study of ourselves, is most worthy of our application because of the magnificent spectacle which it presents to us. Joining observation to calculation and elucidating the one by the other, this science determines with an admirable precision the distances and the most complicated movements of the heavenly bodies; it points out the very forces by which these movements are produced or altered. Thus it may justly be regarded as the most sublime and the most reliable application of Geometry and Mechanics in combination, and its progress may be considered the most incontestable monument of the success to which the human mind can rise by its efforts.

The use of mathematical knowledge is no less considerable in the examination of the terrestrial bodies that surround us. All the properties we observe in these bodies have relationships among themselves that are more or less accessible to us. The knowledge or the discovery of these relationships is almost always the only object we are permitted to attain, and consequently the only one we ought to propose for ourselves. Thus, it is not at all by vague and arbitrary hypotheses that we can hope to know nature; it is by thoughtful study of phenomena, by the comparisons we make among them, by the art of reducing, as much as that may be possible, a large number of phenomena to a single one that can be regarded as their principle. Indeed, the more one reduces the number of principles of a science, the more one gives them scope, and since the object of a science is necessarily fixed, the principles applied to that object will be so much the more fertile as they are fewer in number. [30] This reduction which, moreover, makes them easier to understand, constitutes the true “systematic spirit.” One must be very careful not to mistake this for the “spirit of system,” with which it does not always agree. We will speak more fully of this matter later.

But as the reduction of which we speak becomes more or less laborious in proportion to the degree of difficulty and the vastness of the object we embrace, so likewise we will have a greater or lesser right to demand of those who apply themselves to the study of Nature that they furnish us with such a reduction. For example, the magnet, one of the bodies that has been studied the most and about which such surprising discoveries have been made, has the property of attracting iron and of communicating this property to it. It turns toward the poles of the world with a variation which is itself subject to rules and is no less astonishing than a more exact direction would be. And finally, it has the property of forming a greater or lesser angle of inclination with the horizontal line according to the location on the globe where it is placed. All these singular properties, dependent on the nature of the magnet, probably relate to some general property which is the origin of them all and which up to now is unknown to us and perhaps will remain so for a long time. Since such knowledge and the necessary enlightenment concerning the physical cause of the properties of the magnet are lacking, it would doubtless be an investigation most worthy of a philosopher to reduce, if possible, all these properties to a single one, while showing the liaison that they have with one another. But the more useful such a discovery would be to the progress of physical science, the more we have occasion to fear that it will elude our efforts. I say the same of a large number of other phenomena whose enchainment perhaps belongs to the general system of the universe.

The only resource that remains to us in an investigation so difficult, although so necessary and even pleasant, is to collect as many facts as we can, to arrange them in the most natural order, and to relate them to a certain number of principal facts of which the others are only the consequences. If we presume sometimes to raise ourselves higher, let it be with that wise circumspection which befits so feeble an understanding as ours.

Such is the plan we must follow in that vast part of physics called General and Experimental Physics. [31] It differs from the physico-mathematical sciences in that it is properly only a systematic collection of experiments and observations. On the other hand, the physico-mathematical sciences, by applying mathematical calculations to experiment, sometimes deduce from a single and unique observation a large number of inferences that remain close to geometrical truths by virtue of their certitude. Thus, a single experiment on the reflection of light produces all of Catoptrics, or the science of the properties of mirrors. A single experiment on the refraction of light produces the mathematical explanation of the rainbow, the theory of colors, and all of Dioptrics, or the science of  [32] concave and convex lenses. From a single experiment on the pressure of fluids, we derive all the laws of their equilibrium and their movement. Finally, a single experiment on the acceleration of falling bodies opens up the laws of their descent down inclined planes and the laws of the movements of pendulums.

It must be confessed, however, that geometers sometimes abuse this application of algebra to physics. Lacking appropriate experiments as a basis for their calculations, they permit themselves to use hypotheses which are most convenient, to be sure, but often very far removed from what really exists in Nature. Some have tried to reduce even the art of curing to calculations, and the human body, that most complicated machine, has been treated by our algebraic doctors as if it were the simplest or the easiest one to reduce to its component parts. It is a curious thing to see these authors solve with the stroke of a pen problems of hydraulics and statics capable of occupying the greatest geometers for a whole lifetime. As for us who are wiser or more timid, let us be content to view most of these calculations and vague suppositions as intellectual games to which Nature is not obliged to conform, and let us conclude that the single true method of philosophizing as physical scientists consists either in the application of mathematical analysis to experiments, or in observation alone, enlightened by the spirit of method, aided sometimes by conjectures when they can furnish some insights, but rigidly dissociated from any arbitrary hypotheses. [33]

Let us stop here a moment and glance over the journey we have just made. We will note two limits within which almost all of the certain knowledge that is accorded to our natural intelligence is concentrated, so to speak. [34] One of those limits, our point of departure, is the idea of ourselves, which leads to that of the Omnipotent Being, and of our principal duties. The other is that part of mathematics whose object is the general properties of bodies, of extension and magnitude. Between these two boundaries is an immense gap where the Supreme Intelligence seems to have tried to tantalize the human curiosity, as much by the innumerable clouds it has spread there as by the rays of light that seem to break out at intervals to attract us. One can compare the universe to certain works of a sublime obscurity whose authors occasionally bend down within reach of their reader, seeking to persuade him that he understands nearly all. We are indeed fortunate if we do not lose the true route when we enter this labyrinth! Otherwise the flashes of light which should direct us along the way would often serve only to lead us further from it.

The limited quantity of certain knowledge upon which we can rely, relegated (if one can express oneself this way) to the two extremities of space to which we refer, is far indeed from being sufficient to satisfy all our needs. The nature of man, the study of which is so necessary and so highly recommended by Socrates, is an impenetrable mystery for man himself when he is enlightened by reason alone; and the greatest geniuses, after considerable reflection upon this most important matter, too often succeed merely in knowing a little less about it than the rest of men. The same may be said of our existence, present and future, of the essence of the Being to whom we owe it, and of the kind of worship he requires of us.

Thus, nothing is more necessary than a revealed Religion, which may instruct us concerning so many diverse objects. Designed to serve as a supplement to natural knowledge, it shows us part of what was hidden, but it restricts itself to the things which are absolutely necessary for us to know. The rest is closed for us and apparently will be forever. A few truths to be believed, a small number of precepts to be practiced: such are the essentials to which revealed Religion is reduced. Nevertheless, thanks to the enlightenment it has communicated to the world, the common people themselves are more solidly grounded and confident on a large number of questions of interest than the sects  [35] of the philosophers have been.

