FUNDAMENTAL
PHILOSOPHY.

BY
REV. JAMES BALMES.

TRANSLATED FROM THE SPANISH
BY
HENRY F. BROWNSON, M.A.

IN TWO VOLUMES.
VOL. II.

D. & J. SADLIER & CO., 164 WILLIAM STREET,
BOSTON:—128 FEDERAL STREET.
MONTREAL:—COR. OF NOTRE DAME AND ST. FRANCIS XAVIER STS.
1856.

Entered according to Act of Congress, in the year 1856,
By D. & J. Sadlier & Co.,
In the Clerk's Office of the District Court of the United States for the Southern
District of New York.

NEW YORK:
BILLIN & BROTHER, PRINTERS, XX NORTH WILLIAM ST.

[CONTENTS OF VOL. II.]

[BOOK FOURTH.]

ON IDEAS.

FUNDAMENTAL PHILOSOPHY.

[CHAPTER I.]

CURSORY VIEW OF SENSISM.

1. Having spoken of sensations, we come now to ideas. We must, however, before making this transition, inquire if there be in our mind ought else than sensation, if all the inward phenomena which we experience be ought else than sensations transformed.

Man, when he rises from the sphere of sensations, from those phenomena which place him in relation with the external world, meets a new order of phenomena, of whose presence he is equally conscious. He cannot reflect upon sensations without being conscious of something more than sensation; nor on the recollection or the inward representation of sensations, without discovering something distinct both from the recollection and from the representation.

2. According to Aristotle, there is nothing in the understanding which has not first been in the senses; and the schools have for long ages re-echoed this thought of the philosopher: nihil est in intellectu quod prius non fuerit in sensu. The order, therefore, of human knowledge, is from the external to the internal. Descartes pretended that we ought to invert this order, and proceed from the internal to the external. Malebranche, his disciple, went farther, and was of opinion that the understanding, enfolded in itself, should hold only the least possible intercourse with the external world. According to him, no atmosphere is so fatal to intellectual health as that of the world of the senses; sensations are an inexhaustible fountain of error, and the imagination is an enchantress only the more dangerous because she has fixed her dwelling at the very portal of the intellect, which, with her seductive beauty and gorgeous ornaments, she hopes to rule at her pleasure.

3. Locke strove to rehabilitate the old Aristotelian maxim, joined, however, to the criterion of observation: besides sensation he admitted only reflection, but he taught that the mind was endowed with innate faculties. His disciple, Condillac, not satisfied with this, taught that all the actions of our mind were simply sensations transformed: instead of distinguishing with Locke two sources of our ideas, the senses and reflection, he thought it more exact to admit only one, as well because reflection is in its root only sensation, as because it is rather the channel by which ideas originating in the senses pass, than their source.

Judgment, reflection, desires, and passions are in Condillac's estimation nothing else than sensation transformed in various modes. It seemed to him, therefore, very idle to suppose the mind to have received immediately from nature the faculties with which it is endowed. Nature has given us organs which show us by pleasure or pain what we ought to seek or to avoid; but here she stops, and leaves to experience the task of leading us to contract habits and finish the work she has commenced.[1]

4. In view of this system, in which not even natural faculties are conceded to the soul, and those which it does possess are considered as only simple effects of sensation, it is worthy of remark how soon its author contradicts himself; for, almost in the same breath, he professes to be an occasionalist, and pretends that the impressions of our organization are nothing more than the occasion of our sensations. Can there be a natural faculty more inexplicable than that of placing one's self in relation with objects which do not produce sensations, but are only the occasion of their production. If such a faculty as this be conceded to the mind, why may we not admit others? Is not that a very singular natural faculty which perceives by means of causes operating only occasionally? In this case, is there not attributed to the mind a natural faculty of producing sensations on occasion of organic impressions, or is it not supposed to be an immediate relation with another and superior being which produces them? Why may not this internal activity, this receptivity, apply itself to ideas? Why must not other innate faculties be conceded to the mind? And why does he pretend not to suppose them, when his whole argument is based upon the supposition of their existence?

Hostile as he professes to be to hypotheses and systems, Condillac is eminently addicted both to systems and hypotheses. He imagines an origin and a nature of ideas of his own, and to them he insists that every thing must conform. To give a better idea of Condillac's opinions, and to combat them at once successfully and loyally, we will briefly analyze the groundwork of his Treatise on Sensations, the book on which he most prides himself, and in which he flatters himself to have given to his doctrine its highest degree of clearness and certainty.

[CHAPTER II].

CONDILLAC'S STATUE.

5. Condillac supposes a statue, which he animates successively with each of the senses: then beginning with the sense of smell, he says; "So long as our statue is limited to the sense of smell, its knowledge cannot go beyond odors; it can neither have any idea of extension, of space, or of any thing beyond itself, nor of other sensations, such as color, sound, taste."[2] If, according to the conditions of the supposition, all activity and every faculty be denied to this statue, it certainly can have no other idea or sensation, and it may be added that even its sensation of smell will be for it no idea.

"If we present it a rose," continues Condillac, "to us it will be a statue which smells a rose; but for itself it will be only the smell of a rose. It will then be the smell of the rose, the pink, the jasmine, or the violet, according to the objects which operate upon its organ; in a word, with respect to it, these odors are only its own modifications and manners of being, and it cannot believe itself any thing else, since these are the only sensations of which it is susceptible."

6. It is very obvious that at the first step, the statue must take a great leap. Close upon the apparent simplicity of the sensible phenomenon, reflection, one of those acts which suppose the intellect already well developed, is introduced. First the statue believes itself something; it believes itself the odor; next consciousness of itself in relation to the impression it has just received, is attributed to it; then it is made to form a kind of judgment, whereby it affirms the identity of itself with the sensation. This, however, is impossible, unless we have something besides bare sensation; but we neither have nor can have at this stage any thing beyond this purely passive impression, an isolated phenomenon, upon which there can be no reflection of any kind whatever; and the statue can have no other reflection of itself than this sensation, which in the reflective order has no title to be so called. Condillac's hypothesis rigorously applied, presents only a phenomenon leading to nothing; and the moment he leaves sensation to develop it, he admits an activity in the mind distinct and very different from sensation, which destroys his whole system.

The statue confined to the sensation of smell will never believe itself smell; such a belief is a judgment, and supposes comparison, no trace of which can be discovered in the sensible phenomenon, considered in all its purity, as Condillac requires in his hypothesis. He begins his analytical investigations by introducing conditions which he at the same time supposes to be eliminated. He undertakes to explain every thing by sensation alone, and his first step is to amalgamate sensation with operations of a very different order.

7. Condillac calls the capacity of feeling, when applied to the impression received, attention. So if there be but one sensation, there can be but one attention. If various sensations succeeding each other leave some trace in the memory of the statue, the attention will, when a new sensation is presented, be divided between the present and the past. The attention directed at one and the same time to two sensations becomes comparison. Similarities and differences are perceived by comparison, and this perception is a judgment. All this is done with sensations alone; therefore attention, memory, comparison, and judgment are nothing but sensations transformed. In appearance nothing clearer, more simple, or more ingenuous; in reality nothing more confused or false.

8. First of all, this definition of attention is not exact. The capacity of feeling, by the very fact of being in exercise, is applied to the impression. It does not feel when the sensitive faculty is not in exercise, and this is not in exercise except when applied to the impression. Consequently, attention would be nothing but the act of feeling; all sensation would be attention, and all attention sensation; a meaning which no one ever yet gave to these words.

9. Attention is the application of the mind to something; and this application supposes the exercise of an activity concentrated upon its object. Properly speaking, when the mind holds itself entirely passive, it is not attentive; and with respect to sensations it is attentive when by a reflex act we know that we feel. Without this cognition there can be no attention, but only sensation more or less active, according to the degree in which it affects our sensibility. If Condillac means to call the more vivid sensation attention, the word is improperly used; for it ordinarily happens that they who feel with the greatest vividness are precisely those who are distinguished for their want of attention. Sensation is the affection of a passive faculty; attention is the exercise of an activity; and hence it is that brutes do not participate of it except inasmuch as they possess a principle of activity to direct their sensitive faculties to a determinate object.

10. Is the perception of the difference of the smell of the rose and that of the pink a sensation? If we are answered that it is not, we infer that the judgment is not the sensation transformed; for it is not even a sensation. If we are told that it is one sensation, we then observe that if it be either that of the rose or that of the pink, it follows that with one alone of these sensations we shall have comparative perception, which is absurd. If we are answered that it is both together, we must either interpret this expression rigorously, and then we shall have a sensation which will at once be that of the pink and that of the rose, the one remaining distinct from the other so as to satisfy the conditions of comparison; or we must interpret it so as to mean that the two sensations are united; in which case we gain nothing, for the difficulty will be to show how co-existence produces comparison, and judgment, or the perception of the difference.

The sensation of the pink is only that of the pink, and that of the rose only that of the rose. The instant you attempt to compare them, you suppose in the mind an act by which it perceives the difference; and if you attribute to it any thing more than pure sensation, you add a faculty distinct from sensation, namely that of comparing sensations, and appreciating their similarities and differences.

11. This comparison, this intellectual force, which calls the two extremes into a common arena, without confounding them, discovers the points in which they are alike or unlike each other, and, as it were, comes in and decides between them, is distinct from the sensation; it is the effect of an activity of a different order, and its development must depend on sensations as exciting causes, as a condition sine qua non; but this is all it has to do with sensations themselves; it is essentially distinct from them, and cannot be confounded with them without destroying the idea of comparison, and rendering it impossible.

No judgment is possible without the ideas of identity or similarity, and these ideas are not sensations. Sensations are particular facts which never leave their own sphere, nor can be applied from one thing to another. The ideas of similarity and identity have something in common applicable to many facts.

12. What next happens to a being limited to the faculty of experiencing various sensations? It will receive without comparing them. It is certain that when it feels in one manner it will not feel in another, that one sensation is not another; but this sensitive being will take no notice of the variety. Sensations will succeed sensations, but will not be compared with each other. Even supposing them to be remembered, the memory of them will be nothing more than a less intense repetition of the same sensations. If it be admitted that this sensitive being compares them, and perceives their relations of identity or distinction, of similarity or difference, a series of reflex acts are admitted which are not sensations.

13. Nor can the memory, properly so called, of sensations, be explained by them alone; and here again Condillac is wrong. The statue may recollect to-day the sensation of the smell of the rose which it received yesterday, and this recollection may exist in two ways: first, by the internal reproduction of the sensation without any external cause, or relation to time past, and consequently without any relation to the prior existence of a similar sensation; and then this recollection is not for the statue a recollection properly so called, but only a sensation more or less vivid: secondly, by an internal reproduction with relation to the existence of the same or another similar sensation at a preceding time, in which recollection essentially consists; and here there is something more than sensation; here are the ideas of succession, time, priority, and identity, or similarity, all distinct and separable from sensation.

Two entirely distinct sensations may be referred to the same time in the memory; and then the time will be identical, and the sensations distinct. The sensation may exist without any recollection of the time it before existed, or even without any recollection of having ever existed; consequently, sensation involves no relation of time; they are distinct and very different matters, and Condillac deceives himself when he undertakes to explain the memory of sensations by mere sensations.

14. These reflections utterly refute Condillac's system. Either he admits something besides sensation or he does not; if he does, he violates his own original supposition; if he does not, he cannot explain any abstract idea, nor even the sensitive memory: he will therefore be obliged to admit with Locke reflection upon sensations, and for the same reason, other faculties of the soul.

15. It is easy to comprehend why certain philosophers have maintained that all our ideas come from the senses, if we understand them to mean that sensations awaken our internal activity, and, so to speak, supply the intellect with materials: but it is not so easy to see how it can be advanced as a certain, clear, and exceedingly simple truth that there is in our mind nothing but these materials, these sensations. We have only to fix our attention for a moment upon what passes within us to discover many phenomena distinct from sensation, and various faculties which have nothing to do with sensation. If Condillac had been satisfied with maintaining that these faculties needed sensation as a kind of excitement in order to be developed, he would have advanced nothing contrary to sound philosophy: but for him to pretend that all that is excited and all that is developed is only the principle which excites, and to insist that this is confirmed by actual observation, is openly to contradict observation itself, and to render it absolutely impossible for him to make the least progress in the explanation of intellectual activity, unless he abandons the supposition upon which his whole system is founded. Nevertheless, the author of the Treatise on Sensations seems to be perfectly satisfied with his system: the actual impression is the sensation; the recollection of the sensation is the intellectual idea. If this is not sound, it is at least deceptive: with the appearance of nice observation he stops at the surface of things, and does not fatigue the pupil. Every thing comes from sensation; but this is because Condillac makes his statue talk as he pleases, without paying the least attention to his hypothesis of sensation alone.

16. This system, by reason of its philosophical meagerness, is fatal to all moral ideas. What becomes of morality if there are no ideas, except sensations? What becomes of duty if every thing is reduced to sensible necessity, to pleasure or pain? And what becomes of God, and of all man's relations to God?

[CHAPTER III.]

DIFFERENCE BETWEEN GEOMETRICAL IDEAS AND THE SENSIBLE REPRESENTATIONS WHICH ACCOMPANY THEM.

17. Sensible representations always accompany our intellectual ideas. This is why in reflecting upon the latter we are apt to confound them with the former. We say, in reflecting upon them, not in making use of them. We none of us, have any trouble in making use of ideas according to circumstances; the error lies in the reflex, not in the direct act. It will be well to bear this last observation in mind.

18. It is next to impossible for the geometrician to meditate upon the triangle without revolving in his imagination, the image of a triangle as he has seen it drawn a thousand times; and he will, for this reason, be disposed to believe that the idea of the triangle is nothing else than this sensible representation. Were it thus, Condillac's assertion that the idea is only the recollection of the sensation would be verified in the idea of the triangle. In fact, this representation is the sensation repeated: the only difference between the two affections of the mind is that the actual sensation is caused by the actual presence of its object, wherefore it is more fixed and vivid. To prove that the difference is not essential, but consists only in degree, it is sufficient to observe, that if the imaginary representation attain a high degree of vividness we cannot distinguish it from sensation, as it happens to the visionary, and as we have all experienced in our dreams.

19. By noticing the following facts, we shall readily perceive how different the idea of the triangle is from its imaginary representation.

I. The idea of the triangle is one, and is common to all triangles of every size and kind; the representation of it is multiple, and varies in size and form.

II. When we reason upon the properties of the triangle, we proceed from a fixed and necessary idea; the representation changes at every instant, not so, however, the unity of the idea.

III. The idea of a triangle of any kind in particular is clear and evident; we see its properties in the clearest manner; the representation on the contrary is vague and confused, thus it is difficult to distinguish a right-angled from an acute-angled triangle, or even a slightly inclined obtuse-angled triangle. The idea corrects these errors or rather abstracts them; it makes use of the imaginary figure only as an auxiliary, in the same manner as we give our demonstrations when we draw figures upon paper, abstracting their exactness or inexactness, often when we know that they are not exact, which they cannot always be.

IV. The idea of the triangle is the same to the man born blind and to him who has sight; and the proof of this is that both, in their arguments and geometrical uses, develop it in precisely the same manner. The representation is different, for us it is a picture, which it cannot be for the blind man. When he meditates upon the triangle he neither has, nor can have, in his imagination, the same sensible representation as we, since he wants all that can relate to the sensation of sight. If the blind man experiences any accompanying representation of the idea, he can have received it only from the sense of touch; and in the case of large triangles, the three sides of which cannot be touched at the same time, the representation must be a successive series of sensations of touch, just as the recollection of a piece of music is essentially a successive representation. With us the representation of the triangle is almost always simultaneous, excepting the case of exceedingly large triangles, much larger than we usually see, in which case, especially when we are unaccustomed to consider such, it seems necessary to go on extending the lines successively.

20. What has been said of the triangle, the simplest of all figures, may with still greater reason be said of all others, many of which cannot be distinctly represented by the imagination, as we see in many-sided figures; and even the circle, which for facility of representation rivals the triangle, we cannot so perfectly imagine as to distinguish it from an ellipse whose foci are only at a trifling distance from each other.

[CHAPTER IV.]

THE IDEA AND THE INTELLECTUAL ACT.

21. Having shown that geometrical ideas are not sensible representations, we can safely conclude that no kind of ideas are. Could there be a difficulty concerning any, it would be concerning geometrical ideas, for the objects of the latter can be sensibly represented. When objects have no figure, they cannot be perceived by any of the senses; to speak in such a case of sensible representations is to fall into a contradiction.

22. These considerations draw a dividing line between the intellect and the imagination; a line which all the scholastics drew, which Descartes and Malebranche respected and made still more prominent, but which Locke began to efface, and Condillac entirely obliterated. All the scholastics recognized this line; but they, like many others, used a language which, unless well understood, was of a character to obscure it. They called every idea an image of the object, and explained the act of the understanding as if there were a kind of form in the understanding which expressed the object, just as a picture presented to the eyes offers them the image of the thing pictured. This language arose from the continual comparison which is very naturally made between seeing and understanding. When objects are not present we make use of their pictures, and thus, since objects themselves cannot be present to our understanding, we conceive an interior form which performs the part of a picture. On the other hand, sensible things are the only ones which are strictly susceptible of representation; we never discover within ourselves the form in which the objects are portrayed, except in the case of imaginary representations; and therefore it was rash to call this an idea, and every idea an imaginary representation, in which the whole system of Condillac consists.

23. St. Thomas calls the representations of the imagination phantasmata, and says that so long as the soul is united to the body we cannot understand except per conversionem ad phantasmata; that is, unless the representation of the imagination, which serves as material for the formation of the idea, and assists in clearing it up, and heightening its colors, precedes and accompanies the intellectual act. Experience teaches that whenever we understand, certain sensible forms relative to the object which occupies us, exist in our imagination. Now, they are the images of the figure and color of the object, if it have any; now, the images of those with which they are compared, or the words which denote them in the language we habitually speak. Thus, even when thinking of God, the very act by which we affirm that he is most pure spirit, offers a kind of representation to the imagination under a sensible form. When we speak of eternity, we see the Ancient of days, as we have often seen him represented in our churches; when we speak of the infinite intelligence, we imagine perhaps a sea of light; infinite mercy, we picture to ourselves as a pitying likeness; justice, with angry countenance. To force ourselves to form some conception of the creation, we fancy a spring whence light and life both flow, and thus also we endeavor to render immensity sensible by imagining unlimited extension.

The imagination always accompanies the idea, but is not itself the idea; and we perceive the evident and unimpeachable proof of the distinction between the two, if we ask ourselves, while in the very act of imagining a sea of light, an old man, an angry or placid countenance, a fountain or extension, if God is any one of these, or any thing resembling them; for, we very promptly answer, no, that this would be impossible. All this demonstrates the existence of an idea which has no connection with these representations, but essentially excludes what is contained in them.

24. What we have said of the idea of God, may be said of many other ideas. Rarely do we understand any thing into which the idea of relation does not enter as an indispensable element. How then is relation represented? In the imagination, in a thousand different manners; as the point of contact of two objects; as the link which unites them. But is relation any one of these? No! When we inquire in what it does consist, is there the slightest shadow of doubt that it is no one of these? Certainly not.

25. It is an error to call every idea an image, if you mean to consider ideas as something distinct from the intellectual act, which places itself before the understanding when it is in the exercise of its functions. An image is that which represents, as a likeness: and how, I ask, do we know that this representation or likeness exists? And how do we know that in order to reason we need an internal form, which is, as it were, a picture of the object? What is a picture beyond the sensible order? There are, it is true, similarities in the intellectual order, but not in the sense in which we perceive them in the material order. I think; so does my neighbor: here is a similarity, since the same thing is found in both one and the other, identical in species, but not in number. But this similarity is of a different order from that of sensible similarities.

26. When we understand, we know that which is in the object understood; but whether this be understood by a simple act of the intellect, or a medium be required to represent the similarity, we do not know. We understand the thing, not the idea; and it is as difficult to say how the intellect perceives without the idea, as it is to say how the supposed representation refers to its object. How does our idea refer to an object? If by itself, then by itself alone, since it is purely internal, it refers to the external, and requires no intermediary to place the subject in relation with external objects. What it does, the intellectual act of itself alone can also do. If we perceive the relation of the idea with the object by means of another idea, this intermediate idea presents the same difficulty as the preceding idea; and so at last we must come to a case in which there is a transition from the intellect to the object without any intermediary.

If we see an object which is the image of another not known, we shall see the object in itself, but we shall not know that it has the relation of image, unless informed that it has: we shall know its reality, but not its representation. The same will happen in ideas which are images; these, therefore, do not at all explain how the transition from the internal act to the object is made; for this would require them to do for the understanding that which we find them unable to do for themselves.

27. There is something mysterious in the intellectual act, which men seek to explain in a thousand different ways, by rendering sensible what they inwardly experience. Hence so many metaphorical expressions, useful only so long as they serve merely to call and fix the attention, and give an account of the phenomenon, but hurtful to science if they go beyond these limits, if it be forgotten that they are metaphors, and are never to be confounded with the reality.

By intelligence we see what there is in things, we experience the act of perception; but when we reflect upon it we grope in the dark, as if there were a dense cloud about the very source of light, preventing us from seeing it with clearness. Thus the firmament is at times flooded with the light of the sun, although the sun is encircled with clouds and hidden from our view, so that we cannot even determine its position upon the horizon.

28. One cause of obscurity in this matter is the very effort to clear it up. The act of the understanding is, in its objective part, exceedingly luminous, since by it we see what there is in objects; but in its subjective nature, or in itself, it is an internal fact, simple indeed, but incapable of being explained by words. This is not a peculiarity of the intellectual act, it is common to all internal phenomena. What is it to see, to taste, to hear? What is a sensation, or feeling of any kind whatsoever? It is an inward phenomenon, of which we are conscious, but which we cannot decompose into parts; nor can we explain with words the combination of these parts. A word is enough to indicate the phenomenon, but this word has no meaning for him who does not now experience this phenomenon, or has not oat some former time experienced it. No possible explanations would ever enable a man born blind to understand color, or a deaf man sound.

The act of understanding belongs to this class; it is a simple fact which we can point out, but not explain. An explanation supposes various notions, the combination of which may be expressed by language; in the intellectual act there are none of these. When we have said, I think, or, I understand, we have said all. This simplicity is not destroyed by objective multiplicity; the act by which we compare two or more objects is just as simple as the act by which we perceive a single object. If one act be not enough, more will follow; and finally one act will unite or sum them all up; but it will not be a composite act.

[CHAPTER V.]

COMPARISON OF GEOMETRICAL WITH NON-GEOMETRICAL IDEAS.

29. The idea is a very different thing from the sensible representation, but it has certain necessary relations with it which it will be well to examine. When we say necessary, we speak only of the manner in which our mind, in its actual state, understands, abstracting the intelligence of other spirits, and even that of the human mind when subject to other conditions than those imposed by its present union with the body. So soon as we quit the sphere in which our experience operates, we must be very cautious how we lay down general propositions, and take care not to extend to all intelligences qualities which are possibly peculiar to our own, and which, even with respect to it, will perhaps be entirely changed in another life. Having made these previous observations, which will be found of great utility to mark the limits of things there is danger of confounding, we now proceed to examine the relations of our ideas with sensible representations.

30. A classification of our ideas into geometrical and non-geometrical naturally occurs when we fix our attention upon the difference of objects to which our ideas may refer. The former embrace the whole sensible world so far as it can be perceived in the representation of space; the latter include every kind of being, whether sensible or not, and suppose a primitive element which is the representation of extension. In their divisions and subdivisions the latter present simply the idea of extension, limited and combined in different ways; but they offer nothing in relation to the representation of space, and even when they refer to it, they only consider it inasmuch as numbered by the various parts into which it may be divided. Hence the line which in mathematics separates geometry from universal arithmetic; the former is founded upon the idea of extension, whereas the latter considers only numbers, whether determinate, as in arithmetic properly so called, or indeterminate, as in algebra.

31. Here we have to note the superiority of non-geometrical to geometrical ideas,—a superiority plainly visible in the two branches of mathematics, universal arithmetic and geometry. Arithmetic never requires the aid of geometry, but geometry at every step needs that of arithmetic. Arithmetic and algebra may both be studied from their simplest elementary notions to their highest complications without ever once involving the idea of extension, and consequently without making use of one single geometrical idea. Even infinitesimal calculus, in a manner originating in geometrical considerations, has been emancipated from them and formed into a science perfectly independent of the idea of extension. On the contrary, geometry cannot take a single step without the aid of arithmetic. The comparison of angles is a fundamental point in the science of geometry, but it cannot be made except by measuring them; and their measure is an arc of the circumference divided into a certain number of degrees, which must be counted; and thus we come to the idea of number, the operation of counting, that is, into the field of arithmetic.

The very proof by superposition, notwithstanding its eminently geometrical character, stands in need of numeration, inasmuch as the superposition is repeated. We do not require the idea of number to demonstrate by means of superposition the equality of two arcs perfectly equal; but in order to appreciate the relation of their quantity we compare two unequal arcs and follow the method of placing the less upon the greater several times, we count, we make use of the idea of number, and find we have entered upon the ground of arithmetic. We discover the equality of two radii of a circle, when we compare them by superposition, abstracting the idea of number; but if we would know the relation of the diameter to the radii, we employ the idea of two; we say the diameter is twice the radius, and again enter the domains of arithmetic. As we proceed in the combination of geometrical ideas, we make use of more and more arithmetical ideas. Thus the idea of the number three necessarily enters into the triangle; and the sum of three and the sum of two both enter into one of its most essential properties; the sum of the three angles of a triangle is equal to two right angles.

32. The idea of number cannot be replaced by the sensible intuition of the figure whose properties and relations are under discussion. In many cases this intuition is impossible, as, for example, in many-sided figures. We have little difficulty in representing to our imagination a triangle, or even a quadrilateral figure, but the difficulty is greater in the case of the pentagon, and greater still in the hexagon and heptagon; and when the figure attains a great number of sides, one after another escapes the sensible intuition, until it becomes utterly impossible to appreciate it by mere intuition. Who can distinctly imagine a thousand-sided figure?

33. This superiority of non-geometrical over geometrical ideas is very remarkable, since it shows that the sphere of intellectual activity expands in proportion as it rises above sensible intuition. Extension, as we have before seen,[3] serves as the basis not only of geometry, but also of the natural sciences, inasmuch as it represents in a sensible manner the intensity of certain phenomena; but it can by no means enable us to penetrate their inmost nature, and guide us from that which appears to that which is. This and other subordinate ideas are, so to speak, inert, and from them springs no vital principle to fecundate our understanding, and still less the reality; they are an unfathomable depth in which our intellectual activity may toil, perfectly certain of never finding any thing in it which we ourselves have not placed there; they are a lifeless object which lends itself to all imaginable combinations without ever being capable of producing any thing, or of containing any thing not given to it. The naturalists in considering inertness as a property of matter, have perhaps regarded more than they are aware the idea of extension, which presents the inertness most completely.

34. The ideas of number, cause, and substance abound in results, and are applicable to all branches of science. We can scarcely speak without expressing them; it might almost be said that they are constituent elements of intelligence, since without them it vanishes like a passing illusion. They extend to every thing, apply to every thing, and are necessary, whenever objects are offered to the intellectual activity, in order that the intellect can perceive and combine them. It makes no difference whether the objects be sensible or insensible, whether there be question of our intelligence or of others subject to different laws; whenever we conceive the act of understanding we conceive also these primitive ideas as elements indispensable to the realization of the intellectual act. They exist and are combined independently of the existence, and even of the possibility, of the sensible world; and they would also exist in a world of pure intelligences, even if the sensible universe were nothing but an illusion or an absurd chimera.

On the other hand, take geometrical ideas and remove them from the sensible sphere; and all that you base upon them will be only unmeaning words. The ideas of substance, cause, and relation do not flow from geometrical ideas; if we regard them alone, we see an immense field extending into regions of unbounded space; but the coldness and silence of death reign there. If we would introduce beings, life, and motion into this field we must seek them elsewhere; we must use other ideas, and combine them, so that life, activity, and motion may result from their combination, in order that geometrical ideas may contain something besides this inert, immovable, and vacant mass, such as we imagine the regions of space to be beyond the confines of the world.

35. Geometrical ideas, properly so called, as distinguished from sensible representations, are not simple ideas, since they necessarily involve the ideas of relation and number. Geometry cannot advance one step without comparing them; and this comparison almost always takes place by the intervention of the idea of number. Hence it is that geometrical ideas, apparently so unlike purely arithmetical ideas, are really identical with them so far as their form or purely ideal character is concerned; and are only distinguishable from them when they refer to a determinate matter, such as extension as presented in its sensible representation. The inferiority therefore of geometrical ideas already mentioned, only refers to their matter, or to their sensible representations, which are presupposed to be an indispensable element.

36. Another consequence of this doctrine, is the unity of the pure understanding, and its distinction from the sensitive faculties. For, the very fact that the same ideas apply alike to sensible and to insensible objects, with no other difference than that arising from the diversity of the matter perceived, proves that above the sensitive faculties there is another faculty with an activity of its own, and elements distinct from sensible representations. This is the centre where all intellectual perceptions unite, and where that intrinsic force resides, which, although excited by sensible representations, develops itself by its own power, makes itself master of these impressions, and converts them, so to speak, by a mysterious assimilation, into its own substance.

37. Here we repeat what we have already remarked, concerning the profound ideological meaning involved in the acting intellect of the Aristotelians, so ridiculed because not understood. But we leave this point and proceed to the careful analysis of geometrical ideas, to discover, if possible, a glimpse of some ray of light amid the profound darkness which envelops the nature and origin of our ideas.

[CHAPTER VI.]

IN WHAT THE GEOMETRICAL IDEA CONSISTS; AND WHAT ARE ITS RELATIONS WITH SENSIBLE INTUITION.

38. In the preceding chapters we have distinguished between pure ideas and sensible representations, and we seem to have sufficiently demonstrated the difference between them, although we limited ourselves to the geometrical order. But we have not explained the idea in itself; we have said what it is not, but not what it is; and although we have shown the impossibility of explaining simple ideas, and the necessity of our being satisfied with indicating them, we do not wish to be confined to this observation, which may seem to elude the difficulty rather than to solve it. Only after due investigations, by which we shall be better able to understand what is meant by designate, will it be allowable to confine ourselves to their designation, for it will then be seen that we have not eluded the difficulty. Let us begin with geometrical ideas.

39. Is a geometrical idea, without any accompanying or preceding sensible representation, possible? It would seem that we can have none. What meaning has the idea of the triangle if not referred to lines forming angles and enclosing a space? And what do lines, angles, and space mean, without sensible intuition? A line is a series of points, but it represents nothing determinate, nothing susceptible of geometrical combinations, except it be referred to that sensible intuition in which the point appears to us as an element generating by its movement that continuity which we call a line. What would become of angles without the real or possible representation of these lines? What would become of the area of the triangle were we to abstract a space, a surface which is or may be represented? We might challenge all the ideologists in the world to assign any sense to the words used in geometry if absolute abstraction be made all sensible representation.

40. Geometrical ideas, such as we conceive them, have a necessary relation to sensible intuition. In order the better to understand this relation, let us define the triangle to be the figure enclosed by three right lines. This definition involves the following ideas: space, enclosed, three, lines. With a space and three lines which do not enclose the figure, we have no triangle; the word enclosed cannot therefore be omitted. If you enclose a space, but with more than three lines, the result will not be a triangle; and if you take less than three lines you can have no enclosure. The idea of three is therefore necessary to the idea of the triangle. It is useless to add that the idea of line is as necessary as the others, since without it no triangle can be conceived. Different and distinct ideas, it is true, are here combined, but they are all referred to one sensible intuition, although in an indeterminate manner. We here abstract the longness or shortness of the lines and their forming larger or smaller angles. But we cannot thus abstract in the case of determinate intuitions; for every determinate intuition has its own peculiar qualities; otherwise it would not be a determinate representation, and consequently not sensible as it is supposed to be. But although the reference be to an indeterminate intuition, it always supposes some intuition either actual or possible, since otherwise the material of combination would be wanting to the understanding; and the four ideas involved in the triangle would be empty and unmeaning forms, and their combination extravagant if not absurd.

41. The idea then of the triangle seems to be simply the intellectual perception of the relation between the lines presented to the sensible intuition, considered in all its generality, without any determining circumstance limiting it to particular cases or species. This explanation admits nothing intermediate between the sensible representation and the intellectual act, which, exercising its activity upon the materials presented by sensible intuition, perceives their relations, and this pure and simple perception constitutes the idea.

42. We shall understand this better if, instead of the triangle, we take a many-sided figure, such as a polygon of a million sides, which cannot be clearly presented to the sensible intuition. The idea of this figure is as simple as that of the triangle; we perceive it by an intellectual act, express it by a single word, and can calculate its properties and relations with the same exactness and certainty as we can those of the triangle, although it is absolutely impossible to represent it distinctly to our imagination. When we reflect upon what it offers to the intellectual act, we notice the same elements as in the idea of the triangle, with this single difference that the number three is changed into million. We can have no sensible representation of all these lines; but the understanding has sufficiently combined the idea of line with that of number to perceive its object, a million. Here, then, we perceive the same elements as in the triangle; but it is upon these elements, considered in general without any other determination than results from the fixed number, that the perceptive act operates.

43. The idea of a polygon in general, abstracting the number of its sides, offers in its sensible representation, nothing determinate to the mind, nothing but the abstract idea of a right line, the general idea of an enclosed space. The relation which these objects of the intellectual, act even in the midst of their indeterminateness, have amongst themselves, is perceived by the intellectual act. This perceptive act is the idea. Every thing beyond this is useless, and not only useless but affirmed without reason.

44. It will perhaps be asked how the understanding can perceive what passes without it, since sensible intuition is a function of a faculty distinct from the understanding? In reply, we shall abstract the questions discussed in the schools concerning the powers of the mind, and be content to remark that whether these be really distinct among themselves, or only one power exercising its activity upon different objects and in different manners, it will be alike necessary to admit a consciousness common to all the faculties. The soul which feels, thinks, recollects, desires, is one and the same, and is alike conscious of all these acts. Whatever be the nature of the faculties by which she performs these acts, she it is that performs them and knows that she performs them. There is then in the soul a single consciousness, the common centre where dwells the inward sense of every activity exercised, and of every affection received, to whatever order they may belong. However, supposing the case the most unfavorable to our theory, that the faculty to which sensible intuition corresponds, is really distinct from the faculty which perceives the relations of the objects offered by sensible intuition; does it therefore follow that the understanding cannot without something intermediate exercise its activity upon objects presented by this intuition? Certainly not. The act of pure understanding and that of sensible intuition, are indeed different, but they meet in consciousness, as in a common field; and there they come in contact, the one exercising its perceptive activity upon the material supplied by the other.

[CHAPTER VII.]

THE ACTING INTELLECT OF THE ARISTOTELIANS.

45. I shall now briefly explain the scholastic theory of the manner in which the understanding knows material things. This explanation will show how much reason we had to assert that this doctrine of the schools can be ridiculed only when not understood, and that, whatever its foundation, it cannot be denied to possess an ideological importance.

46. The schoolmen began with this principle of Aristotle, nihil est in intellectu quod prius non fuerit in sensu; "There is nothing in the understanding which has not previously been in the senses." Conformably to this principle they maintained that before the soul received impressions from the senses, the understanding was like a clean table upon which nothing had been written: sicut tabula rasa in qua nihil est scriptum. According to this doctrine all our knowledge flows from the senses; and at first sight the system of the schools might seem to be very similar to, if not identical with, that of Condillac. Both seek the origin of our cognitions in sensation; both teach that there is no idea in our understanding prior to sensation. But the two systems are, notwithstanding these apparent similarities, very different, and even diametrically opposed.

47. The fundamental principle of Condillac's theory is, that sensation is the sole operation of the mind; and that whatever exists in our mind is nothing more than the sensation transformed in various ways. Prior to sensible impressions, this philosopher admits no faculty; the development of sensation is all that fecundates the soul, not by exciting its faculties, but by generating them. The school of the Aristotelians took, indeed, sensations for the starting-point, but did not consider them as producing intelligence; on the contrary, they were very careful to mark the limits of the sensitive faculties, and of the understanding in which they recognized a peculiar and innate activity altogether superior to the faculties of the sensible order. We have only to open any one of the innumerable works of this school, to meet on every page such words as intellectual force, light of reason, participation in the divine light, and others in the same style, in which a primary activity of our mind, not communicated by sensations, but prior to them all, is expressly recognized. The acting intellect, intellectus agens, which figures so much in this ideological system, was a standing condemnation of the system of transformed sensation advocated by Condillac.

48. The Aristotelians, governed by their favorite idea of explaining every thing by matter and form, modified the meaning of these words according to the exigencies of the objects to which they applied them, and considered the faculties of the soul as a class of forces incapable of acting unless united to a form which brought them into action. Thus they explained sensations by species, or forms, which placed the sensitive power in act. The imagination was a force which, although it sometimes rose above the external senses, contained nothing but species of the sensible order, subject also to the necessary conditions of this faculty. These species were the forms which placed the imaginative force in act, and without which it could not exercise its functions. The Aristotelians, after having thus explained the phenomena of the external senses, and of the imagination, undertook to explain those of the intellectual order; and in this they displayed their genius by inventing an auxiliary which they named the acting intellect. The necessity of making two principles in seeming contradiction accord, was the reason of this invention.

On the one hand the Aristotelians held that our cognitions all flowed from the senses; and on the other they asserted that there was an essential and intrinsic difference between feeling and understanding. Having drawn this dividing line, the sensitive and intellectual orders were separated; but as it was on the other side requisite to establish some communication between these two orders, it was necessary for them, if they wished to save the principle, that all our ideas come from the senses, to discover some point where the two channels might unite.

The cognition of material things could not be denied to the pure understanding; but as this was not an innate cognition and could not be acquired by it, they were under the necessity of establishing some communication by means of which the understanding might comprehend objects without soiling its purity by sensible species. The imagination contained them, already purified from the grossness of the external senses; in it they existed more aerial, purer, and less remote from immateriality; but they were still at an immense distance from the intellectual order, and had themselves to support the burden of those material conditions which never allowed them to attain the altitude necessary to be put in communication with the pure understanding. In order to know, the understanding requires forms to unite themselves to it intimately; and although it be true that it discerned them far down in the lower regions of the sensitive faculties, yet it could descend to them without compromising its dignity, and denying its own nature. In this conflict they required a mediator; it was the acting intellect. We will now proceed to explain the attributes of this faculty.

49. The sensible species contained in the imagination, the true picture of the external world, were not of themselves intelligible, because enveloped, not with matter properly so called, but with material forms, to which the intellectual act could only indirectly refer. If they could have discovered a faculty capable of rendering intelligible what is not intelligible, this difficult problem would have been satisfactorily solved; as in this case the mysterious transformer by applying its activity to the sensible species, would elevate them from the category of imaginary species, phantasmata, to that of pure ideas or sensible species, and thus make them serve the intellectual act. This faculty is the acting intellect; a real magician which possesses the wonderful secret of stripping sensible species of their material conditions, of smoothing every roughness which prevents them from coming in contact with the pure understanding, and transforms the gross food of the sensitive faculties into the purest ambrosia, fit to be served at the repast of spirits.

50. This invention merits to be called ingenious rather than extravagant, poetical rather than ridiculous. But its most remarkable feature is, that it involves a profound philosophical sense, as well because it marks an ideological fact of the highest importance, as because it indicates the true way of explaining the phenomena of intelligence in their relations to the sensible world. This remarkable fact is the difference, even with respect to material objects, between sensible representations and pure ideas. The indication of the true way consists in presenting the intellectual activity as operating upon sensible species, and converting them into food for the mind.

Let us leave the poetical part to the explanation of the schools, and see if what it involves be worth as much, to say the least, as what Kant advanced when, combating sensism, he distinguished between the pure understanding and sensible intuitions.

[CHAPTER VIII.]

KANT AND THE ARISTOTELIANS.

51. Lest I be accused of levity in comparing Kant's philosophy with that of the schools, in what relates to the distinction between the sensitive and intellectual faculties, I shall give a rapid examination of this philosopher's doctrine so far as the present matter is concerned.

Since the German philosopher is in the habit of expressing himself with great obscurity, and of using an obsolete language liable to different interpretations, I shall insert his own words, so that the reader may judge for himself, and rectify any inaccuracies into which I may fall, in comparing Kant's doctrine with that of the Aristotelians.

"In whatever manner," says Kant, "and by whatever means a cognition may be referred to objects, that which makes the cognition refer immediately to things, and to which all thought is a means, is intuition. This intuition exists only inasmuch as the object is given us, which is not possible, at least for us men, except so far as it affects the mind in some way. The capacity of receiving impressions by the manner in which objects affect us is called sensibility. By means of sensibility objects are given to us: it alone supplies us with intuitions: but they are thought by the understanding, and from it arise conceptions. All thought must ultimately be referred, either directly, or indirectly by means of certain signs, to intuitions, and consequently to sensibility, since no object can be given to us in any other.

"The action of an object upon the representative faculty, so far as we are affected by it, is sensation. The intuition, which is referred to an object by means of sensation, is called empirical. The immediate object of an empirical intuition is called a phenomenon."[4]

The distinction between the faculty of feeling and that of conceiving is fundamental in Kant's system: and we see that he gives it a hasty exposition before beginning his investigations on Æsthetics or the theory of sensibility. Further on, in treating of the operations of the understanding, he has more fully developed his doctrine: and by the emphasis he puts upon it, it would seem evident that he regarded it as of high importance, and perhaps as a discovery of a region entirely unknown to the philosophical world. Thus he speaks of it in his Transcendental Logic:

"Our knowledge proceeds from two intellectual sources; the first is the capacity of receiving representations, (the receptivity of impressions,) the second is the faculty of knowing an object by these representations, (the spontaneity of conceptions.) By the former the object is given to us; by the latter, it is thought in relation to this representation (as mere determination of the mind.) Intuition and conception constitute the elements of all our knowledge; so that neither conceptions without an intuition in some manner corresponding to them, nor an intuition without conceptions, can give knowledge.

"We call sensibility the capacity (receptivity) of our mind to receive representations, so far as affected in any way whatever: on the contrary, the faculty of producing representations, or the spontaneity of knowledge, is called understanding. Our nature is such that there can be no intuition not sensible, that is to say, which only comprehends the manner in which we are affected by objects. The understanding is the faculty of thinking the object of sensible intuition. Neither of these properties of the soul is preferable to the other. Without sensibility no object could be given to us; without the understanding none could be thought. Thoughts without contents are empty; intuitions without conceptions are blind. It is, then, just as necessary to make conceptions sensible,—that is, to give them an object in intuition, as to make intuitions intelligible, by subjecting them to conceptions. These two faculties or capacities cannot interchange their functions. The understanding can perceive nothing,[5] and the senses can think nothing. Knowledge results only from their union. Their attributes, therefore, ought not to be confounded; on the contrary, there is every reason to distinguish them, and to separate them with great care. We distinguish then the science of the laws of sensibility in general, that is to say, Æsthetics, from the science of the laws of the understanding in general, that is, from Logic."[6]

Mark well the meaning of this doctrine. Two facts are established; sensible intuition, and the conception of it; consequently the existence of two faculties, sensibility, and the understanding, is affirmed. To the first correspond sensible representations; to the latter conceptions. These two faculties, though different, are closely interlinked; and they are mutually necessary in order to produce cognitions. But how do they give each other that mutual aid they stand in need of?

"The understanding," Kant elsewhere says, "has been thus far defined only negatively, as a not-sensible faculty of knowing." But as we can have no intuition independently of sensibility, it follows that the understanding is not a faculty of intuition. Excepting intuition, there remains no way of knowing other than by conceptions; wherefore we infer that the knowledge of every intellect, at least every human intellect, is a knowledge by conceptions; not intuitive, but discursive. All intuitions, as sensible, rest upon affections, and consequently, all conceptions upon functions. I understand by functions, the unity of action necessary to arrange different representations under one common representation. Conceptions, then, are grounded on the spontaneity of thought, as sensible intuitions on the receptivity of impressions. The understanding can make no use of these conceptions except to judge by means of them, and as intuition is the only representation which has an immediate object, no conception can ever be immediately referred to an object, but only to some other representation of this object, whether this be an intuition, or even a conception. Judgment is the mediate cognition of an object, and consequently the representation of a representation of the object. In every judgment there is a conception applicable to many things, and under this plurality it comprises also a given representation, immediately referable to the object. Thus, in the judgment: all bodies are divisible; the conception of divisible is common to different conceptions, among which that of body is the one it here particularly refers to. But this conception of body relates to certain phenomena we have in view; these objects are then mediately represented by the conception of divisibility. All judgments are functions of unity in our representations, since instead of one immediate representation, there comes in another more elevated, which includes the first and many others, and conduces to the cognition of the object; and a great number of possible cognitions are reduced to one alone. But we may reduce all the operations of the understanding to judgment; so that the understanding in general may be represented as a faculty of judging; because, from what has been said, it is the faculty of thinking. Thought is cognition by conceptions; but conceptions, as predicates of possible judgments, may be referred to any representation whatever of an object, however indeterminate. Thus the conception of body signifies something, for example, a metal, which may be known by this conception. It is then a conception only because it contains in itself other representations by means of which it may be referred to objects. It is then the attribute of a possible judgment, for instance, of this: every metal is a body.[7]

52. There are in this doctrine of Kant, two things to be distinguished: first, the facts upon which it is based; and secondly, the manner in which he examines and applies them, and the consequences he deduces from them.

We detect at once a radical difference, as far as the observation of ideological facts is concerned, between Kant's system and that of Condillac. While the latter discovers in the mind no fact but sensation, no immediate faculty more noble than that of feeling, the former upholds as a fundamental principle the distinction between sensibility and the understanding. And here the German triumphs over the French philosopher, for in his support stand both observation and experience. But this triumph over sensism had already been obtained by many philosophers, the scholastics in particular. With Kant and Condillac they admitted that all our cognitions came from the senses; but they had also noted what Kant afterwards saw, but Condillac did not discover that sensations by themselves alone could never suffice to explain all the phenomena of our soul, and that, besides the sensitive faculty, it was necessary to admit another very different, called understanding.

Kant regarded sensations as materials furnished to the understanding, which it combined in various ways, and reduced to conceptions. "Thoughts without contents," he said, "are empty; intuitions without conceptions are blind. It is then just as necessary to make conceptions sensible, that is, to give them an object in intuition, as to make intuitions intelligible by subjecting them to conceptions." Who does not perceive in this passage, the acting intellect of the Aristotelians, although expressed in other words? Substitute sensible species for sensible intuition, intelligible species for conception and we recognize a doctrine very like that of the scholastics. Let us see. Kant says: to enable us to acquire knowledge, the action of the senses, or sensible experience is necessary. The scholastics said: there is nothing in the understanding which has not previously been in the senses: nihil est in intellectu quod prius non fuerit in sensu.

Kant says: sensible intuitions of themselves are blind. The scholastics said: sensible species, or those of the imagination, also called phantasmata, are not intelligible.

Kant says: it is necessary to make conceptions sensible by giving them an object in intuition. The scholastics said: it is impossible to understand, either by acquiring science, or by using that already acquired, unless the understanding directs itself to sensible species, "sine conversione ad phantasmata."

Kant says: it is indispensable to render intuitions intelligible by subjecting them to conceptions. The scholastics said: it is necessary to make sensible species intelligible in order that they may be the object of the understanding.

Kant says: we judge by means of conceptions; and that judgment is the mediate cognition of an object, and consequently its representation. The scholastics said: we know objects by means of an intelligible species, which is derived from the sensible species, and is its intelligible representation.

Kant says, that in every judgment there is a conception applicable to many things, and that under this plurality it comprises also a given representation which is referred immediately to its object. The scholastics said, that the intelligible species was applicable to many things, because universal; that, when separated from a sensible and particular species, it abstracts from all material and individuating conditions, and consequently embraces all individual objects in one common representation.

Kant uses the words conception, and to conceive, to denote the intellectual act, form, or whatever it may be, by which the understanding, making use of sensible intuitions, combines the materials offered by sensibility conformably to the laws of the intellectual order. The scholastics likewise taught that the intelligible species, called also species impressed, fecundated the understanding by producing in it an intellectual conception, whence resulted the word, internal locution, or species expressed, which they also styled conception.

Kant says, that the cognition of human intelligence is a cognition by conceptions, not intuitive, but discursive and general, and that out of the sphere of sensibility there is for us no true intuition. The scholastics said: our understanding, in this life, has a necessary relation to the nature of material things, and for this reason it cannot primo et per se, know immaterial substances: hence it happens that we know them perfectly only by certain comparisons with material things, and chiefly by way of removal, per viam remotionis, in a negative way.

53. The sample we have just given is exceedingly interesting, since it enables us to appreciate as they merit the points of similarity in these two systems, which occupy a prominent place in the history of ideology,—a similarity which has not always hitherto been sufficiently noticed, although apparent upon the simple perusal of the German philosopher. Nor is this extraordinary: the study of the scholastics is exceedingly difficult; one must accommodate one's self to the language, the style, the opinions, and the prejudices of their epoch, and travel over much useless ground to collect a little pure ore. Note well, however, that I do not pretend to discover the "Critic of Pure Reason" in the works of the scholastics, I would only mark a fact but little known; it is that whatever is good, fundamental, and conclusive against the sensism of Condillac, in the German philosopher's system, had been said ages before by the scholastics.

Are we hence to infer that Kant took his doctrine from these authors? We cannot say; but we believe it may, with some reason, be asserted, that possibly the German philosopher, a man of vast reading, most retentive memory, and very laborious, may have received certain inspirations, reminiscences of which glimmer through his doctrines. A writer is not a plagiarist, although he make ideas his own which have originated with others. But it is often true that man imagines he creates, when he only recollects.