With respect to the mathematical sciences, which constitute the second of the limits of which we have spoken, their nature and their number should not overawe us. It is principally to the simplicity of their object that they owe their certitude. Indeed, one must confess that, since all the parts of mathematics do not have an equally simple aim, so also certainty, which is founded, properly speaking, on necessarily true and self-evident principles, does not belong equally or in the same way to all these parts. Several among them, supported by physical principles (that is, by truths of experience or by simple hypotheses), have, in a manner of speaking, only a certitude of experience or even pure supposition. To be specific, only those that deal with the calculation of magnitudes and with the general properties of extension, that is, Algebra, Geometry, and Mechanics, can be regarded as stamped by the seal of evidence. Indeed, there is a sort of gradation and shading, so to speak, to be observed in the enlightenment which these sciences bestow upon our minds. The broader the object they embrace and the more it is considered in a general and abstract manner, the more also their principles are exempt from obscurities. It is for this reason that Geometry is simpler than Mechanics, and both are less simple than Algebra. This will not be a paradox at all for those who have studied these sciences philosophically. The most abstract notions, those that the common run of men regard as the most inaccessible, are often the ones which bring with them a greater illumination. Our ideas become increasingly obscure as we examine more and more sensible properties in an object. Impenetrability, added to the idea of extension, seems to offer us an additional mystery; the nature of movement is an enigma for the philosophers; the metaphysical principle of the laws of percussion is no less concealed from them. In a word, the more they delve into their conception of matter and of the properties that represent it, the more this idea becomes obscure and seems to be trying to elude them. [36]

Thus one can hardly avoid admitting that the mind is not satisfied to the same degree by all the parts of mathematical knowledge. Let us go further and examine without bias the essentials to which this knowledge may be reduced. Viewed at first glance, the information of mathematics is very considerable, and even in a way inexhaustible. But when, after having gathered it together, we make a philosophical enumeration of it, we perceive that we are far less rich than we believed ourselves to be. I am not speaking here of the meager application and usage to which a number of these mathematical truths lend themselves; that would perhaps be a rather feeble argument against them. I speak of these truths considered in themselves. What indeed are most of those axioms of which Geometry is so proud, if not the expression of a single simple idea by means of two different signs or words? Does he who says two and two equals four have more knowledge than the person who would be contented to say two and two equals two and two? Are not the ideas of “all,” of “part,” of “larger,” and of “smaller,” strictly speaking, the same simple and individual idea, since we cannot have the one without all the others presenting themselves at the same time? As some philosophers have observed, we owe many errors to the abuse of words. It is perhaps to this same abuse that we owe axioms. My intention is not, however, to condemn their use; I wish only to point out that their true purpose is merely to render simple ideas more familiar to us by usage, and more suitable for the different uses to which we can apply them. I say virtually the same thing of the use of mathematical theorems, although with the appropriate qualifications. Viewed without prejudice, they are reducible to a rather small number of primary truths. If one examines a succession of geometrical propositions, deduced one from the other so that two neighboring propositions are immediately contiguous without any interval between them, it will be observed that they are all only the first proposition which is successively and gradually reshaped, so to speak, as it passes from one consequence to the next, but which, nevertheless, has not really been multiplied by this chain of connections; it has merely received different forms. It is almost as if one were trying to express this proposition by means of a language whose nature was being imperceptibly altered, so that the proposition was successively expressed in different ways representing the different states through which the language had passed. Each of these states would be recognized in the one immediately neighboring it; but in a more remote state we would no longer make it out, although it would still be dependent upon those states which preceded it and designed to transmit the same ideas. Thus, the chain of connection of several geometrical truths can be regarded as more or less different and more or less complicated translations of the same proposition and often of the same hypothesis. These translations are, to be sure, highly advantageous in that they put us in a position to make various uses of the theorem they express—uses more estimable or less, in proportion to their import and consequence. But, while conceding the substantial merit of the mathematical translation of a proposition, we must recognize also that this merit resides originally in the proposition itself. This should make us realize how much we owe to the inventive geniuses who have substantially enriched Geometry and extended its domain by discovering one of these fundamental truths which are the source and, so to speak, the original of a large number of others.

It is the same with the physical truths and with the properties of bodies whose connection we perceive. All of these properties gathered together offer us, properly speaking, only a simple and unique piece of knowledge. If others in larger quantity seem detached to us and form different truths, we owe this sorry advantage to the feebleness of our intelligence, and we may say that our abundance in that regard is the effect of our very poverty. Electrical bodies, in which so many curious but seemingly unrelated properties have been discovered, are perhaps in a sense the least known bodies, because they appear to be more known. That power of attracting small particles which they acquire when they are rubbed, and that of producing a violent commotion in animals, are two things for us. They would be a single one if we could reach the primary cause. The universe, if we may be permitted to say so, would only be one fact and one great truth for whoever knew how to embrace it from a single point of view. [37]

The different parts of knowledge, whether useful or pleasing, of which we have hitherto spoken and which owe their origin to our needs, are not the only ones which must have been cultivated. There are other branches of knowledge which are related to them and to which, therefore, men applied themselves at the same time they applied themselves to the former. We would have spoken of them all at the same time had we not thought it more appropriate and more in harmony with the philosophic order of this Discourse to consider first and without interruption the general study that men have made of bodies, the study by which men began, although other investigations were soon joined to it. Here is the approximate order in which these other studies must have followed one another.

The advantage men found in enlarging the sphere of their ideas, whether by their own efforts or by the aid of their fellows, made them think that it would be useful to reduce to an art the very manner of acquiring information and of reciprocally communicating their own ideas. This art was found and named Logic. It teaches how to arrange ideas in the most natural order, how to link them together in the most direct sequence, how to break up those which include too large a number of simple ideas, how to view ideas in all their facets, and finally how to present them to others in a form that makes them easy to grasp. This is what constitutes this science of reasoning, which is rightly considered the key to all our knowledge. However, it should not be thought that it [the formal discipline of Logic] belongs among the first in the order of discovery. The art of reasoning is a gift which Nature bestows of her own accord upon men of intelligence, and it can be said that the books which treat this subject are hardly useful except to those who can get along without them. People reasoned validly long before Logic, reduced to principles, taught how to recognize false reasonings, and sometimes even how to cloak them in a subtle and deceiving form. [38]