54. Although the German philosopher agrees with the scholastics in the observation of the primitive faculties of our mind, he differs from them in their application; and whilst they go on preparing a philosophical dogmatism, he marches towards a despairing skepticism. Nothing that all the most eminent philosophers have regarded as indisputable, can stand in the eyes of the German philosopher. True, he has distinguished the sensible from the intelligible order; he has recognized two primitive faculties in our soul; sensibility and the understanding; he has indicated the line which divides them, and carefully remarked that it should never be effaced; but, on the other hand, he has reduced the sensible world to a collection of pure phenomena, and explains space in such a way as to render it extremely difficult to avoid the idealism of Berkeley. He has also, so to speak, walled in the understanding by preventing all communication with it, excepting by sensible experience, and has resolved all the elements that meet in it into empty forms, which lead to nothing when there is question of applying them to the not-sensible, and which can teach us nothing concerning the great ontological, psychological, and cosmological problems which have been the object of the meditations of the profoundest metaphysicians, who, to resolve them, have published a vast amount of sublime doctrines, just cause of a noble pride in the human mind which knows the dignity of its nature, vindicates its lofty origin, and discerns from afar the immensity of its destiny.

[CHAPTER IX.]

HISTORICAL VIEW OF THE VALUE OF PURE IDEAS.

55. Now that we have shown the points of similarity between Kant's system and that of the scholastics, we propose to note their differences chiefly in what concerns the application of these doctrines. To give an idea of the gravity and transcendentalism of these differences, we have only to remark the discrepancy of their results. The Aristotelians built upon their principles a whole system of metaphysical science, which they considered the noblest of sciences, and which, like a rich and brilliant light, fecundates and directs all others; whereas Kant, starting with the same facts, destroys metaphysical science by taking from it all power to know objects in themselves.

56. We here find Kant in opposition not only to the scholastics, properly so called, but also to all the most eminent metaphysicians who had preceded him. On the side of the scholastics in this matter may be cited Plato, Aristotle, Saint Augustine, Saint Anselm, Saint Thomas, Descartes, Malebranche, Fenelon, and Leibnitz.

57. No one can deny the transcendency of these questions, if he be not totally ignorant how vital it is to the human mind to know if a science superior to the purely sensible order be possible, whereby man may extend his activity beyond the phenomena offered by matter. These questions are exceedingly profound, and must not be lightly treated. The difficulty and the great abstruseness of the objects treated, the importance, the transcendency of the consequences to which they lead, according to the road followed, demand that no labor whatever should be spared to penetrate these matters. It is easy to assure one's self that upon these questions depends the conservation of sound ideas of God and of the human mind; man's most important and lofty considerations.

To give this matter a thorough examination, let us go back to the origin of the divergence of these philosophical opinions, and let us investigate the reason why, starting with the same facts, they arrive at contradictory results. This requires a clear exposition of the opposite doctrines.

58. All philosophers agree in admitting the fact of sensibility; concerning it there can be no doubt; it is a phenomenon attested by consciousness in so palpable a manner, that not even skeptics could ever deny the subjective reality of the appearance, however much they called in question its objective reality. Idealists, when they deny the existence of bodies, do not deny their phenomenal appearance, their appearance to the mental eye under a sensible form. Sensibility then, and the phenomena it exhibits, have in all ages been primary data in ideological and psychological problems; there may be a discrepancy with respect to the nature and consequences of these data, but there can be none as to their existence.

59. The history of ideological science shows us two schools; one of which admits nothing but sensation, and explains all the affections and operations of the mind by the transformation of the senses; while the other admits primitive facts distinct from sensation; other faculties than that of feeling, and recognizes in the mind a line dividing the sensible from the intellectual order.

60. This latter school is divided into two others; one of which regards the sensible order as not only distinct, but also separate from the intellectual order, and in some sense at war with it; and it therefore maintains that the intellectual can receive nothing from the sensible order, except malign exhortations which either mislead it, or enervate its activity. Hence the system of innate ideas in all its purity; hence the metaphysics of an intellectual order entirely exempt from sensible impressions, metaphysics which, cultivated by eminent geniuses, has in modern times been professed by the author of the Investigation of Truth, with sublime exaggeration. The other ramification of the school also admits the pure intellectual order, but does not hold it to be contaminated by being brought into communication with sensible phenomena; on the contrary, it is rather inclined to believe that the problems of human intelligence, such as it exists in this life, cannot be resolved without fixing the mind upon the aforesaid communication.

61. Experience teaches that this communication exists, conformably to a law of the human mind, and that to contend against the law is to struggle against a truth attested by consciousness: to attempt to destroy it would be a rash undertaking, a kind of mental suicide. For this reason, the school of which we have just spoken, accepts the facts, such as internal experience presents them, and endeavors to explain them by indicating the points where the sensible and intellectual orders may come into communication without being destroyed or confounded.

62. The school that admits the existence of the two orders, the sensible and the intellectual, and at the same time admits the possibility and the reality of their reciprocal communication and influence, has, for its fundamental principle, that the origin of all cognition is in the senses, these being the exciting causes of intellectual activity, and a kind of laborers who supply it with materials, which it then combines in the manner necessary to raise the scientifical structure.

63. Thus far, Kant and the scholastics agree; but here they separate at a point of the greatest importance, and the result is that they pass on to conflicting consequences. The scholastics believed that there were in the understanding true ideas having true objects, and that they might discuss them, independently of the sensible order, with perfect security. They even admitted the principle that there can be nothing in the understanding which was not previously in the senses; but pretended, nevertheless, that there really was something in the understanding, which might conduce to the knowledge of the truth of immaterial, as well as of material things in themselves. The ideas of the purely intellectual order originate in the senses as movers of the intellectual activity; but this activity, by means of abstraction and other operations, forms to itself ideas of its own, by whose aid it may go beyond the sensible order in its search for truth.

64. In their explanation of the purely intellectual order, metaphysicians, both scholastics and anti-scholastics agree, so far as there is question of giving a real objective value to ideas, and of making them a sure means of discovering truth independently of sensible phenomena. However much these schools disagree as to the origin of ideas, they agree in all that relates to their reality and value.

65. Kant, at the same time that he admits the principle of the scholastics, that all our cognitions come from the senses, and recognizes with them the necessity of acknowledging a purely intellectual order, a series of conceptions different from sensible intuition, maintains that these conceptions are not pure cognitions, but empty forms, which of themselves mean nothing, teach the mind nothing, and cannot, in the least, aid us to know the reality of things. These conceptions mean nothing unless filled, so to speak, with sensible intuitions. If these intuitions are wanting, they correspond to nothing, and can be of none but a purely logical use; that is to say, the understanding will think upon and combine them, without, indeed, falling into contradiction, but also without ever coming to any conclusion.

"That the understanding," Kant says, "can never make a transcendental, but only an empirical use, either of its a priori principles, or of its conceptions, is a principle which, if known with conviction, leads to the most important consequences. The transcendental use of a conception in any principle, consists in referring it to things, in general, and in themselves; whilst the empirical use is in referring the conception to phenomena alone, that is, to the objects of a possible experience, by which we may easily see that this latter use is the only one that can stand. To every conception is necessary, first of all, a logical form of a conception in general, of the thought: and secondly, the possibility of subjecting to it an object, to which it may refer; but without this object it wants all sense, it contains nothing, although it may involve the logical function necessary to form a conception by means of certain data. The object cannot be given to a conception except in intuition; and although pure intuition may be a priori possible before the object, it cannot, however, receive its object, and consequently its objective value, otherwise than by the empirical intuition of which it is the form. All conceptions and with them all principles, although they be possible a priori, do, notwithstanding, refer to empirical intuitions, that is, to data of possible experience. Without this they have no objective value; they are nothing but a mere play, whether of the imagination or of the understanding, with the respective representations of the one or the other faculty.

"That the same is the case with all the categories and principles formed from them, is apparent from this, that we cannot really define a single one of them; that is to say, we cannot render the possibility of their object intelligible without attending to the conditions of sensibility, and consequently to the form of the appearances; conditions to which these categories must be confined as to their sole objects. If this condition be taken away, all meaning, that is, all relation to the object is destroyed, and by no example can we be made to conceive what is the proper meaning of these conceptions.

"If no account be made of all the conditions of sensibility which denote them (he is speaking of the categories) as conceptions of a possible empirical use, if they be taken to be conceptions of things in general, and consequently, of transcendental use, nothing remains to be done, so far as they are concerned, but to preserve the logical functions in judgments, as the condition of the possibility of the things themselves, without being able to show in what case, their application and their object, and consequently they themselves, may, in the pure understanding, and without the intervention of sensibility, have a meaning and an objective value.

"It incontestably follows from what has been said, that pure conceptions of the understanding can never have a transcendental use, but only an empirical use; and that the principles of the pure understanding do not refer to the objects of the senses, except when the senses are in relation with the general conditions of a possible experience; but never to things in general, without relation to the way in which we may perceive them."[8]

66. Thus Kant destroys all metaphysical science, and, involved in its deplorable ruins, perish the most fundamental, most precious, and most sacred ideas of the human mind. According to him, transcendental analysis makes us see that the understanding can never pass the limits of sensibility, the only limits within which objects are given to us in intuition. These principles which were regarded as eternal pillars of the scientific edifice sink into empty forms, into words without meaning, so soon as they rise from the sphere of sensibility.

Ontology, with its transcendental doctrines, avails not in the eyes of the German philosopher to explain the nature and origin of things. "These principles," he says, "are simply principles of the exposition of phenomena; and the proud name of an ontology which pretends to give an a priori, synthetic cognition of things, in a systematic doctrine, for example, the principle of causality, ought to be replaced by the modest denomination of simple analysis of the pure understanding."

67. It would be hard to find a more noxious doctrine. What is left to the human mind when all means of rising from the sensible sphere are taken away? To what is our understanding reduced, if its most fundamental ideas, and its noblest principles can teach nothing concerning the nature of things? If the corporeal world is for us nothing but a collection of sensible phenomena, beyond which we can know nothing, our cognitions have nothing real, they are all purely subjective; the soul lives on illusions, and vanishes with its imaginary creations, to which there is nothing to correspond in reality. Space is but a subjective form; time is but a subjective form; pure ideas are empty conceptions, and all in us is subjective. We know nothing of objects, we are totally ignorant of what is; we know only what appears. This is pure skepticism; assuredly it was not necessary to consume so much time in analytical investigations to get thus far. The doctrine of Kant presents no extravagance so outrageous, no error so hideous, as the works of Fichte, Schelling, and Hegel; but it contains the germ of the greatest extravagance, and of the most fatal errors. He has made a philosophical revolution, which some have incautiously deemed a progress; but doubtless they did not detect the skepticism it contains, which is the more dangerous, the more it is enveloped in analytical forms.

68. Notwithstanding the importance justly attached to the refutation of the German philosopher's errors, I do not deem it necessary to combat his doctrines step by step; this system of refutation labors under the serious objection that it gives little satisfaction to the reader, who seems to see one edifice torn down, but not replaced by another. I consider it more useful carefully to examine questions as they arise in the order of their subjects, to establish my opinion as best I can, and there to refute Kant's errors as I find them obstructing the march of truth. It is ordinarily very easy to say what a thing is not; but it is not so easy to say what it is; and it is not proper that the advocates of sound doctrine should be charged with impugning false doctrines, and not caring to expose their own. We believe that in these matters sound philosophy may be presented to the light of the day struggling against error, and that it ought not to rest satisfied with being the instrument of war to overthrow its adversary, but that it should aspire to found a noble and enduring edifice upon the very site the other occupied.

The minds of men are not satisfied with simple refutations; they desire to have a doctrine substituted in the place of the one impugned. Whoever impugns, denies; and the understanding is not satisfied with negations; it wants affirmation, for it cannot live without positive truth.

We have permitted ourselves this brief digression, which is indeed far from being useless; for at the sight of the transcendency of the German philosopher's errors I have recollected the necessity of careful, assiduous, and profound labor to oppose this deluge of errors which threatens to inundate the whole field of truth; and we could not do less than insist upon this point, and observe that it is not enough to tear down, but that it is also necessary to build up. Refutations will soon come; but let positive doctrines abound. It is not enough to cover the long line of frontiers where error makes its attacks, with light and active troops which may fall upon the enemy; it is necessary to found colonies, foci of cultivation and civilization, who will defend the country, at the same time that they make it flourish and prosper.

[CHAPTER X.]

SENSIBLE INTUITION.

69. Intuition, properly so called, consists in the act of the soul by which it perceives an object that effects it: this the signification of the Latin word derived from the verb intueri, to see a thing which is present, indicates.

70. Intuition belongs only to perceptive powers, to those by which the subject affected distinguishes between its affection and the object causing it. We do not pretend to say that this must be a reflex distinction, but simply that the internal act must refer to an object. If we suppose a being to experience various affections, but to neither refer them to any object, nor reflect upon them itself; this being can never with propriety be said to have true intuition, for intuition seems to involve the exercise of an activity occupied with a present object. The object of intuition need not always be an external being; it may be an affection or action of the soul made objective by a reflex act.

71. The sensations which are with the greatest propriety called intuitive, are those of sight and touch; for, since it is impossible for us, when we perceive extension, to regard it as a purely subjective fact, the acts of seeing and feeling necessarily involve relation to an object. The other senses, although they may have a certain relation to extension, do not perceive it directly, so that were they to stand alone, they would partake more of the affective than of the intuitive; that is, the soul would be affected by the sensations, but would be under no necessity of referring them to external objects. If reflection made upon these sensations come to teach, as in effect it would teach that their cause is a being distinct from those that experience them, there would be no true intuition; not for the senses, because they would remain foreign to complex combinations; nor for the understanding, because it would then know the cause of the sensations, not by intuition, but by discursion.

72. We infer from this, that not every sensation is an intuition; and that the imaginary reproductions of past sensations, or the imaginary production of possible sensations, although repeatedly styled intuitions, are, since they do not refer to an object, unworthy of the name. We ought, nevertheless, to observe that the phenomena of purely internal sensibility do, perhaps, owe to the habit of reflection their non-reference to objects. Reflection perceives the difference of time, the more or less vividness of sensations, their greater or less constant connection, and also other circumstances; and it is enabled by these to distinguish between representations which do really refer to an object, such as external sensations, and those that have only a past or possible object, such as purely internal representations. Thus experience teaches us that the purely internal sensibility, wholly abandoned to itself, transfers whatever is presented to it to the external world, without the aid of reflection, and converts imaginary appearances into realities. This is verified in sleep, or even in our waking hours, when by some cerebral inversion the sensibility works by itself alone, and entirely free of reflection.

73. The reason why the sensibility left to itself, renders all its impressions objective, is to be looked for in the fact, that being a non-reflective faculty, it cannot distinguish between a purely internal affection, and one coming from without. Since comparison, however inconsiderable it may be, always implies reflection, sensibility does not compare. Hence it happens that when the subject does nothing but feel, it cannot appreciate the differences of sensations, by calculating the degrees of their vividness, nor ever perceive the existence or want of order and constancy in their connection.

The faculty of feeling is perfectly blind to all but its determinate object; whatever it does not discover in this so far as it is its object, does in no manner exist for it. We can now see why, when left to itself, it will render its impressions objective, and believe itself intuitive by converting simple appearances into realities.

74. It is worthy of notice, that of the sensitive faculties, some would always be intuitive, that is, would always refer to an external object, if reflection did not accompany them; whilst others would never be intuitive, not even if separated from reflection, or unaccompanied by those which are by their nature intuitive. To the former class belong the representative faculties, properly so called, that is, those which affect the sensitive subject by presenting to it a form, the real or apparent image of an object. Such are those of sight and of touch, which can neither exist nor be conceived without this representation. Other sensations, on the contrary, offer no form to the sensitive subject; they are simple affections of the subject, although they proceed from an external cause; if we refer them to objects, this we do by reflection; and when this warns us that we have in attributing to the object not only the principle of causality, but also the sensation in itself, carried the reference too far, we easily recognize the illusion, and lay it aside. This does not occur in representative sensations; no one, no matter how great efforts he may make, will ever be able to persuade himself that beyond himself there is nothing real, nothing resembling the sensible representation in which objects are presented as extended.

75. When we say that some sensations would not be intuitive were they not accompanied by reflection, we do not mean to say that man refers them to an object, after explicit reflection, for we cannot forget what we have already said when explaining at length the instinctive way in which our faculties develop themselves prior to all reflection, in their relations with the corporeal world; but only that no necessary relation to an object as represented can be discovered in these sensations considered in themselves, and in perfect isolation; and that, probably, if a confused reflection be not mingled with the instinct which makes us render them objective, there at least enters some influence of other sensations, which are by their proper object representative.

[CHAPTER XI.]

TWO COGNITIONS: INTUITIVE AND DISCURSIVE.

76. Now that I have explained sensible, I pass to intellectual intuition. There are two modes of knowing; the one is intuitive, the other discursive. Intuitive cognition is that in which the object is presented to the understanding, such as it is, and upon which the perceptive faculty has to exercise no function but that of contemplation; it is therefore called intuition, from intueri, to see.

77. This intuition may take place in two ways. It may either present the object itself to the perceptive faculty, and unite them without any intermediacy; or by the intervention of an idea or representation, capable of putting the perceptive faculty in action, so that it may, without the necessity of combination, see the object in this representation. The first requires the object perceived to be intelligible by itself, since otherwise there could be no union of the object understood with the subject understanding; the second needs a representation to supply the place of the object, and consequently it is not indispensable that this should be immediately intelligible.[9]

78. Discursive cognition is that in which the understanding does not have the object itself present, but forms it itself, so to speak, by uniting in one whole conception several partial conceptions, whose connection in one subject it has found out by ratiocination.

In order to render more apparent the difference between intuitive and discursive cognition, I will illustrate it by an example. "We see a man; his physiognomy is presented to us, such as it is; no combinations are necessary, none could possibly make him appear differently. We see his characteristic features, such as they are; but the collection of them is not a thing produced by our combinations; it is an object given to the perceptive faculty which has nothing to do but to perceive it." When an object is offered to our understanding in this way, the cognition we have of it will be intuitive.

We have said that the object of intellectual intuition may be united immediately to the perceptive faculty, or that it may be presented to it by a medium which acts the part of the object. Keeping in view the same example, we might say that these two classes of intuitions correspond to those of the man seen by himself, or in his portrait. There would be in both cases intuition of his physiognomy, but no combination would be necessary, and none could possibly form it.

But suppose some one to tell us of a person whom we have never seen, and whose portrait cannot be shown to us. He would be obliged, in order to give us an idea of his physiognomy, to enumerate one by one his characteristic features, by the union of which we shall form an idea of the likeness he has just described. To this imaginary representation may be compared discursive cognition, by which, although we do not see the object, we in some sense construct it, as it were, from the assemblage of those ideas which we have by means of discursion interlinked, and formed into one whole conception representing the object.

79. Kant, in his Critic of Pure Reason, speaks repeatedly of intuitive and discursive cognition; but he does not explain with perfect clearness the distinctive characteristics of these two classes of cognition. Let it not, however, be supposed that the discovery of these two ways of perceiving is due to the German philosopher. Many ages before him, the theologians had known them; nor could it be otherwise, since the distinction between intuition and discursion is intimately connected with one of the fundamental dogmas of Christianity.

It is well known that our religion admits the possibility and reality of a true cognition of God, even in this life. The sacred text tells us that we may know God by his works; that the invisible things of God are manifested to us by his visible creatures; that the heavens narrate his glory, and the firmament announces the works of his hands; that they who have thus known God are inexcusable, because they have not glorified him as they ought; but this same religion teaches us that the Blessed, in the life to come, will know him in a very different manner, will see him as he is, face to face. It was Christianity then that marked the difference between intuitive and discursive cognitions, between the cognition by which the understanding, proceeding from effects to their cause, and uniting in it the ideas of wisdom, omnipotence, goodness, holiness, and infinite perfection, rises to God; and the cognition in which the mind does not need to advance, drawing its conclusions by aid of discursion, from various conceptions, in order to force from them an idea of God, in which the Infinite Being will offer himself clearly to the eyes of the mind, not in a conception elaborated by reason, nor under the sublime mysteries of faith, but such as he is, in himself, as an object given immediately to the perceptive faculty, not as an object discovered by the force of discursion, or presented under august shadows. And here we find another proof of the great profoundness hidden under the dogmas of the Christian religion. This distinction is to be met with in the catechism, and yet who would have suspected that religion had taught us a doctrine so important to ideological science? If the child be asked, who is God, he replies by enumerating his perfections, and showing thereby that he knows him. If you ask this same child, to what end man has been created, he will answer, to see God, etc.

Here again is the distinction between discursive cognition, or by conceptions, and intuitive cognitions; with the former one is said, simply to know, with the latter to see.

[CHAPTER XII.]

THE SENSISM OF KANT.

80. Kant maintained that while in the present life, we have only sensible intuition; and he considers the possibility of a purely intellectual intuition, whether for our own or for other minds doubtful. But as we have seen elsewhere (ch. IX.) that he does not attribute any value to conceptions separated from intuition, we infer that he is, notwithstanding his long dissertations upon the pure understanding, a confirmed sensist; and that the authors of the Critic of Pure Reason, and of the Treatise on Sensations, differ much less than at first sight might be supposed. If our mind has no other intuition than the sensible, and the conceptions of the pure understanding are, if they do not include some one of these intuitions, nothing but empty forms; if when we abstract these intuitions, there are in the understanding only purely logical functions, which mean nothing, and in no sense deserve to be called cognitions; it follows that there is in our mind nothing but sensations, which may be methodically distributed in conceptions, as if packed away in a kind of hut, where they are registered and preserved. According to this philosopher, the understanding is reduced so low, that Condillac himself might admit it.

81. Indeed, in the system of sensations transformed, the mind is supposed to possess a transforming force, since otherwise, it would be impossible to explain all ideological phenomena by mere sensation, and the very title of the system would be a contradiction. This being so, would any sensistic scruple have prevented Condillac from admitting the synthesis of the imagination, the relations of all sensible intuitions to the unity of apperception, and finally, a variety of logical functions, to classify and compare sensible intuitions? So far is this from being the case, it would seem that the root of all these doctrines might be found in the system of the French philosopher, whose fundamental principles, when summed up, amount to this: that nothing can be seen in the mind besides sensations; but he does not therefore deny it a force capable of transforming, classifying, and generalizing them.

82. Here, then, is another check to the originality of the German philosopher; he has, to combat sensism, said in substance just what, ages before, all the schools repeated; and now when he undertakes to follow a new road to the explanation of the purely intellectual order, he falls into Condillac's system. His empty conceptions, without meaning, without application, beyond the sensible order, amount to no more than what Condillac taught when analyzing the generation of ideas, and showing how they flowed from sensations by means of successive transformations. Could there be any difficulty, it would be concerning words, not things: no sensist ought to hesitate accepting whole and entire the Critic of Pure Reason, when once he has seen what applications the German spiritualist makes of his doctrines. It would be very desirable for those who insist that the spiritualism of Kant is decidedly destructive of Condillac's sensism, to weigh well these observations.

[CHAPTER XIII.]

EXISTENCE OF PURE INTELLECTUAL INTUITION.

83. It is not true that the human mind even in this life has no intuition other than the sensible. There are within us many non-sensible phenomena, of which we are clearly conscious. Reflection, comparison, abstraction, election, and all the acts of the understanding and will, include nothing of the sensible. We should like to know, to what species of sensibility, abstract ideas, and the acts by which we perceive them, belong; these among others: I desire, I do not desire, I choose this, I prefer this to that. Not one of these acts can be presented by sensible intuition; they are facts of an order superior to the sphere of sensibility, and yet we have in our mind a clear and lively consciousness of them; we reflect upon them, make them the object of our studies, distinguish them one from another, and classify them in a thousand different ways. These facts are presented to us immediately; we know them, not by discursion, but by intuition; therefore it is false that the intuition of the soul refers to none but sensible phenomena, for it encounters within itself an expanded series of non-sensible phenomena, which are given to it in intuition.

84. It is of no use to say that these internal phenomena are empty forms, and mean nothing, unless referred to a sensible intuition. Whatever they may be, they are something distinct from this same sensible intuition; and we perceive this something, not by discursion, but by intuition; therefore, besides sensible intuition, there is another of the purely intellectual order.

The question is not whether these pure conceptions have, or have not, a certain power to enable us to know objects in themselves; but it is simply to ascertain if they do exist, and if they are sensible. That they exist, is certain; consciousness attests this fact, and all ideologists admit it. That they are sensible, cannot be maintained without destroying their nature; and least of all can Kant maintain this, since he has so carefully distinguished between sensible intuition and these conceptions.

85. This sea of non-sensible phenomena, which we experience within us, is like a mirror wherein the depths of the intellectual world are reflected. Minds, it is true, are not presented immediately to our perception, and to know them we need a discursive process; but we shall, upon careful examination, find in this intuition of our inward phenomena the representation, imperfect though it be, of what is verified in intelligences of a superior order. Thus we have in a certain mode idea-images, since there can be no better image of one thought than another thought, nor of one act of the will than another act of the will. Thus we know minds distinct from our own, by a kind of mediate, not immediate, intuition, in so far as they are presented to our consciousness as the image in a mirror.