This most valuable art of assigning a suitable connection to ideas, and consequently of facilitating the passage from one to the other, furnishes the means of effecting at least a partial reconciliation among men who seem to differ the most. Indeed, all our knowledge is ultimately reduced to sensations that are approximately the same in all men. And the art of combining and relating direct ideas in reality adds nothing to them except a more or less exact arrangement and an enumeration which can be rendered more or less intelligible to others. The difference between the man who combines ideas easily and the one who combines them with difficulty is scarcely greater than that between the man who judges a picture at one glance and the one who needs to have all the parts pointed out to him one after another in order to appreciate it. Both have experienced the same sensations in their first glance, but these sensations have only slid over the second man, so to speak. To lead him to the same point at which the other man arrived instantaneously, it would only have been necessary to stop him and make him concentrate for a longer time on each sensation. By this means, the reflective ideas of the first man would have become as much within reach of the second as the direct ideas. Hence it is perhaps true that there is hardly a science or an art which cannot, with rigor and good logic, be taught to the most limited mind, because there are but few arts or sciences whose propositions or rules cannot be reduced to some simple notions and arranged in such a close order that their chain of connection will nowhere be interrupted. As the mind operates more or less slowly, that chain will be required in greater or less degree, and the only advantage possessed by great geniuses  [39] is that they have less need of it than others, or rather they are able to form it rapidly and almost unconsciously.

The science of communication of ideas is not confined to putting order in ideas themselves. In addition it should teach how to express each idea in the clearest way possible, and consequently how to perfect the signs that are designed to convey it; and indeed this is what men have gradually done. Languages, born along with societies, doubtless began as only a rather bizarre collection of signs of all sorts, and consequently, the natural bodies which impinge upon our senses were the first objects to be designated by names. But so far as we can judge, languages in this first beginning  [40] were intended only for the most pressing use, and they must have been very imperfect and limited, and subject to very few definite principles. The arts or sciences which were of absolute necessity may have made considerable progress while the rules of diction and of style were yet to be born. The communication of ideas hardly suffered in any case from this lack of rules or even from the paucity of words; or rather it suffered only to the degree required to oblige each man to augment his own knowledge by stubborn effort, without depending too much upon others. Too much communication can sometimes benumb the mind and prejudice the efforts of which it is capable. If one observes the prodigies of some of those born blind, or deaf and mute, one will see what the faculties of the mind can perform if they are lively and called into action by difficulties which must be overcome.

However, since there are some incontestable advantages in being able to convey and receive ideas easily in mutual intercourse, it is not surprising that men have sought more and more to augment that facility. To do so, they began by reducing signs to words, because words are, so to speak, the symbols that we have most readily at hand. In addition, the order in which words are generated followed the order of the operations of the mind: after individual objects, names were given to the sensible qualities, which, though they do not exist by themselves, exist in these individual objects and are held in common by several of them. Little by little those abstract terms were achieved, some of which serve to tie ideas together, others to designate the general properties of bodies, and others to express purely intellectual notions. All those terms which children take such a long time to learn undoubtedly took even longer to find. Finally, men reduced the usage of words to precepts and formed Grammar, which can be regarded as one of the branches of Logic. When enlightened by a subtle and refined Metaphysics, Grammar separates the shadings of ideas and teaches how to distinguish these shadings through different signs. It sets rules so that signs can be utilized to the greatest advantage, and often discovers, through that philosophic spirit which delves back to the source of everything, the reasons for the apparently bizarre selection which makes one sign preferred to another. And finally it leaves to that national caprice called “usage” only what absolutely cannot be taken away from it. [41]

While communicating ideas to one another, men try also to communicate their passions. They succeed in doing this by Eloquence. As Logic and Grammar speak to the mind, Eloquence was created to speak to sentiment, and can impose silence even upon reason. The prodigious effect that it has worked upon an entire nation, often through a single individual, is perhaps the most striking evidence of the superiority of one man over another. It is most surprising that men have believed they could make rules take the place of such a rare talent. It is almost as if they wanted to reduce genius to precepts. The man who first alleged that we owe orators to art either was not one of their number or was quite ungrateful to Nature. Nature alone can create an eloquent man. Men themselves are the first book that he must study in order to succeed; the great models are the second. And everything that these illustrious writers have left us of a philosophical or intellectual nature concerning the talent of the orator only proves how difficult it is to approach them. They were too enlightened to claim that they were showing the way; they doubtless wished merely to mark out its pitfalls. Those pedantic puerilities which have been honored by the name of Rhetoric, or rather which only serve to render that name ridiculous, are to the oratorical art what scholasticism is to true philosophy. They are capable of giving only the most false and barbarous idea of Eloquence. However, although people have begun to recognize rather universally the abuse of these puerilities, their long-established position as a distinguished branch of human knowledge does not yet permit us to banish them. [42] Perhaps, to the honor of our discernment, that time will one day come.

It is not enough for us to live with our contemporaries and to dominate them. Being animated by curiosity and self-esteem, we try, in our natural eagerness, to embrace the past, the present, and the future all at the same time. We wish simultaneously to live with those who will follow us and to have lived with those who have preceded us. From these [desires] come the origin and the study of History, which, while uniting us with past centuries through the spectacle of their vices, their virtues, their knowledge, and their errors, transmits our own [virtues and defects] to the centuries of the future. It is from History that we learn to hold men in high regard solely for the good that they do and not for the imposing pomp which surrounds them. The sovereigns, those quite wretched men from whom everything conspires to hide the truth, can judge themselves ahead of time at this terrible and honest tribunal; the testimony of History toward those of their predecessors who resemble them is the image of posterity’s judgment upon themselves.

Chronology and Geography are the two offshoots and supports of the science of which we are speaking. The one, Chronology, locates men in time, so to speak. The other, Geography, distributes them over our globe. Both draw considerable help from the history of the earth and of the heavens, that is, from historical facts and celestial observations. And if it were permitted here to borrow the language of the poets, one could say that the sciences of time and place are daughters of Astronomy and History. [43]

One of the principal rewards of the study of empires and their revolutions lies in the examination of how men, having been separated into various great families, so to speak, have formed diverse societies, how these different societies have given birth to different types of governments, and how they have tried to distinguish themselves both by the laws that they have given themselves and by the particular signs that each has created in order that its members might communicate more easily with one another. Such is the source of that diversity of languages and laws which has become an object of considerable study, to our misfortune. Such is also the origin of Politics, a sort of ethics of a particular and superior kind, to which the principles of ordinary ethics can on occasion be accommodated only with much subtlety. Penetrating into the essentials of the government of states, Politics distinguishes what can preserve, enfeeble, or destroy them. Perhaps this is the most difficult study of all, by virtue of the profound knowledge of peoples and men it demands and because of the extent and the variety of the talents that it presupposes. Such is the case especially when the man of politics endeavors not to forget that natural law, being anterior to all particular conventions, is thus the first law of peoples, and that to be a statesman one must not cease to be a man.