86. The communication of minds by means of speech and other natural or conventional signs, is a fact of experience intimately connected with all intellectual, moral, and physical necessities. When a mind is put into communication with another, the cognition it has of what passes in the other is not by mere general conceptions, but by a kind of intuition, which although mediate, does not therefore fail to be true. The thought, or affection of another communicated to our mind by means of speech, excites in us a thought, or affection, similar to that of the mind communicating them. We do, then, not only know, but see, in our own consciousness, the consciousness of another; and so perfect is at times the likeness, that we anticipate all that he is about to tell us, and unroll within ourselves the same series of phenomena that are verified in the mind of him with whom we are in communication. It happens thus when we say: "I understand perfectly what N. thinks, what he wants, what he is trying to express."

87. This observation seems to us of great service to place beyond all doubt that there are in our mind, independently of the sensible order, conceptions, not empty, but referable to a determinate object. The cognition of the phenomena of the purely intellectual order, transmitted to us by means of speech, or other signs, does not destroy the character of the intuition, since we here find all the necessary conditions assembled; internal representation, and its relation to a determinate object affecting us.

88. This analysis of ideological facts, whose existence cannot be doubted, demonstrates the falseness of Kant's doctrine, that there are in our mind none but sensible intuitions; as well as the non-existence of the German philosopher's problem: whether it is possible, or not, for objects to be given to other minds in an intuition other than the sensible. This very problem is found solved within us, since the attentive observation of the internal phenomena, and the reciprocal communication of minds, has given us to know not only the possibility, but also the existence of intuitions different from the sensible.

[CHAPTER XIV.]

VALUE OF INTELLECTUAL CONCEPTIONS.—ABSTRACTION MADE FROM INTELLECTUAL INTUITION.

89. Although we should admit that our mind can have no intuition but the sensible, it could not thence be inferred that conceptions of the purely intellectual order are empty forms, and in nowise conducive to the knowledge of objects in themselves. It has always been understood that general ideas are not intuitive, since by the very fact that they are general they cannot be referred immediately to a determinate object; and yet no one ever doubted that they could serve to give us true cognitions.

90. It is certain that general ideas, of themselves alone, do not lead to any positive result; or, in other words, they do not make us know existing beings; but if they be joined to other particular ones, a reciprocal influence is established between them, from which cognition results. When we make the general affirmation: "Every contingent being requires a cause;" this proposition, although very true, means nothing in the order of facts, if we abstract the existence of contingent beings and causes of every kind. In such a case, the proposition will express a relation of ideas, not of facts: the cognition which results therefrom will be merely ideal, not positive.

91. This relation of ideas tacitly involves a condition, which gives them, so far as facts are concerned, a hypothetical value; for, when we affirm that every contingent being must have a cause, we are not to be understood to affirm a relation of ideas destitute of all possible application; but rather, on the contrary, to intend that if any contingent being exists, it must have a cause.

92. In order that this hypothetical value of ideas may be converted into a positive value, nothing is necessary but that the condition involved in the general proposition: "Every contingent being must have a cause," be verified. Of itself alone this teaches us nothing concerning the real world; but from the moment that experience shows us a single contingent being, the general proposition, before sterile, becomes exceedingly fruitful. So soon as experience shows us a contingent being, we know the necessity of its cause; we also infer the necessity of the proportions, which the activity producing must preserve with the thing produced; knowing the qualities of the latter, we infer those which ought to be found in the former. In this manner, resting upon two bases, one of which is ideal truth and the other real truth, or data supplied by experience, we construct a true positive science referred to determinate facts.

93. Since the being that thinks necessarily has consciousness of itself, no thinking being can be limited to the cognition of purely ideal truths. Even if we were to suppose it perfectly isolated from all other beings, in absolute non-communication with every thing not itself, so as neither to exert any influence upon them, nor to be influenced by them, it could not be reduced to the cognition of a purely ideal order; for, by the very fact that it is thinking, it is conscious of itself, and consciousness is essentially a particular fact, a cognition of a determinate being, since without it there could be no consciousness.

94. This observation overturns to its very foundation the system which pretends to bar all communication between the real and ideal orders. It shows also that experience is not only possible, but absolutely necessary to every thinking being, since consciousness is by its very nature an experience, and the clearest and surest experience. The truths of the ideal order are then necessarily interlinked with those of the real order: to suppose all intercommunication between them impossible, is to disown a fundamental fact of ideological and psychological science, consciousness.

95. To render the truth and exactness of the preceding doctrine more evident, let us suppose a man, or rather a human mind, absolutely ignorant of the existence of an external world, of every body, and even of every spirit; one that knows nothing concerning its own origin or destiny, but one that would nevertheless at the same time exercise its intellectual activity, without which it would be a lifeless thing, and could offer no field to observation. Let us suppose him to have general ideas, such as of being and of not-being, of substance and accidents, of the absolute and the conditioned, of the necessary and contingent. Manifestly he may combine them in various ways, and arrive at the same purely ideal results to which we ourselves arrive. There is no supposition more favorable to a series of abstract cognitions independent of experience, and yet not even in this case would the truths known be limited to the purely ideal order; it would even here be impossible for them not to descend to the real order, if the thinking being were not dispossessed of all consciousness of itself.

Indeed, by the very fact that a being is supposed capable of thinking, it is supposed able to say to itself, I think. This act is eminently experimental, and it needs only to be united with general truths in a common consciousness, to enable the isolated being to rise above itself, and create for itself a positive science, by which to pass from the world of ideas to that of facts. The instability of its thoughts, and the permanence of the being that experiences them, offer to it a practical case in which the general ideas of substance and accident are particularized. The successive appearance and disappearance of its own conceptions will show to it the ideas of being and of not-being realized; the recollection of the time when its own operations commenced, beyond which the memory of its existence does not extend, will enable it to know the contingency of his own being; and this fact, combined with the general principles which express the relations between contingent and necessary beings, will suggest to the thought that there must be another that communicated to it its existence.

[CHAPTER XV.]

ILLUSTRATIONS OF THE VALUE OF GENERAL CONCEPTIONS.

96. However vague the ideas an isolated being would form of objects distinct from itself, they will never be so vague as not to refer to a real thing. The mind may not know the nature of this reality, but it knows for certain that it exists. A man blind from his birth can form no clear idea of colors, nor of the sensation of seeing; but is he therefore ignorant that sensation exists, and that the words, color, seeing, and others which refer to sight, have a positive and determinate object? Certainly not. The blind man does not know in what these things, of which he hears, consist, but he knows that they are something; those of his conceptions that refer to them may be called imperfect, but they are not vain; the words by which he expresses them, have for him a positive, although incomplete meaning.

97. There is a great difference between incomplete and indeterminate conceptions; the former may refer to a positive thing, although imperfectly known; the latter include nothing but a relation of ideas, meaning nothing in the order of facts. We will render this difference more apparent by explaining the example of the preceding paragraph.

A man blind from his birth has no intuition of colors, nor of any thing that refers to the sense of sight; but he is sure that there exist external facts which correspond to an internal affection called seeing. This idea is incomplete, but it has a determinate object. The words of those who possess the sense of sight reveal to him its existence; he knows not, what it is, but, that it is; in other words, he does not know its essence, but its existence. Let us now suppose the possibility of an order of sensations different from ours, and in nowise resembling those which we experience, to be called in question. The conception referred to the new sensations would not only be incomplete, but would have no relation to any real object. The general idea, then, of affection of a sensitive being, will be all that our mind will have; but it will know nothing of its existence, and can form only mere conjectures as to the conditions of its possibility. This example illustrates our idea. We find in the man blind from his birth, who hears of what pertains to the sense of sight, an incomplete conception, but one to which the existence of a series of facts, known to his mind, corresponds. But in ourselves, if we reflect upon a kind of sensations different from our own, we find conceptions, having, indeed, a general object, but of whose realization we know nothing.

98. Thus is it explained how our mind, without having intuition of a thing, can, nevertheless, know it, and be perfectly certain of its existence. We have here demonstrated that conceptions may, although they do not refer to a sensible intuition, have a value, not only in the order of ideas, but also in that of facts.

99. In order to prove the sterility of all conception beyond sensible intuition, Kant adduces one reason, which is, that we cannot define the categories and the principles which flow from them without referring to the objects of sensibility. This is no proof at all; for, in the first place, the impossibility of a definition does not always arise from the fact that the conception to be defined is empty; but it very frequently results from the conception being simple, and consequently not susceptible of a division into parts that may be expressed by words. How will he define the idea of being? No matter how he attempts to define it, the thing to be defined will enter into the definition: the words, thing, reality, existence, all signify being.

It is very natural, since sensible intuition is the basis of our relations with the external world, and consequently with our fellow-men, that when we purpose to express any relation whatever, we should call to our aid sensible applications; but we are not thence to infer that there is not in our mind, independently of them, a real truth contained in the conception which we wish to explain.

100. This capacity of knowing objects under general ideas, is a characteristic property of our mind, and we cannot, in our inability to penetrate to the essence of things, think without this indispensable auxiliary. In the ordinary course of human affairs, it often happens that we need to know the existence of a thing and of some of its attributes, but do not require a perfect knowledge of it. In such cases, general ideas, aided by some data of experience, put us in mediate communication with the object not presented to our intuition. But why cannot the same thing be verified with respect to non-sensible beings, which alone are the object of intellectual intuitions? I know not what exception can be taken to these observations, founded as they are upon observation of internal phenomena, and confirmed by common sense.

[CHAPTER XVI]

VALUE OF PRINCIPLES, INDEPENDENTLY OF SENSIBLE INTUITION.

101. The principle of contradiction, indispensable condition of all certainty, of all truth, and without which the external world, and intelligence itself, would become a chaos, offers us a good example of the intrinsic value of purely intellectual conceptions independent of sensible intuition.

No determinate idea is united to the conception of being when we affirm the impossibility of a thing being and not-being at the same time, or the exclusion of not-being by being; and so far we absolutely abstract all sensible intuition. Whatever be its object, whatever its nature and the relations of its existence; be it corporeal or incorporeal, composite or simple, accident or substance, contingent or necessary, finite or infinite, always will it be found true that being excludes not-being; the absolute incompatibility of these two extremes will always be verified, so that the affirmation of the one is always, in all cases, and under all imaginable suppositions, the negation of the other.

This being so, to limit the value of these conceptions to sensible intuition, would be to destroy the principle of contradiction. The limitation of the principle is equivalent to its nullification. Its absolute universality is closely allied to its absolute necessity; if it be curtailed, it is made contingent; for, if the principle of contradiction may fail us in one instance, it fails us in all. To admit the possibility of what is absurd, is to deny its absurdity. If the contradiction of being and not-being does not exist in every supposition, it exists in no supposition.

102. The difficulty is to know how the transition from the principle of contradiction to real truths, is made; because not affirming any thing determinate in it, but solely the repugnance of yes to no, and of no to yes, we assert that it would be impossible to affirm either one of these extremes without denying the other; and as on the other hand, it is impossible, if we confine ourselves to the principle of contradiction, for it to include any thing more than the most general relation between two general ideas, we conclude that it is of itself alone, perfectly sterile and unable to conduct us to any positive result. This is all true; but it contradicts in no point what we have said concerning the intrinsic value of general conceptions.

We have remarked that truths of the purely ideal order have none but a hypothetical value, and that in order to produce a positive science, they require facts to which they may apply. We have also remarked, that experience furnishes these facts, and that every thinking being possesses one at least, consciousness of itself. Every thinking being will therefore, provided it discover in its own consciousness facts to which it may apply it, make a positive use of the principle of contradiction.

103. Even were we to admit the supposition that there is in our mind no intuition but the sensible, it could not therefore be concluded that general principles, and more particularly that of contradiction, can have no positive value; because, if we suppose these principles combined with sensible intuition to produce a cognition of other beings out of the order of sensibility, it would follow that we really know them, although they were not given to us in immediate intuition. And this is verified in the human mind, when it rises by discursion to the cognition of the non-sensible. On the one hand, the data furnished by experience, and on the other, general and necessary truths, form a connection constituting a positive science, which guides us with perfect security to the cognition of objects not subject to immediate experience.

This theory is so clear, so evident, so rooted in the consciousness of our own acts, so perfectly in accordance with all that we observe in the proceedings of the human mind, that it causes us a strange surprise to meet philosophers, whose erroneous doctrines oblige us to explain and defend it.

104. The transition from the known to the unknown is a proceeding characteristic of our understanding; and this transition is impossible if the reality of every cognition, not referred to an intuition, be denied. Whatever is presented to us in this latter way, is given to us, is present to our sight, and we have no necessity of seeking it. If, therefore, no object be really known, unless offered in intuition, all intellectual progress becomes impossible: all the advances of our mind are reduced to combinations of the forms presented to the sensibility, and even these lead to nothing whenever they cease to be intuitive; that is, when they no longer relate to determinate objects immediately perceived. The Critic of Pure Reason is the destruction of all reason: for it examines itself with suicidal intent, or in order to prove that it contains nothing positive.

Science cannot survive the reduction of general principles to one only value relative to sensible intuitions. What we have demonstrated concerning the principle of contradiction, is a fortiori applicable to all other principles. If this be not saved, all must perish in the wreck. Moreover, the very basis of the necessity involved in these principles is threatened. We know nothing, save that there is within us a series of phenomena which seem necessary. But what use can we make of them beyond the subjective order? None at all. Behold us then in the most perfect skepticism, condemned to simple appearances, with no means of knowing any reality.

105. No! the human mind is not condemned to so despairing a sterility: reason is not an empty word; ratiocination is not a puerile play, only fit to serve as an amusement. In the midst of the prepossessions, errors, and extravagance of human misery, towers on high that force, that admirable activity, by which the mind springs beyond itself, knows what it does not see, and foresees what it will one day feel. Nature is veiled to our eyes; impenetrable secrets surround us; whichever way we turn deep shadows hide the reality of objects: but through this darkness we discern from afar some scintillation of light. Notwithstanding the profound silence which reigns over the sea of beings, whose surges toss us about like imperceptible atoms in the immensity of the ocean, we hear at times mysterious voices tell us the course we must keep to reach unknown shores.

[CHAPTER XVII.]

RELATIONS OF INTUITION WITH THE RANK OF THE PERCEPTIVE BEING.

106. The perfection of intelligence involves extension and clearness of its intuitions; the more perfect it is, the more intuitive it will be. The infinite intelligence does not know by discursion, but by intuition: it does not need to seek objects: it sees them all before itself. It sees with intuition of identity what belongs to its own essence, and with intuition of causality every thing that does or can exist outside of itself. Other minds have an intuition so much the more perfect as they are more elevated in the order to which they belong; so that cognition by conceptions indicates an imperfection of intelligence.

107. The relations of one being with other beings will therefore depend upon the rank it holds in the scale of the universe. God, infinite being, and the cause of all that does or can exist, has intimate and immediate relations with the whole universe, considered not only in its entireness but even in its smallest particles. There is consequently in God a most perfect representation of all beings taken not only in their generality, but also in their minutest differences. The Being, cause of all, does not know objects by vague conceptions, by means of representations which only show what all beings have in common, but as he has made their slightest differences, they must be presented to him with perfect clearness. His cognition is founded upon a reality which is himself; his understanding does not fluctuate through an ideal and hypothetical world; but, fixed with clearest intuition upon infinite reality, he sees all that the infinite being is, and all that it can produce with its infinite activity. For God there is no experience proceeding from without, for nothing can exert any influence upon him; all his experience consists in the knowledge and love of himself.

108. Created beings, occupying a determinate place in the scale of the universe, relate to it only under certain aspects. Their relations with their fellow beings are brought to a point of view, to which their perceptive faculties are subordinated. The representativeness, which they contain in themselves, must be proportionate to the cognition that has to produce it. Hence it follows that every intelligent being will have its representativeness adapted to the functions it has to exercise in the universe. If the being do not pertain to the order of intelligences, its perceptive faculties will be limited to sensible intuitions, in a measure corresponding to the place it is destined to occupy.

109. We have seen that general ideas and the intuition of determinate objects fecundate the intellectual faculties. From this we infer that every intelligence stands in need of intuitions, if its cognitions are not to be limited to a purely hypothetical order.

The human mind, destined to a union with the body, and to a continual communication with the corporeal universe, has received the gift of sensible intuition as the basis of its relations with bodies. The same is the case with brutes. Sensible intuition has been given to them because they must have continual relations with the external world: but, being confined to the functions of animal life, they have no intuitions superior to the sphere of sensibility, nor do they possess the force necessary to convert sensible representations into objects of intellectual combinations.

110. There is an immense difference between brutes and man, in the scale of beings. Since every intelligence is conscious of itself, and can fix its attention upon its acts, the human mind knows its own intuitively, and therefore discovers in itself an intuition superior to the sensible. Besides these intuitions, we have the power of discursion by which we form representations, and by them attain to the cognition of objects not offered immediately to our perception.

Thus, starting with the data furnished by external and internal experience, and aided by those general principles which involve the primary conditions of every intelligence and of every being, we are enabled to penetrate to the world of reality, and to know, although imperfectly, the assemblage of beings which constitute the universe, and the infinite cause which made them all.

[CHAPTER XVIII.]

ASPIRATIONS OF THE HUMAN SOUL.

111. A close observation of internal phenomena shows that the human soul aspires to something far beyond all that it actually possesses. Not satisfied with the objects given to it in immediate intuition, it darts forward in pursuit of others of a superior order; and even in those that are offered to it immediately, it is not contented with the aspect under which they appear, but seeks to know what they are. The purely individual does not satisfy the soul. Nailed to one point in the immense scale of beings, it is unwilling to limit itself to the perception of those that are in its environs, and form, as it were, the atmosphere wherein it must live; it aspires to the cognition of those that precede and follow it, and seeks to know the connection, to discover the law from which results the ineffable harmony that presides over the creation. It finds its purest pleasures in rising from the sphere where the limitation of its faculties holds it confined. Its activity is greater than its strength; its desires superior to its being.

112. We discover the same phenomenon in the sentiment and the will as in the understanding. Man has, to satisfy his necessities, and provide for the preservation of the individual and of the race, sensations and sentiments which direct him to determinate objects; but at the side of these affections, limited to the sphere in which he is circumscribed, he experiences sentiments of a more elevated character, which make him spring beyond his orbit, and absorb, so to speak, his individuality in the ocean of infinity.

When man comes in contact with nature in herself, despoiled of all conditions relating to individuals, he experiences an indefinable sentiment, a kind of foretaste of the infinite. Go into an uninhabited region and sit down by the sea side; hark to the deafening roar of the waves breaking at your feet, and the whistling of the winds which have raised them; with eyes fixed on this immensity, see the azure line where the vault of heaven unites with the waters of the ocean: stand on a vast and desert plain, or in the heart of ancient forests; contemplate in the silence of night the firmament studded with stars, following their course in tranquillity, as they have followed it for ages past, and will follow it for ages to come: without effort, or labor of any kind, abandon yourself to the spontaneous movements of your soul, and you will see how sentiments spring up in it and move it to its very centre; how they elevate it above itself, and absorb it, as it were, in immensity. Its individuality vanishes from its own eyes, as it feels the harmony presiding over that immense creation of which it forms but a most insignificant part. In such solemn moments is it that inspired genius chants the glories of creation, and lifts one corner of the veil that hides the resplendent throne of the supreme Creator from the eye of mortals.

113. That calm, grave, and profound sentiment which masters us on such occasions, has no relation to individual objects; it is an expansion of the soul at a touch of nature, as the flower expands to the rays of the sun in the morning, it is a divine attraction by which the author of all created things raises us above the dust in which we drag out our brief days. Thus the heart and the understanding harmonize; thus the one foretastes what the other knows; thus we are warned in different ways, that the exercise of our faculties is not limited to the narrow orbit conceded to us upon this earth. Let us be on our guard, lest the heart be frozen with the coldness of insensibility, and the torch of the understanding quenched by the devastating blasts of skepticism.

[CHAPTER XIX.]

ELEMENTS AND VARIETY OF THE CHARACTERS OF SENSIBLE REPRESENTATION.

114. I now come to examine the primitive elements of our mental combinations. I shall begin with their sensible elements. Extension enters into every act of representative sensibility; without it nothing is represented to us, and sensations are reduced to mere affections of the soul, having no relation to any object.

115. Extension, of itself, abstracted from its limitability, is susceptible of no combination; it only offers a vague, indefinite, immense representation, from which nothing distinct of itself results. But if limitability be joined to extension, figurability, that is, the infinite field over which geometrical science extends, will result.

116. Extension and limitability are then the two elements of sensible intuition. These elements may be offered to us in two ways, either joined to sensations which present to us determinate objects, or as productions of our own internal activity. If we see the disc of the moon, we have an intuition of the former class; and if we study the properties of a circle by producing within ourselves its representation, this will be an intuition of the latter class.

117. This internal activity, by which, at our will or caprice, we produce an indefinite number of representations, with an indefinite variety of forms, is an important phenomenon and one worthy of attention. It shows us that the productive activity is not limited to the purely intellectual order, since we detect it in the sensible order, not in any way whatever, but as unrolled on an infinite scale. Suppose a right line to be produced to infinity, besides it and in the same plane, we may infinite other lines; the variety of angles in which we may consider the position of the different lines will extend to the infinite; so that with right lines alone, the productive activity in the order of sensibility will know no limit. If we substitute curves for right lines, their combinations in form, in nature, in their respective positions and relations with determinate axes, will likewise be infinite: so that without quitting the sensible order, we discover within ourselves a force productive of infinite representations, and one needing no elements besides terminable or figurable extension.

118. The representative sensible faculty develops itself sometimes by the presence of an object; at other times, spontaneously, without any dependence on the will; and finally, at other times, in consequence of a free act. This is not the place to examine in what way the phenomenon of representation is connected with the affections of the corporeal organs; at present, we propose only to designate and explain facts in the ideological sphere, absolutely abstracting their physiological aspect.

Among the sensible representations just classified, which we may call passive, spontaneous, and free, there are differences worthy of observation.

119. Passive representation is given to the soul, independently of its activity. If we be placed in presence of an object, with our eyes open, it will be impossible not to see it, or even not to see it in a certain manner, if we do not change the direction of our eyesight or other condition of vision. For this reason, the soul seems, in the exercise of its senses, to be purely passive, since its representations necessarily depend on the conditions to which its corporeal organs in their relation to objects, are subject.

120. Spontaneous representation, or the faculty productive of sensible representations, seems also, since it operates independently of external objects and of the will, to be more or less passive, and its exercise to depend upon organic affections. And the fact that these sensations are wont to exist without any order, or at most, if they are recollections of old sensations, with that only which they had at another time, appears to indicate it. It is also worthy of note that these representations are sometimes offered to us, in spite of all the efforts of the will to dissipate and forget them: some are so tenacious as for a long time to triumph over all the resistance of freewill.

It is not easy to explain this phenomenon without recurring to organic causes, which, on determinate occasions, produce the same effect upon the soul, as the impressions of the external senses. It is certain that the internal representation reaches, in certain cases, so high a point of vividness, that the subject confounds it with the impressions of the senses. This can only be explained by saying that the interior organic affection has become so powerful, as to be equivalent to that which the impression of an object operating upon the external organ, could have caused.

121. In this spontaneous production it is to be remarked that present representations do not always correspond with others previously received; but a power of combination is developed in them from which result imaginary objects entirely new. This combination is sometimes exercised in a perfectly blind manner, and then follow extravagant results; but, at other times, this activity subjected to certain conditions produces, independently of free will, objects artistically beautiful and sublime.

Genius is nothing else than the spontaneity of the imagination and sentiment, developed in subordination to the conditions of the beautiful. Artists, not gifted with genius, do not lack strength of will to produce works of genius; nor are they wanting in imagination to reproduce a beautiful object if they have once seen it; they do not lack discernment and taste to distinguish and admire beautiful objects, nor are they ignorant of the rules of art or of all that can be said to explain the character of beauty; what they lack is that instinctively fine spontaneity which develops itself in the most recondite sinuosities of the soul, and far from being dependent upon the free will of its possessor, directs and domineers over him, pursues him in sleep as in the hours of waking, in the time of recreation as in that of business, and often consumes the very existence of the privileged man, as a furious fire bursts the sides of the frail cage that holds it.

122. Free production occurs when representations are offered to us by command of our will, and under the conditions it prescribes, as in works of art, and in the combinations of those figures which constitute the object of the science of geometry.

123. This a priori construction cannot be referred to a type existing in our imagination; since, as this type would then be the sensible representation itself, it would not need to be constructed. How then is it possible to form a representation of which we have not already the image? It is not enough to possess the elements, that is, figurable extension, since with them infinite figures may be constructed; something else then is needed, something to serve as a rule, in order that the desired representation may result.

For the better understanding of this, I would observe that sensible intuitions are allied to general conceptions, by whose aid they may be reconstructed. Although, in reality, no sensible representation is offered to us, of any figure whatsoever, for example, a regular hexagon; the conception formed of the ideas, six, line, equality of angles, is all that we need to produce in our interior the sensible representation of the hexagon, and to construct it within us, if we require it.

This shows us that the free activity producing determinate sensible representations is based upon general conceptions, which, though independent of sensibility, refer to it in an indeterminate manner. Hence, also, it follows, that the understanding may, if it observe the conditions to which the elements furnished by sensibility in their respective cases, are subject, conceive the sensible indeterminately, without the intellectual act being referred to any determinate intuition.

124. If we analyze the object of these general conceptions, referred to sensible intuition, also considered in general, the understanding, while occupied in them, seems to be taken up with things not distinctly offered to it, but retained only by certain signs; confident, however, that it can develop whatever they involve, and contemplate it with perfect clearness.

[CHAPTER XX.]

INTERMEDIATE REPRESENTATIONS BETWEEN SENSIBLE INTUITION AND THE INTELLECTUAL ACT.

125. The question now occurs, whether the understanding, in order to perceive the geometrical relations offered in sensible intuition, does or does not need some intermediate representations which bring it into contact with the sensible order?[10] Such a necessity would, at first sight, seem to exist, since, as the understanding is a non-sensible faculty, sensible elements cannot be its immediate object. But on maturer examination, it seems more probable that there is no necessity of any thing intermediate, except some sign to connect the sensible elements, and to show the point where they must unite, and the conditions to which they are subject. As this sign may, however, be a word, or something else, susceptible of a sensible representation, its mediation will not at all solve the difficulty; since the question will always recur: How is the understanding placed in communication with the sensible sign?

This difficulty arises from the faculty of the soul being considered, not only as distinct, but also, as separate, and as exercising each one of its faculties in its own peculiar and exclusive sphere, entirely isolated from that of all others. This mode of considering the faculties of the soul, though favorable to the classification of their operations, does not accord with the teachings of experience.

It cannot be denied that we observe within ourselves, affections and operations, very unlike each other, and arising from distinct objects, and producing very different results. This has led to a distinction of faculties, and in some degree, to a separation of their functions, so as to prevent them from mixing together and being confounded. But there can be no doubt that all the affections and operations of the soul are, as consciousness reveals, bound to a common centre. Whatever becomes of the distinction of the faculties among themselves, it is very certain, as consciousness tells us, that it is one and the same being that thinks, feels, desires, acts, or suffers: it is certain that this same consciousness reveals to us the intimate communication of all the operations of the soul. We instantaneously reflect upon the impression received; we instantaneously experience an agreeable or disagreeable sensation in consequence of a reflection which occurs to us: we reflect upon the will; we seek or repudiate the object of our thought; there is, so to speak, within us a boiling spring of phenomena of different kinds, all interlinked, modified, produced, reproduced, and mutually influenced by each other in their incessant communication. We are conscious of all these; we encounter them all in one common field, which is the subject that experiences them. What necessity, then, is there to imagine intermediate beings in order to bring the faculties of the soul into communication with each other? Why may it not with its activity, called understanding, occupy itself immediately with sensible representations and affections and with all that is in its consciousness? Supposing this consciousness in its indivisible unity to comprise all the variety of internal phenomena, it does not therefore follow that the intellectual activity of the soul cannot be referred to whatever it contains of active or receptive, without its being necessary to imagine species to serve as courtiers between the faculties, to announce to one what has taken place in the other.

126. The acting intellect of the Aristotelians, admissible in sound philosophy so far as it denotes an activity of the mind applied to sensible representations, does not seem alike admissible, if it be supposed to be the producer of new representations distinct from the intellectual act itself. The understanding is all activity; the receptivity of the soul has nothing to do with it, but to proportion its materials; and the conceptions elaborated in presence of these materials, seem to be nothing else than the exercise of this same activity, subject on the one hand to the conditions required by the thing understood, and subordinated on the other hand to the general conditions of every intelligence.

127. I do not mean to say that the intellectual act does not refer to any object. I replace the idea by other acts of the soul, or by affections or representations of some kind or other, whether active or passive. This being so, if I am asked, for example, what is the immediate object of the intellectual act perceiving of determinate sensible intuition, I reply that it is the intuition itself. If the difficulty of explaining the union of such different things be urged, I answer: first, that this union exists in the unity of consciousness, as the internal sense attests: second, that the same difficulty militates against those who pretend that the understanding elaborates an intelligible species, which it takes from the sensible intuition; and how, I may ask, does the understanding place itself in contact with this intuition when it would elaborate its intelligible species. If this immediate contact be impossible in the one case, it will be equally so in the other; and if they concede it to be possible in their own case, they cannot deny it to be possible in ours also.

When the understanding refers to no determinate intuition, but only to sensible intuitions in general, its immediate object is their possibility also in general, subject to the conditions of the object considered in general, and to those of every intelligence; among which, the principle of contradiction holds a primary place.

[CHAPTER XXI.]

DETERMINATE AND INDETERMINATE IDEAS.

128. We must, under pain of falling into sensism, by limiting the understanding to the perception and combination of objects presented by sensibility, admit other than intellectual acts referable to sensible objects in general. And what, in this case, is the object of the intellectual act, is a question as difficult as it is interesting.

129. The pure understanding can exercise its functions either upon determinate or indeterminate ideas; that is, upon ideas which contain something determinate, something realizable in a being, that is or may be offered to our perception, or upon ideas which represent general relations, without application to any object. Care should be taken not to confound general with indeterminate, or particular with determinate ideas. Every intermediate idea is a general idea, but not vice versa. The idea of being is general and indeterminate; that of intelligence is general but determinate. The particular idea refers to an individual; the determinate to a property, and it does not cease to be determinate although we abstract all relation in it to an existing individual. This distinction opens the way to considerations of the highest importance.

130. When the understanding proceeds by indeterminate conceptions, its principal object seems to be being in its greatest universality. This is the radical and fundamental idea, round which all other ideas are grouped. From the idea of being springs the principle of contradiction, with its infinite applications to every class of objects; from it also flow the ideas of substance and accidents, of cause and effect, of the necessary and the contingent, and every thing contained in the science of ontology, called for this very reason ontology, or the science of being.

131. There is nothing in those conceptions which express the general relations of all beings, to characterize them until they quit their purely metaphysical sphere and descend into the field of reality.

In order to be able to conceive of a real being, we require it to be presented to us with some property. Being and not-being, substance and accidents, cause and effect, are, when combined with something positive, highly fruitful ideas; but taken in general, with nothing determinate assigned to them, they do not offer us any existing, or even possible object.

132. The idea of being presents us that of a thing in the abstract; but if we would conceive of this as existing or as possible, we must imagine this thing to be something with characteristic properties. Whenever we hear an existing thing spoken of, we instinctively ask what it is, and what is its nature. God is essentially being, is infinite being; but nothing would be represented to our mind were we to conceive of him only as of being, and not also as intelligent, active, free being endowed with all the other perfections of his infinite essence.

133. The idea of substance offers us that of a permanent being, which does not, like a modification, inhere in another. This idea, taken in its generality without other determination than that added to the idea of being, by that of subsistence, offers us nothing real or realizable. Permanence in general, subsistence by itself, non-inherence in a subject, do not suffice to enable a substance to exist or to be possible; some characteristic mark, some attribute is also needed, as corporeal, intelligent, free, or any other you please, to determine the general idea of substance.

134. The same may be said of the idea of cause, or productive activity. An active thing, in general, offers us nothing either real or possible. In order to conceive an existing activity, we must refer to a determinate activity; the idea of acting, or of being able to act, in general, does not suffice; we must represent it to ourselves, as exercising itself in one way or another, referring to determinate objects, producing, not beings in general, but beings having their own characteristic attributes. True, we do not need to know what these attributes are; but we do need to know that they exist with their determinateness.

The most universal cause conceivable is God, the first and infinite cause; and although we do not conceive of him as of cause in the abstract, regarding the simple idea of productive activity, but we attach to the general idea of cause the ideas of free will and intelligence. When we say that God is omnipotent, we assign an infinite sphere to his power; we do not know the characteristic attributes of all the beings which can be created by this infinite activity; but we are certain that every existing or possible being must have a determinate nature; and we do not conceive it to be possible for a being to be produced, which, without any determination, would be nothing but being.

135. We do not meet this determination, indispensable as it is to us, if we would conceive of the existence or possibility of a being, in indeterminate ideas, but must take it from experience; wherefore, if our understanding were limited to the combination of those relations offered in indeterminate conceptions, it would be condemned to a perfectly sterile science. We have already seen (Chap. XIV.) that the absolute non-communication of the real with the ideal order is impossible if the intelligible order be not deprived of all consciousness of itself. It is not enough to know, that such a communication exists, but we must ascertain in what points it is verified, and how far it extends.

136. Before passing to this investigation, we would observe, that the doctrine explained in this chapter is not to be confounded with that of the fourteenth chapter. There, it was shown that general ideas of themselves alone, have only a purely hypothetical value, and lead to nothing because they are not combined with any thing positive, furnished by experience; here, we have proved that indeterminate ideas of being, substance, and cause, do not of themselves alone suffice to enable us to conceive of any thing either existing or possible, if they be not accompanied by some determinate idea, which gives a character to the general ideas. There, a hypothetical value, with respect to their existence, was allotted to general ideas: here, we affirm it to be necessary for these ideas to be accompanied by some property that shall render them capable of constituting an essence, at least in the possible order. These are very different things, and must not be confounded; hence the importance of not forgetting the distinction between general and indeterminate, and between particular and determinate ideas.

[CHAPTER XXII.]

LIMITS OF OUR INTUITION.

137. Could we assign limits to the field of experience, and determine exactly how much they inclose, we could also determine the characteristics by which a being may be presented to us as existing or as possible.

138. Passive sensibility, active sensibility, understanding, and will, are, if we be not mistaken, all that our understanding contains; and this is why we cannot conceive of any attribute characteristic of being, except these four. Let us examine these, each in its turn, and with the care required by the importance of the results which will follow this demarcation.

139. By passive sensibility we understand the form under which bodies are presented. As we have already explained it in several places, this form is reducible to figured or bounded extension.

It cannot be denied that this attribute contains a true determination, as there is nothing more determinate than objects presented to our senses, with extension, and figure, and other properties annexed to these fundamental attributes. Motion and impenetrability are determinations which accompany extension, or rather they are relations of extension. To us, motion is the change of the situations of a body in space, or the alteration in the positions of the extension of a body, with respect to the extension of space. Impenetrability is the reciprocal exclusion of two extensions. The idea of solid and liquid, of hard and soft, and other similar ideas, express relations of the extension of a body to their admission, with greater or less resistance, of the extension of another in one and the same place.

Questions upon the nature of extension have no place here. Extension is, so far as we are concerned, a determinate object, presented to us in the clearest intuition. The attribute of passive sensibility has ever been regarded as one of the most characteristic determinations; and this is why it has been made to enter as a fundamental classification in the scale of beings. The distinctions of corporeal and incorporeal, of material and immaterial, of sensible and insensible, are of as frequent use in ordinary language as in that of the schools; and it is obvious that the words, corporeal, material, and sensible, although not perfectly synonymous under some aspects, are usually taken to be such, in so far as they express a kind of beings, whose characteristic properties are those forms under which they are offered to our senses.

140. Active sensibility is the faculty of feeling; and is to us an object of immediate experience, since we have it within us. From the clear presence of sensitive acts, we may easily conceive what feeling is in other subjects than ourselves. We have no consciousness of what passes in another subject when it sees; but we know what it is to see; it is in others the same as in ourselves. In our own consciousness that of others is portrayed. We well know what is spoken of, when we hear a sensitive being mentioned; and this too by a perfectly determinate, not by a vague idea. If the question be raised, whether other senses are possible, the idea of a being endowed with them, loses a certain amount of its determinateness: our understanding has no intuition of what it would be; it discourses upon the reality or possibility by means of general conceptions.

141. Understanding, or the force of conceiving and combining, independently of the sensible order, is another of the data furnished by our own experience. As this is a fact of consciousness, we know it by intuition, not by abstract ideas; it is the exercise of an activity which we feel within ourselves; it is the me which we ourselves are. This activity, by reason of its very union, its identity with the subject perceiving it, is present to us in so intimate a manner that we find no difficulty in perceiving it.

The idea of understanding is intuitive to us, not indeterminate, since it presents an object which is immediately given to our perception in our soul itself. When we speak of understanding, we fix our views upon what passes within ourselves, and we see greater or less perfection in the scale of intelligent beings portrayed in the gradation of the cognitions which we experience within ourselves; and when we would conceive of a far higher understanding, we enlarge and perfect the type we have discovered within ourselves; just as we represent to ourselves greater, more perfect, and more beautiful sensible objects, than those we see, without quitting the sphere of sensibility, but making use of the elements it furnishes to us, and enlarging and embellishing them so as to attain to that ideal type already conceived of in our imagination.

142. The will, although an inseparable companion of the understanding, and even necessary to its existence, is nevertheless a very different faculty from it; for the will offers to our intuition a series of phenomena very unlike the phenomena of the understanding. To understand is not to will; a thing may be known, and yet not willed. One and the same act of the understanding may unite at various times, or in diverse subjects, very different if not contradictory acts of the will; to will and to not will; or inclination and aversion.

The cognition of that series of phenomena called acts of the will, is not a general but a particular, not an abstract but an intuitive, cognition. What necessity is there of abstraction or discursion to ascertain what we will or do not will, what we love or what we abhor? This cognition is intuitive, so far as the acts of our own will are concerned; and although we have no immediate intuition of what the will of others is, we know perfectly well what passes in them, from seeing it in some degree manifested by what we ourselves experience. When we hear the acts of another's will spoken of, have we, by chance, any difficulty in conceiving the object in question? Are we obliged to proceed discursively by abstract ideas? Certainly not! The same occurs in others as in ourselves. When they will, or do not will, they experience just what we ourselves experience when we will or do not will. The consciousness of our will is the image of all others existing or possible. We conceive that will to be more or less perfect, which unites in a higher or lower degree the actual or possible perfections of our own: and if we would conceive a will of infinite perfection, we must elevate to an infinite degree the actual or possible perfection which we discover in the finite will.

143. When the Sacred Text tells us that man is created to the image and likeness of God, it teaches us a truth highly luminous, whether considered in a purely philosophical or in a supernatural aspect. We discover in our soul, in this image of infinite intelligence, not only a multitude of general ideas which carry us beyond the limits of sensibility, but also an admirable representation wherein we contemplate, as in a mirror, every thing that passes in that infinite sea which cannot be known by immediate intuition so long as we remain in this life. This representation is imperfect, is enigmatical; but it is a true representation: in its minutest particles, infinitely increased, we may contemplate the infinite; its feeblest brilliance reflects back to us the splendor of infinity. The slight spark struck from the flint may lead the imagination to that ocean of fire, discovered by astronomers in the orb of day.

[CHAPTER XXIII.]

OF THE NECESSITY INVOLVED IN IDEAS.

144. In all ideas, even in those that relate to contingent facts, there is something of the necessary, something from which science may spring, but something which cannot emanate from experience, however multiplied we suppose it. Every induction resulting from experience is confined to a limited number of facts,—a number, which, even if augmented by all the experience of all men of all ages, would still remain infinitely below universality, which extends to all that is possible.

Moreover, however little we reflect upon the certainty of the truths intimately connected with experience, such as are arithmetical and geometrical truths, we cannot fail to perceive that the confidence with which we build upon them is not founded upon induction, but that we assent to them independently of any particular fact, and consider their truth as absolutely necessary, although we cannot verify it by the touchstone of experience.

145. The verification of ideas by facts is in many cases impossible, because the weakness of our perception and of our senses, and the coarseness of the instruments we use, fail to render us certain that the facts correspond exactly to the ideas. It is sometimes absolutely impossible to establish this proof, since geometrical truth supposes conditions such as cannot be realized in practice.

146. Let us apply these observations to the simplest truths of geometry. Certainly no one will doubt the solidity of the proof called superposition: that is to say, if one of two lines, or surfaces, be placed upon the other, and they exactly correspond, they will be equal. This truth cannot depend upon experience: first, because experience is limited to a certain number of cases, whereas the proposition is general. To say that one serves for all is to say that there is a general principal, independent of experience, since, without recognizing an intrinsic necessity in this truth, the universal could in no other way be deduced from the particular. Secondly, because even where experience avails, it is impossible for us to make it exact, since superposition made in the most delicate manner imaginable, can never attain to geometrical exactness, which repudiates the minutest difference in any point.

It is an elementary theorem, that the three angles of a triangle are equal to two right angles. This truth does not rest upon experience: first, because the universal cannot be deduced from the particular; secondly, because, however delicate be the instruments for measuring angles, they cannot measure them with geometrical exactness; thirdly, because geometry supposes conditions which we cannot realize in practice; lines have no thickness, and the vertices of angles are indivisible points.

147. If general principles depended upon experience they would cease to be general, and would be limited to a certain number of cases. Neither would their enunciation be absolute, even for the cases already observed; for it would of necessity be reduced to what had been observed, that is to say, to a little more or less, but never be perfect exactness. Consequently we could not assert that the three angles of every triangle are equal to two right angles; all that we could say would be, that so far as our experience goes, we have observed that in all triangles the three angles are very nearly equal to two right angles.

This would obviously destroy all necessary truths; and even mathematical truths would be no more certain than the reports of adepts in any profession who recount to us their observations concerning their respective objects.

148. There can be no science without necessary truths; and even the cognition of contingent truths would become exceedingly difficult without them. How do we collect the facts furnished by observation, and adjust them? Is it not by applying certain general truths to them, as, for example, those of numeration? Otherwise we could have no perfect confidence in them, nor in the results of observation.

149. Human reason cannot live, if it abandon this treasure of necessary truths which constitute its common patrimony. Individual reason could take no more than a few short steps, overwhelmed as it constantly would be with the mass of observations; distracted unceasingly by the verifications to which it would always have to recur; in want of some light to serve for all objects; and prohibited ever from simplifying, by uniting the rays of science in a common centre.

General reason would also cease to be, and men would no longer understand each other: every one would be confined to his own experience: and since there would be in the experiences of all men, nothing necessary, nothing to connect them, there would be no unity in them all together: all the sciences would be a field of confusion, to which all restoration of order would be utterly impossible. No language could have been formed; or even if formed could be preserved. We meet in the simplest enunciations of language, as well as in the complication of a long discourse, an abundance of general and necessary truths, which serve as the woof for the weaving-in of contingent truths.

150. To inquire, therefore, if there are necessary truths, is to inquire, if individual, if general reason exists; if what we call reason, and discover in all men, really exists, or is but a fantastical illusion. This reason does exist: to deny it is to deny ourselves: not to wish to admit it, is to reject the testimony of our consciousness, which assures us that it is in the depth of our soul; it is to make impotent efforts to destroy a conviction irresistibly imposed by nature.

151. And here I would remark that this community of reason among all men of all ages and of all climes; this admirable unity, discoverable in the midst of so much variety; this fundamental accord which neither the diversity nor the contradiction of views can destroy, evidently proves that all human souls have one common origin; that thought is not a work of chance; that, besides human intelligences, there is another which serves as their support, illuminates them, and has, from the first moment of their existence, endowed them with all the faculties needed to perceive, and to know what they perceived. The admirable order which reigns throughout the material world, the concert, the unity of plan discoverable in it, are not a more conclusive proof of the existence of God, than are the order, the concert, the unity, offered by reason in its assent to necessary truths.

For our own part, we ingenuously confess, that we can discover no more solid, more conclusive, or more clear proof of the existence of God, than that deduced from the world of intelligences. Beyond this it has another advantage, which is, that it takes for its point of departure the act most immediate to us, the consciousness of our own acts. It is true, the proof best adapted to the capacity of ordinary men, is the one founded on the admirable order reigning over the corporeal world: but this is because they are unaccustomed to meditate upon insensible objects, upon what passes within themselves; wherefore it is that they abound more in direct cognitions than in power of reflection.

The atheist asks how we can be certain of the existence of God, and demands an apparition of the divinity: very well, this apparition exists, not without, but within us: and although it may be pardonable for men of little reflection not to perceive it, most certainly it is not pardonable for those who pretend to be adepts in metaphysical science, not even to endeavor to discover it. The system of Malebranche, which makes men see every thing in God, cannot be sustained, but it shows a very profound thinker.

[CHAPTER XXIV.]

EXISTENCE OF UNIVERSAL REASON.

152. General truths have some relation to particular truths; for since they are not a vain illusion, they must of necessity be connected with some object either existing or possible. Whatever exists is particular; not even possible being can be conceived of, if it be not, so to speak, particularized in the regions of possibility. God himself, being by essence, is not a being in abstract, but an infinite reality. In him, the general idea of the plenitude of being, of all perfection, of infinity, is, so to speak, particularized.

General truths would then be vain illusions did they not refer to something particular either existing or possible. Without this relation, cognition would be a purely subjective phenomenon; science would have no object; knowledge would be had, but there would be nothing known.

The appearance of knowing is never offered to us as a purely subjective fact; that is to say, when we think we know, we think we know something either within or without us, according to the matters which occupy us. Supposing, then, the phenomenon of cognition to be purely subjective, and to become objective for itself, we should have what would constantly lead us into error; for the human reason would be infected with a radical vice, which would oblige it to view these phenomena as means of perceiving the truth, whereas they are only eternal sources of deception.

153. There may arise a doubt in this correspondence of general with particular truth, as to which is the principle; that is, whether general truth is truth by means of particular truths, or the contrary. "All the diameters of a circle are equal;" this is a general truth. If we suppose a circle to exist, all its diameters will be equal. We have already seen that the certainty of the general truth neither does nor can reach us through the particular truth; but neither, on the other hand, does the particular stand in need of the general; so that it seems, that even when we abstract all intelligence, capable of perceiving this general truth, the existing circle will not cease to have all its diameters equal.

154. Moreover, if the truth fail in one single instance, it cannot be general; but the particular may be true although it fail in general. The equality of the diameters of an existing circle is, then, a condition necessary to the general truth; but the general truth is not necessary to the equality of the diameters. It is true in general that all diameters are equal, since this is verified in all either existing or possible, and the general truth is only the expression of this verification; but yet it does not appear that the diameters, in any one particular case, are equal by reason of the general truth. It is true that one particular whole is greater than one of its parts, although considered in itself, abstracted from all general truth; but it would not be true that the whole is greater than one of its parts, if in any one particular whole, the axiom should fail.

155. It would seem that from these observations we could infer that the truth of principles depends upon the truth of facts, and not vice versa. Nevertheless, if we reflect more upon this matter, we shall discover that truth is not based upon particular facts, but upon something superior to them.

I. We cannot from a particular fact infer a universal truth; but from universal truth we can infer the truth of all particular existing or possible facts. The reason why this consequence is legitimate is found in the necessary connection of the predicate and subject; and this necessity cannot be discovered in particular facts of their own nature contingent.

II. Neither can the reason of this necessity be found in the simple proposition enunciating it, since this establishes nothing, but only expresses. The enunciation is true, because it expresses the truth; but the existence of the truth does not depend upon its enunciation.

III. Nor can it depend upon our ideas; for these are not productive of things; all imaginable perceptions cannot change one iota of reality. The idea may express a thing, but does not make it. The relation of ideas with each other, in so far avails as it expresses the relation of objects; if for one moment we permit ourselves to doubt this correspondence, our reason becomes reduced to utter impotence, to a vain illusion of that which ought to be of no account. The properties of the triangle are contained in the idea we have of it; but if this idea were purely subjective, if it had no exact or approximate relation to any real or possible object, it and all that is built upon it, would be mere phenomena of our mind, would signify absolutely nothing, and would have no more weight than the ravings of a madman.

IV. The reason of necessary truths can in nowise be discovered in our understanding; every one perceives them, without thinking of others or even of himself. Truth existed before any individual; and when we shall have disappeared, it will continue the same, it will lose nothing.

V. All men, although they neither do nor can agree, perceive certain necessary truths; all individual intelligences, therefore, have drunk at some common fountain; therefore universal reason exists.

[CHAPTER XXV.]

IN WHAT DOES UNIVERSAL REASON CONSIST?

156. What is universal reason? If we consider it as a simple idea, as an abstraction from individual reason, as something separate from them, but not real, we strike upon the very rock we try to shun. We endeavor to assign a cause of the unity of human reason; and appeal to universal reason; and then to explain in what universal reason consists, we recur to an abstraction from individual reason. Evidently, this is a vicious circle; we place the cause of a fact so fruitful in an abstraction, in a generalization of the very thing we have to explain; we assign to a great effect a cause totally insufficient, which has no existence out of our understanding, and which only grows out of the very effect whose origin we are investigating.

157. A real fact must have a real principle; a universal phenomenon must have a universal cause; a phenomenon independent of all finite intelligence must spring from some cause independent of all finite intelligence. There is, then, a universal reason, the origin of all finite reason, the source of all truth, the light of all intelligences, the bond of all beings. There is, then, above all phenomena, above all finite individuals, a being, in which is found the reason of all beings, a great unity, in which is found the bond of all order, and of all the community of other beings.