Such are the principal branches of that part of human knowledge which consists either in the direct ideas which we have received through our senses, or in the combination or comparison of these ideas—a combination which in general we call Philosophy.  [44] These branches are subdivided into an infinite number of others, the enumeration of which would be enormously long, and belongs more to this work itself [the Encyclopedia ] than to its preface.

Since the first operation of reflection consists in drawing together and uniting direct notions, we of necessity have begun this Discourse by looking at reflection from that point of view and reviewing the different sciences that result from it. But the notions formed by the combination of primitive ideas are not the only ones of which our minds are capable. There is another kind of reflective knowledge, and we must turn to it now. It consists of the ideas which we create for ourselves by imagining and putting together beings similar to those which are the object of our direct ideas. This is what we call the imitation of Nature, so well known and so highly recommended by the ancients. Since the direct ideas that strike us most vividly are those which we remember most easily, these are also the ones which we try most to reawaken in ourselves by the imitation of their objects. Although pleasant objects [of reality] have a greater impact on us because they are real rather than mere imitations, we are somewhat compensated for that loss of attractiveness  [45] by the pleasure which results from imitation. As for the objects which, when real, excite only sad or tumultuous sentiments, imitation of them is more pleasing than the objects themselves, because it places us at precisely that distance where we experience the pleasure of the emotion without feeling its disturbance. That imitation of objects capable of exciting in us lively, vivid, or pleasing sentiments, whatever their nature may be, constitutes in general the imitation of la belle Nature, about which so many authors have written without presenting a clear idea of it. [46] They fail to do so either because la belle Nature can be perceived by only an extremely delicate sensitivity, or perhaps also because in this matter the limits which distinguish the arbitrary from the true are not yet well defined and leave some area open to opinion.

Painting and Sculpture ought to be placed at the head of that knowledge which consists of imitation, because it is in those arts above all that imitation best approximates the objects represented and speaks most directly to the senses. Architecture, that art which is born of necessity and perfected by luxury, can be added to those two. Having developed by degrees from cottages to palaces, in the eyes of the philosopher it is simply the embellished mask, so to speak, of one of our greatest needs. The imitation of la belle Nature in Architecture is less striking and more restricted than in Painting or Sculpture. The latter express all the parts of la belle Nature indifferently and without restriction, portraying it as it is, uniform or varied; while Architecture, combining and uniting the different bodies it uses, is confined to imitating the symmetrical arrangement that Nature observes more or less obviously in each individual thing, and that contrasts so well with the beautiful variety of all taken together. [47]

Poetry, which comes after Painting and Sculpture, and which imitates merely by means of words disposed according to a harmony agreeable to the ear, speaks to the imagination rather than to the senses. In a touching and vivid manner it represents to the imagination the objects which make up this universe. By the warmth, the movement, and the life which it is capable of giving, it seems rather to create than to portray them. Finally, music, which speaks simultaneously to the imagination and to the senses, holds the last place in the order of imitation—not that its imitation is less perfect in the objects which it attempts to represent, but because until now it has apparently been restricted to a smaller number of images. This should be attributed less to its nature than to the lack of sufficient inventiveness and resourcefulness in most of those who cultivate it. It will not be useless to make some reflections on this subject. In its origin music perhaps was intended only to represent noise. Little by little it has become a kind of discourse, or even language, through which the different sentiments of the soul, or rather its different passions, are expressed. But why reduce this kind of expression to passions alone, and why not extend it as much as possible to the sensations themselves? Although the perceptions that we receive through various organs differ among themselves as much as their objects, we can nevertheless compare them according to another point of view which is common to them: that is, by the pleasurable or disquieting effect they have upon our soul. A frightening object, a terrible noise, each produces an emotion in us by which we can bring them somewhat together, and we can often designate both of these emotions either by the same name or by synonymous names. Thus, I do not see why a musician who had to portray a frightening object could not succeed in doing so by seeking in nature the kind of sound that can produce in us the emotion most resembling the one excited by this object. I say the same of agreeable sensations. To think otherwise would be to wish to restrict the limits of art and of our pleasures. I confess that the kind of depiction of which we are speaking here demands a subtle and profound study of the shadings which differentiate our sensations; thus it is not to be hoped that these shadings will be distinguished by an ordinary talent. Grasped by the man of genius, perceived by the man of taste, understood by the man of intelligence, they are lost on the multitude. Any music that does not portray something is only noise; and without that force of habit which denatures everything, it would hardly create more pleasure than a sequence of harmonious and sonorous words stripped of order and connection. It is true that a musician desirous of portraying everything would in many circumstances give us scenes of harmony which would not be grasped by vulgar senses. But all that can be concluded from this is that after having created an art of learning music one ought also to create an art of listening to it. [48]

We will stop enumerating the principal parts of our knowledge here. If one now looks at them all together and attempts to find some general points of view which can serve to differentiate them, one finds that some which are purely practical in nature [arts] have as their aim the execution of something. Others of a purely speculative nature [sciences] are limited to the examination of their object and the contemplation of its properties. [49] Finally, still others derive practical use from the speculative study of their object. Speculation and practice constitute the principal difference that distinguishes the Sciences from the Arts, and it is more or less according to this concept that we have given one or another name to each of the parts of our knowledge. We must acknowledge, however, that our ideas are not yet well established on this subject. Often we do not know what names to give most of those parts of knowledge in which speculation is united with practice, and it is still disputed in the schools, for example, whether Logic is an art or a science. The problem would soon be resolved by answering that it is simultaneously one and the other. How many questions and how much trouble we would spare ourselves if we finally determined the meaning of words in a clear and precise way!