The unity, therefore, of all human reason affords a complete demonstration of the existence of God. The universal reason is; but universal reason is an unmeaning word, unless it denote an intelligent, active being, a being by essence, the producer of all beings, of all intelligences, the cause of all, and the light of all.

158. Impersonal reason, of which some philosophers speak, is an unmeaning word. Either there exists a reason distinct from ours, or there does not: if it does exist, it is not impersonal; if it does not exist, it is impossible to explain the community of human reason: this community would be to us a phenomenon, which we might call impersonal reason, or any thing else we pleased, without it therefore being possible for us to assign it any origin: it would be an effect without a cause; a fact without a sufficient reason.

159. The understanding extends to a world of possibilities, and there discovers a connection of necessary relations, some of dependence, others of contradiction: but if there were no reality whereon to found the possibility, this would be an absurdity; if nothing existed, nothing would be possible.

Upon nothing, nothing can be founded; consequently, not even possibility. The connection of necessary relations which we discover in possible beings, must have a primitive type to which they refer: but in nothing there are no types.

160. The assemblage of human understandings cannot establish possibility. No one of them considered isolately is necessary to general truth; and all together cannot have what no one of them has. We conceive necessary truth, absolutely abstracted from the human understanding: individual understandings appear and disappear, but work no change in the relations of possible beings: on the contrary, the understanding needs, in order to exercise its functions, a collection of pre-existing truths, and without them it cannot work.

What any one individual understanding requires, all require. Their union does not increase the strength of each one: since this union is nothing more than an assemblage formed in our mind, and may not correspond to any thing in reality except the individual understandings, and their respective strength.

161. Necessary truths, therefore, exist before human reason; but their pre-existence is an unmeaning word, if they be not referred to a being, the origin of all reality, and the foundation of all possibility. There is then no impersonal reason properly so called; there is a community of reason in so far as one and the same light illumines all finite intelligences; God the creator of them all.

[CHAPTER XXVI.]

REMARKS ON THE REAL FOUNDATION OF PURE POSSIBILITY.

162. Since the argument proving the necessity of a being in which is laid the foundation of all the relations in the possible order, is one of the most transcendental in all metaphysics, and at the same time one of the most difficult to be perfectly understood, we judge it advisable to enlarge somewhat upon the considerations thrown out in the preceding chapter.

An example, in which we undertake to establish the possibility of things, independently of a being in which is found the reason of all, will serve our purpose better than abstract reflections.

163. "Two circles of equal diameters are equal." This proposition is evidently true. Let us analyze its meaning. The proposition refers to the possible order, and abstracts absolutely the existence of the circles and of the diameters. No case is excepted; all are comprised in the proposition.

164. Neither does the truth refer to our mode of understanding; but on the contrary, we conceive it as independent of our thought. Were we asked, what would become of this truth were we not to exist, we should without hesitation reply that it would be the same, that it acquired nothing by our existence, that it would lose nothing by our extinction. If we believed this truth to depend in any way upon us, it would cease to be what it is, it would no longer be a necessary but a contingent truth.

165. Nor is the corporeal world indispensable to the truth and necessity of the proposition: on the contrary, if we suppose no body to exist, the proposition would lose none of its truth, necessity, or universality.

166. What would happen, if, withdrawing all bodies, all sensible representations, and even all intelligences, we should imagine absolute and universal nothing? We see the truth of the proposition even on this supposition; for it is impossible for us to hold it to be false. On every supposition, our understanding sees a connection which it cannot destroy: the condition once established, the result will infallibly follow.

167. An absolutely necessary connection, founded neither on us, nor on the external world, which exists before any thing we can imagine, and subsists after we have annihilated all by an effort of our understanding, must be based upon something, it cannot have nothing for its origin: to say this, would be to assert a necessary fact without a sufficient reason.

168. It is true that in the proposition now before us, nothing real is affirmed; but if we reflect carefully, we find even here the greatest difficulty for those who deny a real foundation to pure possibility. What is remarkable in this phenomenon, is precisely this, that our understanding feels itself forced to give its assent to a proposition which affirms an absolutely necessary connection without any relation to an existing object. It is conceivable that an intelligence affected by other beings may know their nature and relations; but it is not so easy of comprehension how it can discover their nature and relations in an absolutely necessary manner, when it abstracts all existence, when the ground upon which the eyes of the understanding are fixed, is the abyss of nothing.

169. We deceive ourselves when we imagine it possible to abstract all existence. Even when we suppose our mind to have lost sight of every thing, a very easy supposition, granting that we find in our consciousness the contingency of our being, the understanding still perceives a possible order, and imagines it to be all occupied with pure possibility, independent of a being on which it is based. We repeat, that this is an illusion, which disappears so soon as we reflect upon it. In pure nothing, nothing is possible; there are no relations, no connections of any kind; in nothing there are no combinations, it is a ground upon which nothing can be pictured.

170. The objectivity of our ideas and the perception of necessary relations in a possible order, reveal a communication of our understanding with a being on which is founded all possibility. This possibility can be explained on no supposition except that which makes the communication consist in the action of God giving to our mind faculties perceptive of the necessary relation of certain ideas, based upon necessary being, and representative of his infinite essence.

171. Without this communication the order of pure possibility means nothing: none of the combinations referable to it contain any truth: and this ruins all science. There can be no necessary relations if there be no necessity upon which they are based, and where they are represented; if this condition be wanting, all cognitions must refer to something actually existing; they are even limited to what appears, to what affects us, and they cannot affirm any thing beyond the actual order. Science, in this supposition, is unworthy of the name; it is nothing but a collection of facts, gathered together in the field of experience; we cannot say: "This will be, or will not be; this may be, or may not be;" we are necessarily limited to what is; or, rather, we ought to confine ourselves to that which affects us by simple appearances, and never be able to rise above the sphere of individual phenomena.

[CHAPTER XXVII.]

INDIVIDUAL AND INTELLECTUAL PHENOMENA EXPLAINED BY THE UNIVERSAL SUBSISTING REASON.

172. Starting from the phenomena observable in individual reason, we have arrived at universal reason. Let us, so to speak, make the counterproof; taking this universal subsisting reason, let us see if individual reason in itself and in its phenomena can be explained by it.

I. What are necessary truths? They are the relations of beings, such as they are represented in the being which contains the plenitude of being. These necessary truths, then, stand in need of no individual finite reason; their reason is found in an infinite being.

II. The essence of all beings, abstracted from all particular beings, is something real, not in itself, and separately, but in the being which contains the plenitude of every thing.

III. On this supposition science is not full of empty words, nor of mere creations of our reason, but of necessary relations represented in a necessary being, and known by it from all eternity.

IV. Science is possible; there is some necessity in contingent objects; their destruction does not destroy the eternal types of all being, the only object of science.

V. All individual reason, sprung from the same source, participates in one same light, lives one same life, has one and the same patrimony, is indivisible in the creative principle, but divisible in creatures. The unity, then, or rather the uniformity or community of human reason is possible, is necessary.

VI. The reason, then, of all men is united by the infinite intelligence: God then is in us; and the most profound philosophical truth is contained in these words of the Apostle: "In ipso vivimus, movemur, et sumus."

VII. All philosophy, therefore, which seeks to explain reason, by isolating it, considers only particular phenomena unconnected by a general bond, pretends to construct the magnificent fabric of our reason upon particular facts alone, but does not appeal to a common origin, to one source of light whence all lights have sprung, is a false philosophy, is superficial, at war with theory, and in contradiction with facts. When we reflect upon this, we can but pity Locke, and still more Condillac, and their explanations of human reason by sensations alone.

VIII. Thus we understand why we cannot give the reason of many things; we see them; they are thus: they are necessary; more we cannot say. A triangle is not a circle: what reason can we assign for this? None! It is so; this is all. But why? Because there does actually exist an immediate necessity in the relation represented in the infinite being, which is truth by essence. The same infinite intelligence sees no greater reason of itself, than in itself. It finds every thing, and the relations of all things in the plenitude of its being; but beyond them is nothing. He gave to individual reason, when creating it, an intuition of these relations: no discursion proves them; we see them; this is all.

IX. Some even who admit the subjective value of ideas, either doubting or denying their objectivity, lose sight of this fact. They seek an argument, where there is need only of a vision; they demand degrees where there are none. When human reason sees certain truths, it cannot go farther and doubt of them. It is subject to a primitive law of its nature, which it cannot abstract without ceasing to be what it is. By the very act of seeing the object it is sure of it; the difference between subjectivity and objectivity falls within the space of inferences, but not within that of immediate reason, or the understanding of necessary truths.

173. We leave it to the reader's judgment whether the preceding explanation is more satisfactory than that by impersonal reason; the theory we have attempted to expound has been held by all the most eminent metaphysicians. With God, all is clear; without God, all is a chaos. This is true in the order of facts, and not less so in the order of ideas. Our perception is also a fact; our ideas likewise are facts; over all presides an admirable order; a chain which cannot be destroyed unites all; but neither this order nor this chain depends upon this. The word reason has a profound meaning, for it refers to the infinite intelligence. What is true for the reason of one man cannot be false for the reason of another; there are, independently of all communication among human minds, and of all intuition, truths necessary for all. We must, if we would explain this unity, rise above ourselves, must elevate ourselves to that great unity in which every thing originates, and to which every thing tends.

174. This point of view is high, but it is the only one; if we depart from it we can see nothing, but are forced to use unmeaning words. Sublime and consoling thought! Although man disputes upon God, and perhaps denies him, he has God in his understanding, in his ideas, in all that he is, in all that he thinks; the power of perception communicates God to him; objective truth is founded on God; he cannot affirm a single truth without affirming a thing represented in God. This intimate communication of the finite with the infinite, is one of the most certain truths of metaphysics. Although ideological investigations should produce no other result than the discovery of so important a truth, we ought to consider the time spent in them well improved.

[CHAPTER XXVIII.]

OBSERVATIONS ON THE RELATION OF LANGUAGE TO IDEAS.

175. The relation between thought and language is one of the most important ideological phenomena. When we speak we think; and when we think we speak with an internal language. The understanding needs speech as a kind of guiding thread in the labyrinth of ideas.

176. The connection of ideas by a sign seems necessary. The most universal and most convenient of these signs is language; but we must not forget that it is an arbitrary sign, as is proved by the variety of words used in different languages to express the same idea.

177. The phenomenon of the relation of ideas to language originates in the necessity of perpetuating ideas by determinate signs; and the importance of speech results from its being the most general, most convenient, and most flexible sign. And hence it is that when these circumstances can be united in another sign, the same object is attained. Physically speaking, written language is very different from language spoken; nevertheless, in very many cases it answers equally well.

178. The internal language is, sometimes, rather a reflection in which the idea is enlarged and developed, than an expression of it. True, we do not ordinarily think without speaking inwardly; but as we have already observed, speech is an arbitrary sign, and consequently we cannot establish a perfectly exact parallel between ideas and the internal language.

179. We think with instantaneousness, which defies the succession of words, however rapid we may suppose them to be. It is true that the internal language is far more rapid than the external; but it always involves succession, and requires a greater or less time, according to the words to be spoken.

This observation is important, lest we too greatly exaggerate the relation of ideas to speech. Language is certainly a wonderful channel for the communication of ideas, and a powerful auxiliary of our understanding; but we can, without ignoring these qualities, take care to avoid that exaggeration which seems to pronounce all thought impossible, if some word thought does not correspond to it.

180. We experience often enough the instantaneous occurrence of a multitude of ideas, which we afterwards develop in our discourse. We see this in those quick and lively replies excited by a word, or a gesture, which contradicts our opinions or wounds our feelings. In replying, it is impossible for us to speak inwardly, since the instantaneousness with which we reply forbids it. How often, in listening to an argument, do we instantly detect a fault, which we could not explain with words without a long discourse? How often, in proposing a difficulty to ourselves, do we catch its solution in an instant, although we could not possibly explain it without many words? How often do we at the very first glance discover the flaw in a proof, the force of an argument, or the ease with which it can be retorted upon the proposer of it, and all this without occupying a moiety of the intervals necessary to either external or internal locution? Thus it happens that the sudden thought is not unfrequently expressed by a single gesture, a glance of the eye, a nod of the head, a yes, or a no, an exclamation, or any other similar sign; all far more rapid than it is possible for the words expressive of our thought to be.

181. Let us illustrate this observation by a few examples. Some one says: "All men are naturally equal." The sense of this proposition cannot be known until the word equal is pronounced. How, then, is it that an enlightened and judicious man, will, by an instinctive impulse, answer no, will catch the word at the moment, and refute the empty boast of the declaimer with a flow of reasons? Until after the word, naturally the understanding remained in suspense; there was nothing to show the meaning of the proposition, since instead of equal, might have been said weak, mortal, inconstant, or any other such word; but so soon as the word equal is pronounced, the understanding says no, without having had the time to use an internal or external locution. The exact parallel which some suppose to exist between ideas and speech is, therefore, impossible; and they who defend it are guilty of an exaggeration incompatible with experience.

Another asserts, "justice to have no bounds but the limit of power." All who have any idea of morality, at once answer no: do they, forsooth, need an inward locution? True, in order to explain what is expressed by this no, and upon what it is based, many words are required, and that to reflect upon the proposition one must speak in inwardly; but this is all independent of that intellectual act, signified by the no, and which would have been still more briefly expressed had it been possible.

Another yet may say: "If this fact be attested by the senses, it will be true; and if it be true, it will be attested by the senses." The hearer assents to the former part, but rests in suspense as to the latter part until the word attest is pronounced. Then an instantaneous no leaps from his lips, or is expressed by a negative gesture. Does any interior locution precede? None, for none is possible. The following would be the words expressive of this act: "It is not true that every fact must be attested by the senses; since many facts are true, which do not belong to the sphere of sensibility." Let us examine whether or not these words are compatible with the instantaneousness of the no.

182. It will, perhaps, be objected, that the negation is one thing, and the reason of the negation another: that the simple no suffices for the former, and that it is only for the latter that more words are needed. But this is an equivocation. When the no was said, it was said for a reason, and this reason was the sight of the inconsequence then expressed by the words. Otherwise it would be necessary to admit the negative to be a blind judgment, and given without a reason. This being so, this reason founded upon the judgment, although expressed in the most laconical mode possible, would require some words, to form which, either interiorly or exteriorly, there has been no time. There is a question of calculation. He who hears the proposition cannot know the meaning of it, until the word attest is pronounced, and the sentence brought to a full stop. Before reaching the word attest, the sense of the proposition was unknown; it was not possible to form any judgment, since instead of saying, "If it be true the senses will attest it," he might have said, "If it be true the senses will not belie it."

We have spoken of the full stop, in order to show the instantaneousness of the perception and of the judgment, which proves that the understanding does not determine until the last moment. But let us suppose the same word attest to have been used indeed, but instead of a full stop, to have been followed by these other words, "if this fact falls under their jurisdiction." The words are the same, and yet they do not provoke a negative judgment; and why? Simply because the speaker continued. If he had ceased speaking, or had used an inflection of voice indicative of a period, the no would have risen like a flash. A comma or a period in writing, produce the same effect as a pause or an inflection of the voice in speaking. When we see these signs, we judge instantaneously, with a velocity incomparably greater than any internal or external locution.

It would be easy to multiply examples showing the superiority of thought to speech, so far as rapidity is concerned; but those already adduced seem to us sufficient to prove that there is some exaggeration in saying that "man before speaking his thought, thinks his words," if it be understood that all thought is impossible without a word thought.

[CHAPTER XXIX.]

ORIGIN AND CHARACTER OF THE RELATION BETWEEN LANGUAGE AND IDEAS.

183. Many ideas seem to be like sensations and sentiments; simple facts, incapable of decomposition, for which reason we cannot explain them with words. Words illustrate ideas; but do they not sometimes also confuse them? When we speak of an idea, we reflect upon it, and I have already remarked[11] that the reflective force of our perceptive ideas is much inferior to their direct force.

184. We have sometimes thought that we do, perhaps, know things which we imagine we do not know, and that we are ignorant of things we think we know. It is certain that disputes have been had in all schools of philosophy upon many ideas, without attaining any satisfactory result; and yet these ideas ought to be sufficiently clear to our mind, since we all use them every day without any equivocation. Philosophers have not, as yet, been able to agree upon the ideas of space and time, but the most ignorant men, nevertheless, make use of these words, and whenever the necessity occurs, apply them with exactness. This seems to prove that the difficulty is not in the idea but in its explanation.

185. It has been remarked that there is great truth and exactness in ordinary language, so much so, that the careful observer is astonished at the recondite wisdom hidden in a language; to see how great, how various, and how delicate are the gradations into which the sense of words is distributed. This is not the fruit of reflection; it is the work of reason operating directly, and consequently making use of ideas without reflecting upon them.

186. In ideological investigations some idea of the idea is sought, and it is not noted that if this be necessary to science, another idea of the other idea may be exacted, and that thus an infinite process may be given. It ought to be borne in mind that in treating of simple facts, as well external as internal, no other explanation of them can be demanded than an exposition.

187. Idea-images are a font of error, and probably all ideas explicable by words are not less so. An idea-image induces the belief that there are in our mind no ideas but sensible representations, and the supposition that every idea can be expressed by words, makes us imagine that to be composite which is simple, and attribute to the substance what belongs to the form.

188. A composite idea seems to be a union, or rather a connected series of ideas, which are either excited simultaneously, or follow each other with great rapidity. Our understanding requires words to bind this collection, to retain the thread which connects them; and hence it is, that when the idea is simple, language is not indispensable. It is said that speech is necessary in order to think, it might sometimes be said with more propriety, that it is necessary in order to recollect.

189. When the object occupying our attention is offered to the sensible intuition, we have no need of speech. We can, when we reflect upon a right line, an angle, a triangle, observe that their imaginary representation is all that we require, and that we do not need to bind these objects together by words. The same thing happens in thinking of unity, or on the numbers two, three, and four, which we easily represent to ourselves sensibly. The necessity for speech begins when the imagination loses the distinct representation of objects, and needs to combine various ideas. Did we not assign to a word the idea of a many-sided polygon, we should be in the greatest confusion, and it would be impossible for us to reason upon it.

190. Since, on the one hand, our perceptive faculties do not create their objects, but are limited to the combining of them; and, on the other hand, our perception is not capable of embracing many at one time, it results that the exercise of our faculties is necessarily successive; the unity of consciousness serving as the bond of union to our perceptions. But consciousness has no other means of knowing what passes within it, than to fix its operations by determinate signs, whence flows the necessity of arbitrary signs, which must be sensible, by reason of the relation uniting our intelligence with the sensitive faculties: and it is to be observed, that for this reason, every sign to which we assign an idea, may be the object of one of the senses. The great number and variety of ideas and their combinations, require an exceedingly variable and flexible sign, and this variety and flexibility require certain characters to simplify it, and thus render its retention in the memory more easy, whence the advantages of language: in the midst of its astonishing variety it lays these characters in radical syllables. The conjugation of a single verb alone offers us a considerable number of very different ideas, the retention of which would be excessively difficult, were they not joined by some tie such as the radical syllable: as in the verb to speak, the syllable speak. We see this by the greater labor the irregular verbs cost us than do the regular verbs when learning a language: and it may be remarked in children also, who blunder on the irregularities. We might compare language to the catalogue of a library, which is the more perfect, the more it unites simplicity with variety, so as to designate exactly the classes of the books and the shelves whereon they are to be found.

191. Succession of ideas and operations; here, then, originates the necessity of a sign by which to connect and recollect them: relation of our understanding with the sensitive faculties, is the reason why the signs must be sensible; variety and simplicity of language constitutes its merit so far as the sign of ideas.[12]

[CHAPTER XXX.]

INNATE IDEAS.

192. Among the adversaries of innate ideas there exist profound differences. The materialists maintain that man has received every thing through the senses, in such a way as to make our understanding nothing more than the product of an organism which has been advancing in perfection, just as a machine acquires, by use, a greater facility and delicacy of movement. They suppose nothing but the faculty of sensation to pre-exist in the mind; or, to speak more correctly, they admit no mind, but only a corporeal being, whose functions naturally produce what is called the intellectual development.

The sensists who do not attribute to matter the faculty of thinking, do not admit innate ideas; they confess the existence of the mind, but concede to it non-sensitive faculties; all that it owns must have come to it through the senses, and it can be nothing else than a transformed sensation.

Innate ideas counted other adversaries who were neither materialists nor sensists: such were the scholastics, who on the one hand defended the principle that there is nothing in the understanding which has not previously been in the senses; but, on the other hand, combated both materialism and sensism. The difference between the scholastics and the friends of innate ideas would not perhaps have been so great as it was supposed to be, had the question been proposed in another manner.

193. The scholastics regarded ideas as accidental forms, in such a way that an understanding with ideas may be compared to a piece of canvas covered with figures. The defenders of innate ideas said; "The figures already exist upon the canvas; to see them we have only to raise the veil which covers them." This explanation is somewhat forced, since it openly contradicts experience, which testifies: first, the necessity of the understanding being excited by sensations; secondly, the intellectual elaboration which we experience in thinking, and which teaches us that there is within us a kind of production of ideas.

"The canvas," say the adversaries of innate ideas, is all white, "and in proof witness the unceasing labor of the artist to cover it with figures." But does their doctrine, forsooth, suppose that nothing exists before experience? Do they admit man to be the simple work of instruction, of education? Do they maintain that our interior world is nothing more than a series of phenomena caused by impressions, and that it would have been other than what it is, had it had other impressions? Most certainly not. They admit: first, an inward activity excited and improved by sensible experience: secondly, the necessity of first principles as well intellectual as moral: thirdly, an interior light, to enable us to see them when presented, and to assent to them by an irresistible necessity. We find the words, "Signatum est super nos lumen vultus tui Domine," cited upon every page of those authors.

194. Saint Thomas says that first principles, as well speculative as practical, must be naturally communicated to us: "Oportet igitur naturaliter nobis esse indita, sicut principia speculabilium, ita et principia operabilium."[13] In another place, inquiring whether the soul knows immaterial things in their eternal reasons, (in rationibus æternis,) he says that the intellectual light which is within us, is nothing else than a certain participated likeness of the uncreated life, in which the eternal reasons are contained: "Ipsum enim lumen intellectuale, quod est in nobis nihil est aliud, quam quædam participata similitudo luminis increati, in quo continentur rationes æternæ."[14]

195. We find it, in these passages, expressly taught that there is within us something besides what we have acquired by experience, in which point the scholastics all agree with the defenders of innate ideas. The difference between them is this: the former do not consider the intellectual light to suffice for knowledge, if the forms or species upon which it may reflect are wanting; the latter distinguish the light from the colors, and them they make originate in the light itself.

196. The question of innate ideas, so warmly contested in the schools of philosophy, would never have presented so great difficulties, had it been stated with proper clearness. To do this it was necessary to classify the inward phenomena called ideas in a corresponding manner, and to determine with accuracy the sense of the word innate.

197. According to what we have already said, we hold that there are in our mind sensible representations; intellectual action upon them, or geometrical ideas; ideas purely intellectual, either intuitive or non-intuitive; and general determinate and indeterminate ideas. I will give examples of these cases that they may the better be understood. A particular triangle is represented in our imagination; here, then, is a sensible representation: intellectual act perceiving the nature of the triangle considered in general; here is a geometrical idea, an idea relating to the sensible order: cognition of one of our acts of understanding or will; here is a pure and intuitive idea: intelligence, will, conceived in general; here is a general determinate idea: substance; here finally is a general indeterminate idea.[15]

198. What is understood by innate? That which is not born, which the mind possesses, not acquired by its own labor, nor by impressions coming from the exterior, but by the immediate gift of the author of its nature; the innate is opposed to the acquired, and to inquire if there are innate ideas is to inquire if we have in our mind ideas, before receiving any impressions or doing any act.

199. It cannot be maintained that sensible representations are innate. Experience testifies that without the impressions of the organs we cannot have representations corresponding to them; that once these are placed in action in a proper manner, we cannot help experiencing them. This is applicable to all sensations, whether they be actual, existing, or only recollected. They who undertake to maintain that sensible representations exist in our soul previously to all organic impressions, also advance an opinion unsustainable either by facts of experience or by arguments a priori.

200. It is to be remarked, that the argument founded upon the impossibility of the body's transmitting impressions to the mind, proves nothing in favor of the opinion we combat. Even were the argument conclusive, the necessity of innate ideas could not thence be inferred, since the physical non-communication of the body and the mind would be saved in the system of occasional causes, and it could at the same time be argued that there are no pre-existing ideas, but that they have been caused in the presence, and on occasion of organic affections.

201. Ideas relative to sensible representations seem to consist, not in forms of the understanding, but in its acts exercised upon these same representations.[16]

To call these ideas innate is to contradict experience, and even to ignore their nature. These acts cannot be performed if the object, which is the sensible representation be wanting; and this does not exist without an impression of the corporeal organs. To call these ideas innate, has then, either no meaning at all, or can mean nothing else than the pre-existence of the intellectual activity, subsequently developed in the presence of sensible intuitions.

202. Neither can those intuitive ideas, not referable to sensibility, such as are those we have when reflecting upon the acts of understanding and will, be innate. What in this case serves as the idea, is the very same act of the understanding or of the will which is presented to our perception in consciousness: to say, then, that these ideas are innate is equivalent to saying that these acts exist before they exist. Even when the perception does not refer to present acts, but to past acts now recollected, the argument retains the same force: for it can have no recollection of them if they have not previously existed, since our acts cannot exist before we have performed them.

203. Hence it may be inferred that no intuitive idea is innate, since intuition supposes an object presented to the faculty of perception.

204. General determinate ideas are those which refer to an intuition: they cannot, therefore, exist before it: and since, on the other hand, intuition is impossible without an act, it follows that these ideas cannot be innate.

205. Last of all remain general indeterminate ideas, that is to say, those which of themselves alone offer to the mind, nothing either existing or possible.[17] If we observe carefully the nature of these ideas, we shall see that they are nothing else than perceptions of one aspect of an object considered under a general reason. It cannot be doubted, that one of the characteristics of intelligence is the perception of these aspects; and it is no less indubitable, that it does not thence follow, that we must imagine these ideas to a kind of forms pre-existing in our mind, and distinct from the acts by which it exercises its perceptive faculty. We do not see what ground there can be for affirming these ideas to be innate, and to have lain hidden in our mind previously to the development of all activity, just like things stowed away in the corners of a museum, closed however to the curiosity of spectators.

206. Instead of abandoning ourselves to similar suppositions, it would seem that we ought to recognize in the mind an innate activity, subject to the laws imposed upon it by its Creator, the infinite intelligence. Even granting ideas to be distinct from perceptive acts, it is not necessary to admit them as pre-existing. True, that in such a case it would be necessary to recognize in the mind a faculty productive of the representative species, from which, however, we should not escape by identifying ideas with perceptions. These last are acts springing, so to speak, from the very bottom of our soul, and which appear and disappear like the flowers of a plant: and thus we must in every way recognize in ourselves a power which in due circumstances will not fail to produce what before did not exist. Without this it is impossible to form any idea of what activity is.

207. Resuming the doctrine thus far delivered upon innate ideas, we can reduce it to a formula in the following manner:

I. There are in us sensitive faculties which are developed by organic impressions, either as cause or occasion.

II. We perceive nothing by the senses not subject to the laws of organism.

III. Internal sensible representations cannot be formed of other elements than those furnished by sensations.

IV. Whatever is said concerning the pre-existence of sensible representations to organic impressions, besides being said without any reason, is in contradiction with experience.

V. Geometrical ideas, or ideas relating to sensible intuitions, are not innate; since they are the acts of the understanding which operates upon materials provided by the sensibility.

VI. Intuitive ideas of the intellectual order are not innate, because they are nothing else than the acts of the understanding or will, presented to our perception in reflex consciousness.

VII. General determinate ideas are not innate, since they are the representation of intuitions, upon which some act has of necessity been performed.

VIII. There is no ground of affirming that general indeterminate ideas, which seem to be acts of the faculty perceptive of objects under a general reason, are innate.

IX. All that there is of innate in our mind is sensitive and intellectual activity; but both to be put into motion, require objects to affect them.

X. The development of this activity begins with organic affections; and although it goes far beyond the sphere of sensibility, it always remains more or less subject to the conditions imposed by the union of the soul and body.

XI. The intellectual activity has a priori conditions totally independent of sensibility, and applicable to all objects, no matter what impressions may have been their cause. The principle of contradiction figures as the first among these conditions.

XII. There is then in our mind something a priori and absolute, which cannot be altered, even although all the impressions we receive from objects be totally varied, nor if all the relations we have with them were to undergo a radical change.

[BOOK FIFTH.]

IDEA OF BEING.

[CHAPTER I.]

IDEA OF BEING.

1. There is in our understanding the idea of being. Independent of sensations, and in an order far superior to them, there exist ideas in our understanding, which extend to, and are a necessary element of all thought. The idea of being, or of ens, holds the first rank among these. When the scholastics said that the object of the understanding was being, "objectum intellectus est ens," they enunciated a profound truth, and pointed out one of the most certain and important of all ideological facts.

2. Being, or ens in se, abstracted from all modification and determination, is, considered in its greatest generality, conceived by our understanding. Whatever may be the origin of this idea, or the mode of its formation in our understanding, certain it is that it exists. It is of continual application, and without it it is almost impossible for us to think. The verb to be, expressive of this idea, is found in every language: in every discourse, even in the simplest, we meet this expression: the learned and the ignorant, alike, continually employ it in the same sense, and with equal facility.

The only difference, as to the use of this idea, between the rustic and the philosopher, is, that the one does, the other does not, reflect upon it: but the direct perception is the same in both, equally clear in all cases. Such a thing is or is not; was or was not; will be or will not be; there is something or nothing; we had or did not have; we shall have or shall not have, are all applications of the idea of being, applications made alike by all persons, without the least shadow of obscurity; all comprehend perfectly well the sense of these words, and the mind consequently has the idea corresponding to them. The difficulty, if any there be, begins with the reflex act, in the perception, not of being, but of the idea of being. So far as the direct act is concerned, the conception is so perfectly clear as to leave nothing to be desired.

3. Experience teaches this, but it can also be proved by conclusive arguments. All philosophers agree that the principle of contradiction is evident of itself to all men, that it needs no application, to understand the sense of the words sufficing; which could not be true did not all men have the idea of being. The principle is, that "it is impossible for a thing to be, and not to be at same time." Here, then, is no question of any thing determinate; neither of body nor of mind, of substance nor of accidents, of infinite nor of finite, but of being, of a thing, whatever it may be, in its greatest generality; of which it is affirmed that it cannot both be and not be at the same time. Had we no idea of being, the principle would mean nothing: contradiction is inconceivable when we have no idea of the contradicting extremes, and here the extremes are being and not-being.

4. The same is seen in another principle, closely resembling, if not identical with, that of contradiction: "every thing either is or is not." Here, also, there is question of being in its greatest indeterminateness, considered only as being, as nothing more. Without the idea of being, the axiom could have no meaning.

5. The principle of Descartes, "I think, therefore I am," also includes the idea of being: "I am." When he undertakes to explain it, this philosopher relies upon the fact that what is not, cannot act; thus the idea of being enters not only into the principle of Descartes, but is even the foundation upon which he rests it.

6. Whether we make the inward sense the basis of our cognitions, or prefer the evidence by which one idea is contained in another, it is always necessary to make the idea of being a primary element; we must suppose the understanding to be before it can think; we must suppose thought to be before we can make use of it; we must suppose our sensations and sentiments, the operations and affections of our souls, to be, before we can investigate their causes, their origin, and inquire into their nature; we must suppose ourselves to be, that we are, before we can advance one step in any sense. The idea of being does then exist in our mind, and is an element indispensable to all intellectual acts.

[CHAPTER II.]

SIMPLICITY AND INDETERMINATENESS OF THE IDEA OF BEING.

7. Nothing can be conceived more simple than the idea of being. It cannot be composed of elements. It allows of nothing determinate, since it is in itself absolutely indeterminate. The instant that something determinate is made to enter it, it is in a manner destroyed; it is no longer the idea of being, but of such a being; an idea applied, but not the idea of the being in all its generality.

8. How shall we make it understood what we would express by the word being, or ens? If we say that it comprises all, even the most unlike and opposite things, there is no reason why it may not be understood what it is. To join to the idea of being any determination, is to introduce into it a heterogeneous element, which in no manner belongs to it, and can only accompany it as a pure aggregation, but can never combine with it, without rendering it what it is not. If the idea of subsistence be combined with that of being, we no longer have the pure idea of being, but that of subsistence.

9. The idea of being is then most simple; it cannot be resolved into elements, and cannot consequently spring from speech, unless as from an exciting cause. If we be asked, for example, what we understand by substance, by modification, cause or effect, we explain it by uniting to the idea of being that of subsistence or inherence, that of productive force, or of a thing produced; but it is impossible for us to explain being, otherwise than by itself. We may make use of the words, something, what is, reality, and the like, but all these are inadequate to explain the thing itself; they are but the efforts we make to excite in the understanding of others the idea we contemplate in our own. If we would give further explanations by showing how the idea corresponding to the word being, is applicable to every thing, and in order to do this enumerate the different classes of being, applying the idea to them all, we only succeed in showing the use of the idea and the applications of which it is susceptible; but we do not decompose it. We say, indeed, that there is in all something corresponding to it, but we do not decompose this something; we only point it out.

10. From this we infer that the idea of being is not intuitive to us, and that by its very indeterminateness it excludes all that a determinate object can offer to our perception.

[CHAPTER III.]

SUBSTANTIVE AND COPULATIVE BEING.

11. For the more thorough understanding of this matter, it will be well to distinguish between the absolute and relative ideas of being; that is between what is expressed by the word being, when it designates reality, simple existence, and when it marks the union of a predicate and its subject. In the two following propositions we see very closely the different meaning of the word is; Peter is; Peter is good. In the former the word is designates the reality of Peter, or his existence; in the latter, it expresses the union of the predicate good with the subject Peter. In the former the verb to be is substantive, in the latter it is copulative. The substantive simply expresses the existence; the copulative a determination, a mode of existing. The desk is, signifies the simple existence of the desk; the desk is high, expresses a mode of being, height.

12. Purely substantive being, is nowhere met with, except in the following proposition: being is, or what is is; in all other propositions there is involved, even in the subject itself, some predicate which determines the mode. When we say, the desk is, notwithstanding that the direct predicate of the proposition is the word is, there yet enters into the subject desk a determination of the being of which we speak, and that is of a being which is a desk. We were, then, right in saying that the verb to be, in its purely substantive meaning, is met with in no other proposition than this: being is. This is perfectly identical, absolutely necessary and convertible, that is, the predicate may be observed of all subjects, and the subject of all predicates. Suppose we give the proposition a different form; being is existing; we can still say all being is existing, or the existing is being; that is, all that exists is being.

13. If it be objected that possible being does not exist, we answer that purely possible being is not, strictly speaking, being; but that it does exist, in the same mode in which it is, that is, in the possible order. As we shall, however, treat this question more fully hereafter, we now turn to the propositions in which being is copulative. The desk is, is equivalent to this, the desk is existing. It is true that every real desk is existing, but real is the same as existing; and thus it might, in one sense, be said that the proposition resembles this other: all being is. But here we detect a difference; it consists in this, that the idea of existence does not necessarily enter into that of desk, for we can conceive of a desk which does not exist, but we cannot conceive of a being as such without a being, that is, of a being which is not being. A very notable difference is every way perceptible between the two propositions; in the former, the subject may be affirmed of all predicates by saying, all that is existing is being; but it is evident that we cannot say all that is existing is desk.

14. The reason of this is that the proposition, being is, is absolutely identical; it is the expression of a pure conception reduced to the form of a proposition; and, consequently, the terms which serve as extremes may be taken indiscriminately the one for the other; being is, whatever is, is being; being is existing; every thing existing is being. But different orders of ideas are combined in all other propositions; and, although the common idea of being is applicable to all, as this idea is essentially indeterminate, it does not thence follow that one of the things to which the general idea corresponds is identical with the other, alike entering into the same general idea. Being belongs to every existing desk; but not, therefore, is every thing a desk.

15. Copulative being may be applied without the substantive; thus when we say that the ellipse is curvilinear, we abstract both the existence and non-existence of any one ellipse; and the proposition would be true although no ellipse at all were to exist. The reason is that the verb to be, when copulative, expresses the relation of two ideas.

16. This relation is of identity, but in such a way that more than the union of the two is needed before a predicate can be affirmed of a subject. The head is united to the man, but it cannot, therefore, be said, "man is his head;" the sensibility is united to the reason in the same man, but we cannot say, "sensibility is reason;" whiteness is in union with the wall, but we cannot say "the wall is whiteness."

The affirmation, then, of a predicate expresses the relation of identity, and this is why, when this identity does not exist with respect to the predicate in the abstract, it is expressed in the concrete, in order that something involving identity may enter into it. The wall is whiteness: this proposition is false, because it affirms an identity which does not exist; the wall is white: this proposition is true, because white means something which has whiteness, and the wall is really something which has whiteness; here, then, is the identity which the proposition affirms.[18]

17. The predicate is, then, in every affirmative proposition, identified with the subject. When we perceive, therefore, we affirm the identity. Judgment, then, is the perception of the identity. We do not, however, deny that in what we call assent there is often something more than the simple perception of identity; but we do not understand how we need any thing more than to see it evidently in order to assent to it. What we call assent, adhesion of the understanding, seems to be a kind of metaphor, as if the understanding would adhere, would yield itself to the truth, if it were presented; but in reality we very much doubt if, with respect to what is evident, there be any thing but perception of the identity.

18. Hence it follows, that if the same ideas were to correspond in the very same manner to the same words, the opposition and diversity of judgments in different understandings would be impossible. When, then, this diversity or opposition does exist, there is always a discrepancy in the ideas.

19. We conceive of things, and reason upon them abstracted from their existence or non-existence; or we even suppose them not to exist, that is, conceive of relations between predicates and subjects without the existence of either predicates or subjects. And as all contingent beings may either be or cease to be, and even the first moment of their being be designated, it follows that science, or the knowledge of the nature and relations of beings, founded upon certain and evident principles, has nothing contingent for its object inasmuch as it exists. There is, then, an infinite world of truths beyond contingent reality.

We conclude, from our reflections upon this, that there must be beyond the contingent world a necessary being in which may be founded that necessary truth which is the object of science. Science cannot have nothing for its object; but contingent beings, if we abstract their existence, are pure nothing. There can be no essence, no properties, no relations in what is pure nothing; something therefore is necessary whereon to base the necessary truth of those natures, properties, and relations which the understanding conceives of in contingent beings themselves. There is, then, a God; and to deny him, is to make science a pure illusion. The unity of human reason furnishes us one proof of this truth; the necessity of human science furnishes a second, and confirms the first.[19]

20. We find a conditional proposition involved in every necessary proposition, wherein substantive being is not affirmed nor denied, but the relative, as in this; all the diameters of a circle are equal. Thus, the one we have just cited is equivalent to this one; if there exists a circle all its diameters are equal. For in reality did no circle exist, there would be no diameters, no equality, or any thing else; nothing can have no properties; wherefore in all that is thus affirmed we must understand the condition of its existence.

21. In general propositions the union conceived of two objects is affirmed; but we must take good care to notice that although we are wont to say that what is affirmed is the union of two ideas; this is not, therefore, perfectly exact. When we assert that all the diameters of a circle are equal, we do not mean that this is so only in ideas, that we conceive it so to be, but that it really is so, beyond our own understanding and in reality, and this abstracting our ideas and even our own existence. Our understanding sees then a relation, a union of the objects; and it affirms that whenever these exist, there will also really exist the union, provided the conditions under which the object is conceived be fulfilled.

[CHAPTER IV.]

BEING, THE OBJECT OF THE UNDERSTANDING, IS NOT THE POSSIBLE, INASMUCH AS POSSIBLE.

22. One very important point concerning the idea of being remains to be illustrated, and that is, whether this idea has possible or real being for its object. The scholastics taught that the object of the understanding was being; nor were they altogether without reason in so doing, since one of the things we conceive of with the greatest distinctness, and which is found to be the most fundamental in all our ideas, is the idea of being, containing as it does in a certain manner all other ideas. But as being is distinguished into actual and possible, a difficulty occurs as to which of these categories the idea of being, the chief object of our understanding, is applicable to.

23. The Abbate Rosmini, in his Nuovo Saggio sull' origine delle idee, pretends that the form and the light of our understanding, and the origin of all our ideas, consists in the idea, not of real, but of possible being. "The simple idea of being," he says, "is not the perception of any existing thing, but the intuition of some possible thing; it is no more than the idea of the possibility of the thing."[20]

I very much doubt the truth of this; and there seems also to be some confusion of ideas here. He ought to have defined possibility itself for us, before making the idea of it enter into that of being. I will myself give a definition of it, and this may serve greatly to facilitate the understanding of the whole matter.

24. What is possibility? The idea of possibility, abstracted from its classifications, offers us a general idea of the non-repugnance, or non-exclusion, of two things with respect to each other; just as the idea of impossibility presents us such a repugnance or exclusion. A triangle cannot be a circle. A triangle may be equilateral. In the former case we affirm the repugnance of the ideas of the triangle and of the circle: in the latter, the non-repugnance of a triangle having its three sides equal. It may be said that in these cases there is no question of the existence of the triangle or of the circle; and that the possibility or impossibility is referred to the repugnance of their essences, abstracted from their existence or non-existence, although ideal impossibility draws along with it real impossibility.

25. Since, whenever impossibility is asserted, repugnance also, is asserted, and there can be no repugnance of a thing with itself, it follows that impossibility is only possible when two or more ideas are compared. On the other hand, when there is no repugnance there is possibility; then, no simple idea, of itself alone, can offer to us an impossible object. The object, therefore, of every simple idea is always possible, that is, is not repugnant.

26. Those things only are intrinsically impossible which involve the being and the not-being of the same thing; wherefore they are styled contradictory. When an absurdity of this nature is presented to us, we at once recollect the principle of contradiction, and say, this cannot be, "since it would be and would not be at the same time." Why is a circular triangle impossible? Because it would be and it would not be a triangle at one and the same time.

The idea of not-being does then enter into that of impossibility: without it, there can be no exclusion of being, and consequently, neither contradiction nor impossibility.

27. Possibility may be understood in two ways: I., inasmuch as it expresses only simple non-repugnance; and then what does not exist, is not only possible when it does not involve any contradiction, but also, the existing, the actual; II., inasmuch as it expresses non-repugnance, united to the idea of not being realized; and then it is only applicable to non-existing things. The possible taken in the former sense, is opposed to the impossible; in the latter, it is opposed to the existing; it involves, however, the condition of non-repugnance. In the former case we have possibility simply so called; in the second, pure possibility.

From these remarks we conclude that the idea of possibility adds something to that of being, that is, non-repugnance, non-exclusion; and if there be question of pure possibility, the non-existence of the possible being is likewise added.

28. When the understanding perceives being in itself, it cannot distinguish whether there is or is not repugnance; this is only discoverable by comparison; for the idea of being, in itself simple, does not include comparable terms. The idea of being can encounter no repugnance if it be not applied to some determinate thing, to an essence in which contradictory conditions are imagined, as may be verified by seeking to apply being to a circular triangle.

29. So far is the idea of being in itself from being susceptible of abstraction from the idea of existence, that it is rather the idea itself of existence. When we conceive of being, in all its abstractness, we conceive of nothing else than of existence; these two words denote one and the same idea.

30. We can, in determinate things, conceive of the essence without existence; thus also we can very easily consider all imaginable geometrical figures and examine their properties and relations, abstracted from their existence or non-existence; but the idea of being, as something absolutely indeterminate, if it be abstracted from existence, is also abstracted from itself, is annihilated.

I should be much obliged to any one who would tell me to what the idea of being in general corresponds, abstracted from existence. If, after abstracting all determination, we also abstract being itself, what remains? Some one may answer, there remains a thing which may be. What does a thing mean? In case we abstract every thing determinate, thing can only signify a being; we should have a thing which may be, and this is equivalent to a being which may be. This is very well: but when we speak of a being which may be, is there only a question of an impure possibility? then we do not abstract existence, and the conditions of the supposition are not kept. Is there question of pure possibility? then existence is denied, and the proposition is equivalent to this: a being which is not, but which involves no repugnance. Let us examine the meaning of this expression: "a being which is not." What does the subject, a being, mean? a thing, or rather, that which is. What does a thing mean? a being: then abstraction is made from every thing determinate. Therefore, either the subject of the proposition means nothing, or the proposition is absurd, since it is equivalent to this, a thing which is, which is not, but which involves no repugnance.

31. The origin of the equivocation we combat consists in applying to the idea itself of being that which belongs only to things that are something determinate, conceivable without existence. Pure being, in all its abstractness, is inconceivable without actual being, it is existence itself.

32. Nor does pure possibility mean any thing except in order to existence. What is possible being if it cannot be realized, cannot exist? The idea of being is therefore independent of the idea of possibility; and the latter is only applicable in relation to the former.

33. The idea, then, of being is the very idea of existence, of realization. If we conceive of pure being, without mixture or modification, and subsisting in itself, we conceive of the infinite, we conceive of God: but if we consider the idea of being as participated in a contingent manner, by application to finite things, we then conceive of their actuality or realization.

34. When we apply the idea of being to things, we have no intention of applying to them that of possibility, but that of reality. If we say the desk is, we affirm of the subject desk the predicate contained in the idea of being: and still we do not mean to say that the desk is possible, but that it really exists.

35. Nevertheless, the idea of being excludes that of not-being, in such a way that if the idea of being were only of the possible, it would not exclude that of not-being, since the purely possible even includes not-being; possibility, therefore, does not enter into the sole idea of being; and this idea expresses simply existence, reality.

[CHAPTER V.]

A DIFFICULTY SOLVED.

36. What means the idea of purely possible being? If we maintain that the object of the idea of being is reality, these two ideas, being, and purely possible, would seem to be contradictory: reality is not purely possible, for were it purely possible, it would not exist, and in the non-existing there is no reality. Let us examine this difficulty, and investigate the origin of the idea of pure possibility.

37. Surrounded as we are by contingent beings, contingent beings ourselves, we are incessantly aware of the destruction of some, and the production of others, that is to say, of the transition from being to not-being, and from not-being to being. Our inward sense attests to us this transition from not-being to being; we have ourselves experienced it; all our recollections are limited to a very brief term, before which the world already existed. Thus, then, reason, experience, and inward sense show us that there are some objects which are, and then disappear, and that others, which before were not, now appear. In those things in which we witness this change, we perceive properties and relations which give occasion to a certain combination of our ideas, and this combination subsists whether the objects to which they refer continue or cease to exist. In this way we form a general idea of things which, although they do not exist, may exist; but this subject things, does not express being, but in general finite, determinate objects.

38. Here, then, is the solution of the difficulty. Purely possible being, such as we conceive it to be in the manner explained, involves no contradiction; it does not denote a reality which is not a reality, but an object, or a finite, determinate thing, the idea of which we have, although it do not exist, and whose existence involves no contradiction, or repugnance with any of the conditions contained in its idea. The expression, then, purely possible being, if it be explained in this manner, is nothing more than the generalization of these and other similar propositions. A desk which is not is possible. What do we mean by this? Simply that in the idea of desk there is nothing repugnant to its existing; and purely possible being signifies nothing more than that we have many ideas of finite things which may exist without repugnance. The expression refers to determinate things conceived of by us, but we abstract in this case whether this or that be the essence of which we speak, and comprise all those which offer no repugnance.

39. If it be objected that an infinite, non-existing being would then be a contradictory thing, we admit it without hesitation. If an infinite being do not exist it is an absurdity; and if, when we compare these two ideas, infinity and non-existence, we do not see the repugnance between them with perfect clearness, it is because we do not comprehend the nature of infinity. This is the only reason why the demonstration of the existence of God founded simply on his idea, has been and still is exposed to difficulties. But it is certain that if the infinite being did not exist, it would be impossible. For that is impossible which cannot exist; and did it not already exist it could not exist. This existence could not come from another, since the infinite cannot be a being produced; nor from itself, since it would not exist. We do, it is true, imagine the infinite in its essence, abstracted from its existence; but I repeat that this abstraction is only possible to us because we cannot well comprehend the infinite; could we comprehend it, we should see the repugnance between these terms, infinity and non-existence, with the same clearness as we see that of the triangle and circle.

[CHAPTER VI.]

IN WHAT SENSE THE IDEA OF BEING IS THE FORM OF THE UNDERSTANDING.

40. When it is asserted that the object of the understanding is being, there is room to doubt whether it is meant that the idea of being is the general form of all conceptions, or only that all the understanding conceives is being; or, in other words, whether the quality of object is attributed to being, as being, in such a way that under this form alone objects are conceivable, or only that the quality of being belongs to all that the understanding conceives.

In the first case the proposition might be taken in a reduplicative sense, and would then be equivalent to this: "The understanding conceives nothing save inasmuch as it is being;" in the second it might be taken formally, and be equivalent to this: "whatever the understanding conceives is being."

41. We are of opinion that it cannot be said that the object of the understanding is being only inasmuch as being; in such a way as to make the idea of being the only form of the understanding's conceiving; but that this form is an essential condition to all perception.

42. If we remark that the idea of being, in itself considered, neither includes any determination or variety, nor expresses any thing more than being, in its greatest abstractness, we shall not fail clearly to perceive that this idea of being is not the only form conceived by the understanding; if, therefore, the understanding do not perceive any thing besides this idea in its objects, it cannot know their differences; nor can its perception go beyond that which is common to all, being.

43. If it be said that the differences perceived are modes of being, modifications of that which is represented in the general idea, it is at once agreed that being in itself is not the only form perceived; since both modification and mode of being add something to the idea of being. The rectangular triangle is a kind of triangle: its idea is a modification of the general idea, and no one will pretend that the idea of rectangular adds nothing to that of triangle, or that they are both the same thing. The same is verified in the idea of being and its modifications.