In general the name Art may be given to any system of knowledge which can be reduced to positive and invariable rules independent of caprice or opinion. In this sense it would be permitted to say that several of our sciences are arts when they are viewed from their practical side. But just as there are rules for the operations of the mind or soul, there are also rules for those of the body: that is, for those operations which, applying exclusively to external bodies, can be executed by hand alone. Such is the origin of the differentiation of the arts into liberal and mechanical arts, and of the superiority which we accord to the first over the second. That superiority is doubtless unjust in several respects. Nevertheless, none of our prejudices, however ridiculous, is without its reason, or to speak more precisely, its origin, and although philosophy is often powerless to correct abuses, it can at least discern their source. After physical force rendered useless the right of equality possessed by all men, the weakest, who are always the majority, joined together to check it. With the aid of laws and different sorts of governments they established an inequality of convention in which force ceased to be the defining principle. [50] Even though they united with good reason to preserve this inequality of convention once it was well established, men have not been able to resist complaining against it secretly because of that desire for superiority which nothing has been able to destroy in them. Thus, they have sought a sort of compensation in a less arbitrary inequality. Since physical force enchained by laws is no longer capable of offering any means of superiority, they have been reduced to seeking a principle of inequality in the difference of intellectual excellence—a principle which is equally natural, more peaceful, and more useful to society. Thus the most noble part of our being has in some measure taken vengeance for the first advantages which the basest part had usurped, and the talents of the mind have been generally recognized as superior to those of the body. The mechanical arts, which are dependent upon manual operation and are subjugated (if I may be permitted this term) to a sort of routine, have been left to those among men whom prejudices have placed in the lowest class. Poverty has forced these men to turn to such work more often than taste and genius have attracted them to it. Subsequently it became a reason for holding them in contempt—so much does poverty harm everything that accompanies it. With regard to the free operations of the mind, they have been apportioned to those who have believed themselves most favored of Nature in this respect. However, the advantage that the liberal arts have over the mechanical arts, because of their demands upon the intellect and because of the difficulty of excelling in them, is sufficiently counterbalanced by the quite superior usefulness which the latter for the most part have for us. It is this very usefulness which reduced them perforce to purely mechanical operations in order to make them accessible to a larger number of men. But while justly respecting great geniuses for their enlightenment, society ought not to degrade the hands by which it is served. The discovery of the compass is no less advantageous to the human race than the explication of its properties would be to physical science. Finally, considering in itself the principle of the distinction about which we are speaking, how many alleged scholars are there for whom science is in truth only a mechanical art? What real difference is there between a head stuffed with facts without order, without utility, and without connection, and the instinct of an artisan reduced to mechanical operation?

The contempt in which the mechanical arts are held seems to have affected to some degree even their inventors. The names of these benefactors of humankind are almost all unknown, whereas the history of its destroyers, that is to say, of the conquerors, is known to everyone. However, it is perhaps in the artisan that one must seek the most admirable evidences of the sagacity, the patience, and the resources of the mind. I admit that most of the arts have been invented only little by little and that it required a rather long sequence of centuries to bring watches, for example, to their present point of perfection. But is not the same true of the sciences? How many of the discoveries that have immortalized their authors had been prepared by the works of preceding centuries, sometimes being already brought to their maturity, to the point where they required just one step more to be accomplished? And not to leave watchmaking, why are not those to whom we owe the fusee, the escapement, the repeating-works  [51] of watches equally esteemed with those who have worked successively to perfect algebra? Moreover, if I may believe a few philosophers who have not been deterred from studying the arts by the prevailing contempt for them, there are certain machines that are so complicated, and whose parts are all so dependent on one another, that their invention must almost of necessity be due to a single man. Is not that man of genius, whose name is shrouded in oblivion, well worthy of being placed beside the small number of creative minds who have opened new routes for us in the sciences?

Among the liberal arts that have been reduced to principles, those that undertake the imitation of Nature have been called the Fine Arts because they have pleasure for their principal object. [52] But that is not the only characteristic distinguishing them from the more necessary or more useful liberal arts, such as Grammar, Logic, and Ethics. The latter have fixed and settled rules which any man can transmit to another, whereas the practice of the Fine Arts consists principally in an invention which takes its laws almost exclusively from genius. The rules which have been written concerning these arts are, properly speaking, only the mechanical part. Their effect is somewhat like that of the telescope; they only aid those who see.

From everything we have said heretofore it follows that the different ways in which our mind operates on objects and also the different uses which it derives from these objects are the first available means of generally distinguishing the various parts of knowledge from one another. Everything is related to our needs, whether from absolute necessity, or from convenience and pleasure, or even from custom and caprice. The more the needs are remote or difficult to satisfy, the slower the knowledge intended to satisfy them will be in making its appearance. Think of the progress Medicine would have made at the expense of the purely speculative sciences if it were as certain as Geometry. But there are still other very marked characteristics in the way our knowledge affects us and in the different judgments that our soul makes of ideas. These judgments are designated by the words evidence, certitude, probability, feeling, and taste.

Evidence properly pertains to the ideas whose connection the mind perceives immediately. [53] Certitude pertains to those whose connection can be known only by the aid of a certain number of intermediate ideas, or, what is the same thing, to propositions whose identity with a self-evident principle can be discovered only by a circuit of greater or lesser length. From this it would follow that according to the nature of minds, what is evident for one person would sometimes only be certain for another. Taking the words in another sense, it could also be said that evidence is the result of the operations of the mind alone and is related to metaphysical and mathematical speculations;  [54] and that certitude is more appropriate to physical objects, the knowledge of which is the fruit of the constant and invariable testimony of our senses. Probability applies principally to historical facts and generally to all past, present, and future events that we attribute to a kind of chance because we cannot perceive the causes of them. The part of that knowledge which has the present and the past for its object often produces a conviction as strong as that which comes from axioms, although it is founded merely on testimony. Feeling is of two sorts. The one concerned with moral truths is called conscience. It is a result of natural law and of our conception of good and evil. [55] One could call it evidence of the heart, for, although it differs greatly from the evidence of the mind which concerns speculative truths, it subjugates us with the same force. [56] The other sort of feeling pertains in particular to the imitation of la belle Nature and to what we call beauties of expression. It grasps sublime and striking beauties with rapture, subtly discerns hidden beauties, and proscribes those that merely feign their appearance. Often, indeed, it pronounces severe judgments without bothering to describe in detail the motives for them, because these motives depend upon a multitude of ideas that are difficult to expound all at once and still more difficult to transmit to others. It is to this kind of feeling that we owe taste and genius, which are distinguished from one another in that genius is the feeling that creates and taste the feeling that judges.


After reviewing the different parts of our knowledge and the characteristics that distinguish them, it remains for us only to make a genealogical or encyclopedic tree which will gather the various branches of knowledge together under a single point of view and will serve to indicate their origin and their relationships to one another. We will explain in a moment the use to which that tree may be put according to our claims, but the execution itself is not without difficulty. Although the philosophical history we have just given of the origins of our ideas is very useful in facilitating such a work, it should not be thought that the encyclopedic tree ought to be, or even can be, slavishly subject to that history. The general system of the sciences and the arts is a sort of labyrinth, a tortuous road which the intellect enters without quite knowing what direction to take. Impelled, first of all, by its needs and by those of the body to which it is united, the intelligence studies the first objects that present themselves to it. It delves as far as it can into the knowledge of these objects, soon meets difficulties that obstruct it, and whether through hope or even through despair of surmounting them, plunges on to a new route; now it retraces its footsteps, sometimes crosses the first barriers only to meet new ones; and passing rapidly from one object to another, it carries through a sequence of operations on each of them at different intervals, as if by jumps. The discontinuity of these operations is a necessary effect of the very generation of ideas. However philosophic this disorder may be on the part of the soul, [57] an encyclopedic tree which attempted to portray it would be disfigured, indeed utterly destroyed.

Moreover, as we have already shown in the subject of Logic, most of the sciences which we regard as including the basic principles of all the others, and which ought for this reason to occupy the first places in the encyclopedic arrangement, do not have the first places in the genealogical arrangements of ideas because they were not invented first. Indeed, in the beginning we [human beings] of necessity studied individual things. It is only after having considered their particular and palpable properties that we envisaged their general and common properties and created Metaphysics and Geometry by intellectual abstraction. Only after the long usage of the first signs have we perfected the art of these signs to the point of making a science of them. And it is only after a long sequence of operations on the objects of our ideas that, through reflection, we have at length given rules to these operations themselves.

Finally, the system of our knowledge is composed of different branches, several of which have a common point of union. Since it is not possible, starting out from this point, to begin following all the routes simultaneously, it is the nature of the different minds that determines which route is chosen. Rarely does a single mind travel along a large number of these routes at the same time. In the study of Nature, men at first applied themselves, as if in concert, to satisfying the most pressing needs. But when they came to less absolutely necessary knowledge, they were obliged to divide it among themselves, and each one moved forward in almost equal step with the others. Thus several sciences have been contemporaneous, so to speak. But when tracing in historical order the progress of the mind, one can only embrace them successively.

It is not the same with the encyclopedic arrangement of our knowledge. This consists of collecting knowledge into the smallest area possible and of placing the philosopher at a vantage point, so to speak, high above this vast labyrinth, whence he can perceive the principal sciences and the arts simultaneously. From there he can see at a glance the objects of their speculations and the operations which can be made on these objects; he can discern the general branches of human knowledge, the points that separate or unite them; and sometimes he can even glimpse the secrets that relate them to one another. It is a kind of world map which is to show the principal countries, their position and their mutual dependence, the road that leads directly from one to the other. This road is often cut by a thousand obstacles, which are known in each country only to the inhabitants or to travelers, and which cannot be represented except in individual, highly detailed maps. These individual maps will be the different articles of the Encyclopedia and the Tree or Systematic Chart will be its world map. [58]

But as, in the case of the general maps of the globe we inhabit, objects will be near or far and will have different appearances according to the vantage point at which the eye is placed by the geographer constructing the map, likewise the form of the encyclopedic tree will depend on the vantage point one assumes in viewing the universe of letters. Thus one can create as many different systems of human knowledge as there are world maps having different projections, and each one of these systems might even have some particular advantage possessed by none of the others. There are hardly any scholars who do not readily assume that their own science is at the center of all the rest, somewhat in the way that the first men placed themselves at the center of the world, persuaded that the universe was made for them. Viewed with a philosophical eye, the claim of several of these scholars could perhaps be justified by rather good reasons, quite aside from self-esteem.

In any case, of all the encyclopedic trees the one that offered the largest number of connections and relationships among the sciences would doubtless deserve preference. But can one flatter oneself into thinking it has been found? We cannot repeat too often that nature is composed merely of individual things which are the primary object of our sensations and direct perceptions. To be sure, we note in these individual things common properties by which we compare them and dissimilar properties by which we differentiate them. And these properties, designated by abstract names, have led us to form different classes in which these objects have been placed. But often such an object, which because of one or several of its properties has been placed in one class, belongs to another class by virtue of other properties and might have been placed accordingly. Thus, the general division remains of necessity somewhat arbitrary. The most natural arrangement would be the one in which the objects followed one another by imperceptible shadings which serve simultaneously to separate them and to unite them. [59] But the small number of beings known to us does not permit us to indicate these shadings. The universe is but a vast ocean, on the surface of which we perceive a few islands of various sizes, whose connection with the continent is hidden from us.

One could construct the tree of our knowledge by dividing it into natural and revealed knowledge, or useful and pleasing knowledge, or speculative and practical knowledge, or evident, certain, probable, and sensitive knowledge, or knowledge of things and knowledge of signs, and so on into infinity. We have chosen a division which has appeared to us most nearly satisfactory for the encyclopedic arrangement of our knowledge and, at the same time, for its genealogical arrangement. We owe this division to a celebrated author [Bacon] of whom we will speak later in this preface. [60] To be sure, we have thought it necessary to make some changes in his division, of which we will render an account; but we are too aware of the arbitrariness which will always prevail in such a division to believe that our system is the only one or the best. It will be sufficient for us if our work is not entirely disapproved of by men of intelligence. We do not wish to resemble that multitude of naturalists (censured with such good reason by a modern philosopher) whose energies have been ceaselessly devoted to dividing the productions of Nature into genera and species, consuming an amount of time in this labor which would have been employed to much better purpose in the study of those productions themselves. [61] What would be said of an architect, who, having to build an immense edifice, passed his whole life in drawing the plans for it? Or likewise what would we say of an inquisitive person who, proposing to inspect an enormous palace, spent all his time in observing the entryway?

The objects to which our soul applies itself are either spiritual or material, and our souls are occupied with these objects either through direct ideas or through reflective ideas. The system of direct knowledge consists simply in the purely passive and almost mechanical collection of this same knowledge; this is what we call memory. Reflection is of two kinds (as we have already observed): either it reasons on the objects of direct ideas, or it imitates them. Thus memory, reason (strictly speaking), and imagination are the three different manners in which our soul operates on the objects of its thoughts. We do not take imagination here to be the ability to represent objects to oneself, since that faculty is simply the memory itself of sensible objects, a memory which would be continually in action if it were not assisted and relieved by the invention of signs. We take imagination in the more noble and precise sense, as the talent of creating by imitating.

These three faculties form at the outset the three general divisions of our system of human knowledge: History, which is related to memory; Philosophy, which is the fruit of reason; and the Fine Arts, which are born of imagination. Placing reason ahead of imagination appears to us to be a well-founded arrangement and one which is in conformity with the natural progress of the operations of the mind. Imagination is a creative faculty, and the mind, before it considers creating, begins by reasoning upon what it sees and knows. Another motive which should decide us to place reason ahead of imagination is that in the latter faculty the other two are to some extent brought together. The mind creates and imagines objects only insofar as they are similar to those which it has known by direct ideas and by sensations. The more it departs from these objects, the more bizarre and unpleasant are the beings which it forms. Thus, in the imitation of Nature, invention itself is subjected to certain rules. It is principally these rules which form the philosophical part of the Fine Arts, which is still rather imperfect because it can be the work only of genius, and genius prefers creation to discussion.

Finally, if we examine the progress of reason in its successive operations, we will again agree that it ought to precede imagination in the arrangement of our faculties, because reason in a way leads to imagination by the last operations which it makes on objects. These operations consist entirely in “creating” general beings, so to speak, which no longer fall within the immediate competence of our senses since they are separated from their subject by abstraction. Thus of all the sciences that pertain to reason, Metaphysics and Geometry are those in which imagination plays the greatest part. I ask pardon of those superior wits who are detractors of Geometry; doubtless they do not think  [62] themselves so close to it, although all that separates them perhaps is Metaphysics. Imagination acts no less in a geometer who creates than in a poet who invents. It is true that they operate differently on their object. The first shears it down and analyzes it, the second puts it together and embellishes it. It is true, further, that these different ways of operating stem from different sorts of minds, and for this reason the talents of a great geometer and those of a great poet will perhaps never be found together. [63] But whether or not they are mutually exclusive, they have no right to hold one another in contempt. Of all the great men of antiquity, Archimedes is perhaps the one who most deserves to be placed beside Homer. I hope that this digression by a geometer who loves his art will be pardoned, and that he will not be accused of being an excessive enthusiast; and I return to my subject.

The general distribution of beings into spiritual and material provides a subdivision of the three general branches. History and Philosophy are occupied with each of these two kinds of beings, while imagination deals only with purely material beings, which is a new reason for placing it last in the arrangement of our faculties. At the head of the spiritual beings is God, who necessarily holds the first rank by virtue of His nature and of our need to know Him. Below that Supreme Being are the created spiritual beings whose existence is taught us by Revelation. Next comes man. Composed of two principles, he belongs by virtue of his soul to the spiritual beings and by virtue of his body to the material world. And finally comes that vast universe which we call the corporeal world, or Nature. We do not know why the celebrated author [Bacon] who serves as our guide in this arrangement has placed Nature before man in his system. It seems, on the contrary, that everything engages us to put man in the passageway that separates God and the spiritual beings from material bodies.

Insofar as it is related to God, History includes either Revelation or tradition, and according to these two points of view, is divided into sacred history and ecclesiastical history. The history of man has for its object either his actions or his knowledge, and consequently is civil or literary. In other words, it is divided between the great nations and the great geniuses, between the kings and the men of letters, between the conquerors and the philosophers. Finally, the history of Nature is the history of the innumerable productions that we observe therein, forming a quantity of branches almost equal in number to those diverse productions. Among these different branches, a distinguished place should be given to the history of the arts, which is simply the history of the use which men have made of the productions of Nature to satisfy their needs or their curiosity.

Such are the principal objects of memory. Let us turn now to the faculty that reflects and reasons. Both the spiritual and the material beings on which that faculty acts have some general properties such as existence, possibility, and duration. The examination of these properties constitutes at the outset that branch of Philosophy from which all others in part borrow their principles and which is called Ontology, or the science of being, or general Metaphysics. We descend from there to the different particular beings, and the science of these different beings is divided according to the same plan as that of History.

The science of God, called Theology, has two branches: Natural Theology has only such knowledge of God as reason unaided produces, a knowledge which is not of very great extent. Revealed Theology draws a much more perfect knowledge of that Supreme Being from sacred history. From this same Revealed Theology results the science of created spiritual beings. Here again we have felt we ought to depart from our author [Bacon]. It seems to us that science, considered as belonging to reason, ought not to be divided into Theology and Philosophy as it has been by him. For Revealed Theology is simply reason applied to revealed facts. One can say that it belongs to History by virtue of the dogma that it teaches and to Philosophy by virtue of the consequences that it draws from these dogmas. Thus, to separate Theology from Philosophy would be to cut the offshoot from the trunk to which it is united by its very nature. It seems also that the science of spiritual beings is bound much more closely to Revealed Theology than to Natural Theology. [64]

The first part of the science of man is that of the soul, and that science has for its aim either the speculative knowledge of the human soul or knowledge of its operations. Speculative knowledge of the soul derives in part from Natural Theology and in part from Revealed Theology, and is called Pneumatology or Particular Metaphysics. The knowledge of its operations is subdivided into two branches, these operations being capable of having either the discovery of truth or the practice of virtue for their object. The discovery of truth, which is the aim of Logic, produces the art of transmitting it to others. Thus, the use that we make of Logic is partly for our own advantage, partly for that of others of our species. The rules of Ethics are less related to isolated man and necessarily presume that he is in society with other men.

The science of Nature is simply the science of bodies. But since bodies have general properties which are common to them, such as impenetrability, mobility, and extension, the science of Nature ought therefore to begin with the study of these properties. They have, so to speak, a purely intellectual side, by which they open an immense scope to the speculations of the mind, and a material and sensible side by which we can measure them. Intellectual speculation is related to General Physics, which is, properly speaking, simply the metaphysics of bodies, and measurement is the object of Mathematics, whose divisions extend almost to infinity.

These two sciences lead to Particular Physics, which studies the bodies in themselves and whose sole object is individual things. Our own body ought to hold first rank among the bodies whose properties it is worthwhile for us to know, and it is immediately followed by those which we most need to know for self-preservation. Whence result Anatomy, Agriculture, Medicine, and their different branches. Finally, all the natural bodies submitted to our examination produce the innumerable other parts of reasoned Physics.

Painting, Sculpture, Architecture, Poetry, Music, and their different divisions make up the third general distribution, which is born of imagination and whose parts are comprised under the name of Fine Arts. We can also include them under the general title of Painting [portrayal], because all the Fine Arts can be reduced to that and differ only by the means which they use. Finally, we could relate them all to Poetry by taking this word in its natural signification, which is simply invention or creation.

Such are the principal parts of our encyclopedic tree. They will be found in more detail at the end of this Preliminary Discourse. We have made a sort of chart of them to which we have joined a much more extended explication than has just been given. This chart and this explication have already been published in the Prospectus in order to sound out the pleasure of the public. We have made some changes which will be easy to recognize. They are the fruit either of our reflections or of the counsels of a few philosophers who have been sufficiently public-spirited to take an interest in our work. If the enlightened public gives its approbation to these changes, it will be the reward for our tractableness, and if it does not approve them, we will only be more strongly convinced of the impossibility of designing an encyclopedic tree that would please everyone.

There is this advantage in the general division of our knowledge according to our three faculties: it could also provide the three divisions of the literary world into Scholars, Philosophers, and beaux esprits,  [65] so that, after having designed the tree of sciences, one would be able to construct the tree of men of letters on the same pattern. Memory is the talent of the first [group]; wisdom belongs to the second; and the last have pleasure as their portion. Thus, if one considers memory as a beginning of reflection and adds to it the reflection that combines and the one that imitates, one could say in general that the differences which exist among men are determined by the variation in the number and nature of each man’s reflective ideas. One could also say that reflection, taken in the most extended sense that one can give it, molds the character of the intelligence and distinguishes its different types. For the rest, the three kinds of “republics” into which we have just distributed the men of letters ordinarily have nothing in common, except the lack of esteem in which they hold one another. The poet and the philosopher treat each other as madmen who feed on fancies. Both regard the scholar as a sort of miser who thinks only of amassing without enjoying and who indiscriminately heaps up the basest metals along with the most precious. And the scholar, who considers everything which is not fact to be idle words, holds the poet and the philosopher in contempt as being men who think they are rich because their expenses exceed their resources.

It is thus that people avenge themselves for advantages they do not have. Men of letters would better understand their interests, if, instead of trying to isolate themselves, they recognized the reciprocal need they have of each other’s works and the assistance which they could draw from them. Undoubtedly society owes its principal enjoyments to beaux esprits and its enlightenment to philosophers, but neither of them appreciates how much they owe to memory. Memory includes the primary material of all our knowledge, and the works of the scholars have often furnished the subjects upon which the philosopher and the poet exercise their skills. When the ancients called the Muses the daughters of memory (a modern author has said), they appreciated perhaps how much that faculty of our mind is necessary to all the others. The Romans raised temples to her, just as they did to Fortune.

It remains for us to show how we have tried to reconcile the encyclopedic arrangement with the alphabetical arrangement in this Dictionary. To accomplish this task we have employed three means: the chart at the beginning of the work, the [designation of the] science to which each article is related, and the manner in which the article is treated. Ordinarily the name of the science to which the article belongs has been placed after the word that constitutes the subject of the article. Simply by referring to the chart one can see what rank this science occupied and hence understand the place that the article is to have in the Encyclopedia. If it happens that the name of the science is omitted, a reading of the article will suffice to make clear the science to which it is related, and even if we forget to point out, for example, that the word Bomb belongs to the military art, and the name of a city or country to geography, we have enough confidence in the intelligence of our readers to hope that they will not be shocked by such an omission. Moreover, through the arrangement of the contents of each article, especially in those of some length, it will hardly be possible to avoid seeing that such and such an article is related to another article, which belongs to a different science, and which in turn is related to a third article, and so forth. By means of the precision and frequency of the references to other articles [ les renvois ], we have tried to leave nothing to be desired on that score. For such references in this Dictionary are unusual in that they serve principally to indicate the connection of the materials, whereas in other works of this type, they are intended only to elucidate one article by another. Often, indeed, we have omitted the reference to another article because the terms of art or science which it would have designated are explained in individual articles which the reader will find by himself. Especially in the general articles on the sciences, we have tried to explain the aid which they give one another. Thus, three things make up the encyclopedic arrangement: the name of the science to which the article belongs, the position of that science in the tree, and the connection of the article with others in the same science or in a different science. This connection is indicated by the references to other articles or is easy to understand by means of the technical terms explained in their alphabetical place. We are not concerned here with the reasons which have made us prefer the alphabetical arrangement in this work to all others; these will be explained later when we speak of this collection as a Dictionary of Sciences and Arts.

For the rest, we will make two observations concerning the part of our work which involves the encyclopedic arrangement and which is intended more for enlightened men than for the multitude. The first is that it would often be absurd to expect to find an immediate connection between one article of this Dictionary and another article taken at random. Thus one would look in vain to find by what secret bonds the article Conic Section can be related to the article Accusative. The encyclopedic arrangement does not suppose that all the sciences stem from one another. They are branches which grow out of the same trunk, that is, out of the human intellect. These branches often have no immediate connection among themselves, and several are united only by the trunk itself. Thus, Conic Section concerns geometry, geometry leads to particular physics, this latter to general physics, and general physics to metaphysics. Metaphysics is very close to grammar, to which the word accusative belongs. But when one has arrived at this last point by the route we have just indicated, one is so far from the starting point that it has been completely lost from sight.

Our second remark is that one should not attribute more advantages to our encyclopedic tree than we claim to give it. The general divisions are useful in that they gather together a rather large number of objects, but it is not to be believed that this collection can replace the study of these objects themselves. It is a kind of enumeration of the knowledge that can be acquired—a frivolous enumeration for whoever would wish to let it go at that alone, but useful for whoever desires to go further. A single reasoned article on a particular object of science or art includes more material substance than all the possible divisions and subdivisions of the general terms. And, not to leave the comparison that we have made above with geographical maps, anyone who relied solely upon the encyclopedic tree for all his knowledge would hardly know more than a man who flattered himself that he knew the different peoples who inhabit the globe and the particular states which constitute it because he had acquired a general idea of the globe and its principal parts through world maps. Above all, it ought not to be forgotten in considering our systematic chart that the encyclopedic order which it presents is very different from the genealogical order of the operations of the mind. Nor should one forget that the sciences which are concerned with general beings are useful only insofar as they lead to those which have particular beings as their object, that only these particular beings truly exist, and that if our minds have created general beings, their purpose is to enable one to study successively the properties which, by their nature, exist at the same time in the same substance and cannot physically be separated. These reflections are the due fruit and result of what we have said up until now. And thus it is with them that we will end the first part of this Discourse.

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