44. We have already seen[21] that indeterminate ideas by themselves alone do not lead to positive cognitions; and certainly no idea better merits the name of indeterminate than that of being. Were our understanding limited to it, perception would be nothing but a vague conception, incapable of any combination.

45. Negation itself, as we shall hereafter see, is known to us, but this it could not be were we to admit that the understanding knows nothing save inasmuch as it is being; in which case the indispensable condition of all cognition, the principle of contradiction, would deceive us.

46. These reasons suffice to place beyond all doubt what we have proposed to show, but as this point is intimately connected with what is most transcendental in logic and metaphysics, we will endeavor to explain it more at large in the following chapter.

[CHAPTER VII.]

ALL SCIENCE IS FOUNDED IN THE POSTULATE OF EXISTENCE.

47. We have said that the idea of being is not the sole form perceived, but that it is a form necessary to all perception. We do not mean by this to say that we cannot perceive without the actually existing; but that existence enters in some degree as a condition of every thing perceived. We will explain ourselves. When we simply perceive an object, and affirm nothing of it, it is always offered to us as a reality. Our idea certainly expresses something, but it has nothing excepting reality. Even the perception of the essential relations of things involves the condition that they exist. Thus, when we say that in the same circle or in equal circles equal arcs are subtended by equal chords, we suppose impliedly this condition, "if a circle exists."

48. Since this manner of explaining the cognition of the essential relations of things may seem far-fetched, we will endeavor to present it under the clearest possible point of view. When we affirm or deny an essential relation of two things, do we affirm or deny it of our own ideas or of the things? Clearly of the things, not of our ideas. If we say, "the ellipse is a curve," we do not say this of our idea, but of the object of our idea. We are well aware that our ideas are not ellipses, that there are none in our head, and that when we reflect, for example, upon the orbit of the earth, that this orbit is not within us. Of what, then, do we speak? Not of the idea, but of its object; not of what is in us, but of what is without us.

49. Nor do we mean that we see it thus, but that it is thus; when we say the circumference is greater than the diameter, we do not mean that we see it thus, but that it is thus. So far are we from speaking of our idea, that we should assert it to be true although we did not see it, and even although it were not to exist. We speak of our idea only when we doubt of its correspondence with the object; then we do not speak of reality, but of appearance, and in such cases our language is admirably exact, for we do not say, it is, but, it seems to us.

50. Our affirmations and negations, therefore, refer to their objects. Now, we argue thus: what does not exist is pure nothing, and nothing can either be affirmed or denied of nothing, since it has no property or relation of any kind, but is a pure negation of every thing; therefore, nothing can be affirmed or denied; there can be no combination, no comparison, no perception, except on condition of existence.

We say on condition, because we know the properties and relations of many things which do not exist; but in all that we do know of them, this condition always enters: if they exist.

51. Hence it follows that our science rests always on a postulate; and we purposely use this mathematical expression in order to show that those sciences which are called exact by antonomasy do not disdain this condition which we exact from all science. The greater part of them commence with this postulate: "Let a line be drawn, &c.," "Suppose B to be a right angle, &c.," "Take a quantity A greater than B, &c." This is the way the mathematician, with all his rigor, always supposes the condition of existence.

52. It is necessary to suppose this existence, otherwise nothing could be explained. Common sense teaches us what has escaped some metaphysicians. To prove it, let us see how a mathematician, who never dipped into metaphysics, would talk. We will suppose the interlocutor to set out to demonstrate to us that in a rectangular triangle the square of the hypothenuse is equal to the sum of the squares of the base and perpendicular; and that we, in order to exercise his intelligence, or rather to make him show us, without himself being aware of it, what is passing in his own mind with respect to the perception of its object, put various questions to him, in reality searching, although apparently asked out of ignorance. We will adopt the form of a dialogue for the sake of greater clearness, and will suppose the demonstration to be given from memory, without the aid of figures.

Demonstration. Drop a perpendicular from the right angle to the hypothenuse.

Where?

Why, in the triangle of which we speak, of course.

But, sir, if there be no such triangle——

Why then, what are we talking of?

We are talking of a rectangular triangle, and the case supposed is that there is none.

Is not, but can be. Take paper, a pencil, and ruler, and we will have one right away.

That is to say, you speak of the triangle we may make?

Yes, sir.

Ah, I understand; but then we should have it; now, we have not got it.

All in good time. But if we had drawn it, could we not drop the perpendicular?

Certainly.

That is all I meant to say.

But you were saying drop——

No doubt we cannot drop a perpendicular in a triangle unless the triangle exists, since then there is neither vertex of a right angle, hypothenuse, nor any thing else; but when I say, drop a perpendicular, I always suppose a triangle; and as it is evident that the triangle may exist, I do not express the supposition, but understand it.

I comprehend this; but then we should drop the perpendicular only in this triangle, but you spoke as if we might drop it in all triangles.

I only took this triangle for an example; we can clearly do with all others what we can do with this one.

With all?

Certainly. Can you not see how, in every rectangular triangle, a perpendicular may be drawn from the right angle to the hypothenuse?

Yes, in your figure; but since what is in my head is not a triangle, for I imagine some with sides a thousand miles long, and there is not in my head room enough—

There is no question of what is in your head, but of triangles themselves—

But these triangles do not exist; therefore, we can say nothing of them.

Yes; but may they not exist?

Who doubts it?

Well then, if they do exist, be they large or small, in one position or another, here or there, is it not true that a perpendicular may be drawn from the vertex of the right angle to the hypothenuse?

Evidently.

I have then only to say that, in every rectangular triangle, this perpendicular may be drawn.

Then you do not speak of those which do not exist? Is it not so?

I speak of all, whether they do or do not exist.

But a perpendicular cannot be drawn in a triangle which does not exist. What does not exist is nothing.

But perhaps that which does not exist may exist; and I see with perfect clearness how every thing said would be verified, supposing it to exist. Thus we can and do speak of all existences and non-existences without any exception.

We leave it to the reader to judge if we have not, while thus rudely troubling our good mathematician with our importunate questions, made him reply as would have replied every one not at all acquainted with metaphysics. It is evident that these replies ought to be accepted as reasonable, as satisfactory, and as the only ones in this case that all the mathematicians in the world could give.

This being so, all that we have advanced is found in these replies and explications. All science is founded on the postulate of existence; every argument, to demonstrate even the most essential properties and relations of things, must start with the supposition of their existence.

[CHAPTER VIII.]

THE FOUNDATION OF PURE POSSIBILITY, AND THE CONDITION OF ITS EXISTENCE.

53. We have said that the foundation of the pure possibility of things, and of their properties and relations, is founded in the essence of God, wherein is the reason of every thing.[22] And it may at first sight seem that science needs only this foundation, and does not require to rest upon the condition of the existence of things; because, if essences are represented in God, the object of science is found in the Divine essence; and consequently, the argument founded upon the impossibility of asserting any thing of nothing, is not conclusive. Supposing there to be such a representation, science is not occupied with a pure nothing, but with a real thing; and it has consequently in view a positive object, even when it abstracts the reality of the thing considered.

Let us see how we can solve this difficulty.

54. The necessary relations of things, independently of their existence, must have a sufficient reason; and this can only be in necessary being. The condition, therefore, of existence, presupposes the representation of the essence of the contingent being in necessary being; the condition, therefore, "if it exist," cannot be brought in unless it presupposes the foundation of possibility.

55. This remark shows that there are two questions:—1st: What is the foundation of the intrinsic possibility of things? 2d: Supposing possibility, what condition is involved in so much as it is affirmed or denied of the possible object? The foundation of the possibility is God; and the condition is the existence of the objects considered.

Both are requisite to science; if the foundation of intrinsic possibility be wanting, the condition of existence cannot come in; and if, admitting the possibility, we omit the condition, science has no object.

56. We would remark, for the better understanding of this whole subject, that we do not, in affirming or denying the relations of beings represented in God, treat of what these beings are in God, but of what they would be in themselves were they to exist. In God, all are the same God; for all that is in God, is identical with God. If, then, we consider things only as they are in him, we shall have God, not the things, for object. Certain it is, that in God is the foundation, or the sufficient reason, of geometrical truths: but geometry does not consider them such as they are in God, but such as they are or may be realized. In God, there are neither lines nor dimensions of any kind; he, therefore, is not the object of geometry properly so called. Geometrical truths have in him an objective value or representative value, but not subjective; we should otherwise be obliged to say that God is extensive.

57. Here, then, is seen that what we said above in the place cited, does not conflict with what we have here established; and that to make God the foundation of all possibility, does not exclude the scientific necessity of the condition of existence.

58. We will, in order to place this beyond all doubt, present the question under another aspect, by showing that when God knows finite truths, he sees in them this condition likewise: "If they exist." God knows the truth of this proposition: "Triangles of equal base and altitude are of equal superfices:" this is true as well in the eyes of infinite intelligence, as in ours; were it not thus the proposition would not be true in itself, and we should be in error. This being so, there are in God, who is most simple being, no true figures, although he has the intellectual perception of them. The cognition, then, of God, in what relates to finite things, refers to their possible existence, and consequently involves the condition that they exist.

The cognition of God does not refer to their purely ideal representation, but to their actual or possible reality; when God knows a truth of finite beings, he does not know it from the sole representation of those truths which he has in himself, but from that which they would be were they to exist.

59. Every object may be considered either in the real or in the ideal order. The ideal is their representation in an understanding, which has a value only inasmuch as it refers to possible or actual reality. In this manner alone can the idea have objectiveness, since otherwise it could only be a purely subjective fact, of which, excepting the purely subjective, nothing could be either affirmed or denied. The idea which we have of the triangle aids us, in so far as it has a real or possible object, to know and combine: we refer what we affirm or deny of it to its object: if this disappear, the idea is converted into a purely subjective fact, to which we cannot apply the properties of a triangular figure without an open contradiction.

[CHAPTER IX.]

IDEA OF NEGATION.

60. It is said that the understanding does not conceive nothing: this is true in the sense that we do not conceive nothing as something, which would be a contradiction; but it does not therefore follow, that we do not in any mode conceive nothing. Not-being is nothing, and yet we conceive not-being. This perception is necessary to us; without it we could not perceive contradiction; for which reason the principle of contradiction: "It is impossible for a thing to exist and not to exist at the same time:" fundamental as it is in our cognitions, would fail us.

61. It may be said that to conceive nothing, not-being, is not to conceive, but to not-conceive: this, however, is false, for it is not the same thing to conceive that a thing is not, and not to conceive it. The former involves a negative judgment, and may be expressed by a negative proposition; and the latter is the simple absence of the act of perception; the former is objective, the latter subjective. We do not when asleep perceive things; but this non-perception is by no means equivalent to perceiving that they are not. It may be said of a stone that it does not perceive another stone; but not that it perceives the non-being of the other stone.

62. The perception of not-being is a positive act; and it would be a contradiction to say that it is the very perception of being; for it would follow, that whenever we perceive being, we perceive its negation, not-being, and vice versa, which is an absurdity.

63. When we perceive not-being, we do, it is true, perceive it in relation to being; and it is equally true, an understanding perceiving absolute not-being, without any idea of being, is altogether inconceivable; but this does not prove the two ideas not to be distinct and contradictory.

64. It is remarkable that the idea of negation, besides entering into the fundamental principles of our understanding: "It is impossible for a thing to be and not to be at the same time:" "Every thing either is or is not:" is also necessary to almost all of our perceptions. We do not conceive distinct beings without conceiving that one is not the other, and we cannot form a negative judgment into which negation does not enter. Hence it results that just as the idea of being is absolute and relative, also is the idea of not-being: thus, we say, "The sun is;" "All the diameters of a circle are equal;" and we also say, "The phœnix is not:" "The diameters of an ellipse are not equal."

65. We may ask those who hold that every idea is the image of the object, what sort of an image the idea of not-being would form? This confirms what we have already advanced, that it is a mistake to imagine all ideas as a kind of types, similar to things, and that we cannot oftentimes explain any of those inward phenomena, called ideas, notwithstanding we know and explain their objects by them.

66. It is also said that the object of the understanding is being; but this is inexplicable in the sense that the understanding does not perceive not-being; and can be understood only in the sense that we perceive not-being as coordinated to being, and that not-being of itself alone, cannot be the origin of any cognition.

Remark here an important difference. By the idea of being every thing may be understood; and the more of being there is in the idea, the more do we understand; and if an idea be supposed to represent a being without any limitation, or, which is the same thing, without any negation, we should have a cognition of an infinite being. On the contrary, the perception of not-being teaches us nothing, save inasmuch as it shows us the limitation of determinate beings and their relations; and if we suppose the idea of not-being to be gradually extended, we shall see that in proportion as it approaches its limits, that is, pure not-being, absolute nothing, the understanding loses its object; the points of comparison and the elements of combination fail; all light goes out, and intelligence dies.

67. We know universal, absolute nothing, only as a momentary condition which we imagine, but do not admit. In it we see that it is impossible that something should not exist; for, could any one instant be designated in which nothing existed, nothing could now exist. In this imaginary nothing, we discover no point of departure for the understanding; all combinations become impossible and absurdities; the mind sees itself perishing in the vacuum it has itself created.

68. If the idea of negation be not combined with that of being, it is perfectly sterile; but thus combined, it has a kind of fecundity peculiar to itself. The ideas of distinction, of limitation, and of determination, involve a relative negation, for we do not conceive distinct beings without conceiving that one is not another; nor limited beings, without conceiving that they are wanting, that is, that in some sense they are not; nor determinate beings, without conceiving something which makes them what they are and not others.

[CHAPTER X.]

IDENTITY; DISTINCTION; UNITY; MULTIPLICITY.

69. Let us examine how we may draw from the idea of not-being the explication of the ideas of identity and distinction, unity and multiplicity.

Let us conceive a being, and fix our attention solely on it, and compare it with nothing which is not it, nor permit any idea of not-being to come in; we shall then, with respect to it, have the ideas of identity and unity; or, to speak more exactly, these ideas of identity and unity will be nothing else than ideas of this same being. Ideas of unity and identity are for this reason inexplicable by themselves alone; they are simple, or are confounded with a simple idea in which can be no comparison, and into which if negation enter, it is not noted, nor can be made the object of reflection. Thus, for instance, the idea of not-being enters in some manner into the perception of every limited being; but we can abstract this negation, and consider what the object is, not what it is not.

70. If we perceive a being, and afterwards another being, the perception that one is not the other gives the idea of distinction, and consequently that also of multiplicity. There is, then, no distinction or number without perception of relative not-being combined with being; but this perception is all that is requisite to distinction and number.

71. The ideas of identity and unity are simple, those of distinction and number composite; the former involve no negation, the latter imply a negative judgment; "this is not that." It is impossible for A to be presented to us as distinct from B, if we do not perceive that B is not A; and on the other hand, we need only to know that B is not A, in order to enable us to say they are distinct. These expressions, "A is not B," or, "A and B are distinct," are perfectly identical.

72. From this we infer that the primary combination of our intelligence consists in the perception of being and not-being. By it we perceive identity and distinction, unity and number; by it we compare, affirm, or deny; without it we cannot even think. Without the perception of negation, we can have only the perception of being, that is, an intuition fixed upon an identical object, one and immutable, such as we conceive the Divine Intelligence to be, contemplating the infinity of being in the infinite essence.

73. Does God know negations? Certainly; for when a being ceases to exist, God knows this truth, in which there is a negation. He knows the truth of all negative propositions, whether it expresses substantive or relative being; therefore, he knows negation. But this is no imperfection, since it cannot be an imperfection to know truth; the imperfection is in the objects, which, by the very fact of being finite, include negation, being combined with not-being. Were God not to know negation, it would be because negation is in itself impossible; which would be equivalent to the impossibility of the existence of the finite, and would lead to the absolute and exclusive necessity of one sole infinite being.

[CHAPTER XI.]

ORIGIN OF THE IDEA OF BEING.

74. If it be impossible to think without the idea of being, it exists prior to any reflex act, and it cannot have sprung from reflection. The idea of being must therefore be innate. Let us investigate this question.

75. We have shown in the preceding chapter that we cannot think without the idea of being; let whoever doubts this consult his own experience, and make, if he can, a reflex act into which the idea of being will not enter. We have already seen that we cannot exclude it in the conception of first principles, and beyond these it is certain no one will go.

76. Can this idea have come to us from sensation? Sensation in itself offers us only determinate objects, whereas the idea of being is an indeterminate thing: sensation offers us only particular things, whereas the idea of being is the most general it is possible to have: sensation teaches us nothing, tells us nothing, except what it is, a simple affection of our soul, whereas the idea of being is a vast idea, extending to all, and, fecundating our mind in an admirable manner, is the element of all reflection and alone sufficient to found a science: sensation never leaves itself, nor extends to another sensation; the sense of touch has nothing to do with that of hearing; all belong to an instant of time, and only exist during it, whereas the idea of being guides the mind through every class of beings, the corporeal and the incorporeal, the real and the possible, the temporal and the eternal, the finite and the infinite.

If we discover any thing by sensations, if they produce any intellectual fruit, it is because we reflect upon them; but reflection is impossible without the idea of being.

77. Neither does it seem that the idea of being can be formed by abstraction. To abstract is of necessity to reflect; and reflection is impossible without this idea; therefore, it is necessary to abstraction, and consequently cannot have abstraction for its cause.

78. On the other hand, an exceedingly simple explication of the method in which abstraction is made, may be opposed to this argument apparently so conclusive. We see the paper upon which we write; this sensation involves two things, whiteness and extension. Were we limited to simple sensation, here we should stop, and receive only the impression, extension and whiteness. But having within ourselves a faculty distinct from that of feeling, which makes us capable of reflecting upon the very sensation we experience, we can consider that this sensation has some similarity to others which we recollect to have experienced. We can then consider extension and whiteness in themselves, abstracting the actual affection which they produce in us. Afterwards we can reflect upon the fact that these sensations have something in common with others, inasmuch as they all affect us in a certain manner, and then we have the idea of sensation in general. If, then, we consider that these sensations all have something in common with all that is in us, in so far as they modify us in a certain manner, we shall form an idea of a modification of the me, making abstraction, however, of its being a sensation, a thought, or an act of the will; and if, finally, we abstract from these things being in us, their being substances or modifications, and attend only to the fact that they are something, we shall have attained the idea of being. This idea may, therefore, be formed by abstraction. This explication, seductive as it is by reason of its simplicity, is open to grave objections.

79. From the very beginning of this process we make use, without adverting to it, of the idea of being; we therefore deceive ourselves when we imagine that we form it. We cannot reflect upon extension and whiteness without remarking that they exist, that they are something similar to other sensations. When we think upon what affects us, we know that we are, that that which affects us is, and we speak of its being or not being, of its having or not having something common; and finally, when we abstract the modifications of our mind as being this or that, and regard them only as thing, as something, as a being, we evidently cannot so consider them if there does not exist in us the idea of something in general, that is, of being. Thus being is a predicate which we apply to things; we do, therefore, know this predicate. We only collect in one general and indeterminate idea, particular and determinate things, already existing in our understanding. The successive operations made by means of abstraction are only a decomposition of the object, a classification of it in various general ideas so as to attain to the superior idea of being.

80. It is difficult in view of these reasons, which are all strong, to decide without danger of erring for either of the opinions advanced. Nevertheless, we shall give our own in accordance with the principles we have laid down in different parts of this work. We hold that the idea of being is not innate, in the sense that it pre-exists in our understanding as a type anterior to all sensation and to all intellectual acts;[23] but we see no impropriety in calling it innate, if nothing more be meant than the innate faculty of our understanding to perceive objects under the general reason of being or existence, so often as it reflects upon them. Thus the idea does not flow from sensations; it is recognized as a primary element of pure understanding; but it is not formed by abstraction, which separates it from others, and purifies it, so to speak, itself contributing to this purification. In this sense it may exist before reflection, and yet be the fruit of reflection, according to the various stages in which we consider it. Inasmuch as it is mixed and confused with other ideas, it exists before reflection; but inasmuch as it has been separated and purified, it is the fruit of the same reflection.

81. We must, in order to give a complete solution of the difficulties proposed, give our ideas precision and exactness.

The idea of being is not only general but also indeterminate; it offers to the mind nothing real or even possible, since we do not conceive that a being, which is only being, does or can exist, if no property besides that of being can be affirmed of it. In God is the plenitude of being; he is his own being; with reason does he call himself, I am, who am; but we also affirm of him, with all truth, that he is intelligent, that he is free, and that he possesses other perfections not expressed in the pure and general idea of being.

From this we infer that we ought not to regard the idea of being as a type representing to us something determinate, even something in general.

82. The act by which we perceive being, existence, reality, is necessary to our understanding, but it is confounded with all other intellectual acts, as a condition sine qua non of them all, until reflection comes to separate it from them, purifying it, and making it the object of our perception.

Since, when we perceive, we perceive something, it is evident that the reason of being is always involved in all our perceptions; by the simple fact of knowing we know being, that is, we know a thing. But as we do not always, when we fix our perception upon an object, distinguish the various reasons into which it may be decomposed, although the idea of being is contained in every object perceived, it is not directly perceived by our understanding until reflection separates it from all else.

83. If we reflect upon an azure object, evidently the idea of color enters into that of azure; but without reflection we shall not distinguish the genus, color, and the difference, azure. These two things are not really distinguished in the object perceived; for it would be ridiculous to pretend that in a particular azure-colored object, color is one thing and azure another. Nevertheless we can, when we reflect upon the object, very easily distinguish between the two ideas of color and azure, and we can discuss one without paying attention to the other. Must we say we have the idea of color in general, prior to the sensible representation? Most certainly not: it is only necessary to recognize an innate force of the mind to generalize what is presented to it in particular, and to decompose a simple object into various ideas or aspects.

84. Our understanding is endowed with an intellectual force, by virtue of which it can conceive unity under the idea of multiplicity, and multiplicity under the idea of unity. We discover an example of the latter when we unite what is really multiple in a single conception. Our understanding may be compared to a prism which decomposes a ray of light into many colors; hence different conceptions relating to one simple object. When multiplicity is to be reduced to unity, the intellectual force operates in an altogether contrary manner; instead of dispersing, it unites; the variety of colors disappears, and the ray of light is restored in all its purity and simplicity.

85. Our mind, from the fact that it is limited to know many things by conceptions only, and not by intuitions, requires the faculty of composing and decomposing, of seeing a simple thing under distinct aspects, and of joining different things under a common reason.

We must not fail to observe that the power of generalizing and of dividing, given to our understanding, is a great help to it, indicating, however, its weakness in the intellectual order, and continually warning it to proceed with due circumspection, when it has to decide upon the intimate nature of things.

86. According to this doctrine, general, and more particularly indeterminate ideas result from the exercise of reflection upon our own perceptive acts; and there is in the general idea nothing more than is seen in the particular perception, excepting its own generality produced by the elimination of all individuating conditions. This is especially verified in the idea of being, which, as we have seen, enters as a necessary condition into all our perceptions, and is, moreover, requisite to all operations as well of composition as of decomposition.

We cannot conceive, without conceiving some thing, a being; and this is substantive being. We cannot affirm or deny without saying, is, or is not; and this is copulative being. The idea of being is, therefore, less an idea than a condition necessary to enable our understanding to exercise its functions; it is not a type representing nothing determinate; it is rather the very condition of its life, without which it cannot possibly exercise its activity.

87. But we can, by reflection, perceive this condition of all our thoughts; the idea of being, standing, as it does, involved with the others, is then presented purified to our eyes, and we conceive that general reason of being, or thing, which enters into all our perceptions, but which we had not previously distinguished with sufficient clearness.

[CHAPTER XII.]

DISTINCTION BETWEEN ESSENCE AND EXISTENCE.

88. It has been much disputed in the schools whether existence is distinct from essence. At first sight, this seems an indifferent question; but such it is not, if we attend to the consequences which, in the opinion of respectable authors, flow from it; for they pretend to no less than establishing upon the distinction between essence and existence a characteristic note of the finite, attributing to infinite being alone, the identity of its essence with its existence.

89. That we distinguish between the essence and the existence of things is beyond all doubt; for inasmuch as we know an object realized, we conceive its existence; and inasmuch as we know that this object exists with this or that determination, constituting it in such or such a species, we conceive its essence. The idea of existence represents to us pure reality; the idea of essence offers us the determination of this reality. The schools, however, not satisfied with this, have endeavored to transfer to things that distinction which we discover in our conceptions; but their opinion seems to be subtle rather than solid.

90. The essence of a thing is that which makes it what it is, and distinguishes it from all else; and existence is the act which gives being to essence, or that by which essence exists. It would appear, from these definitions, that there really is no distinction between essence and existence. To render two things distinct, it is requisite that one be not the other; but since essence, abstracted from existence, is nothing, we cannot say that there is a real distinction between them. To what is the essence of a man, if we abstract his existence, reduced? To nothing; and therefore, no relation between them is admissible. We grant that when we abstract the existence of man, we do yet conceive the essence of man; but the question is not whether we distinguish between the idea of man and his existence, but whether there is a real distinction between his own essence and existence.

91. In God are the essences of all things, and in this sense they may be said to be distinguished from finite existence; this does not, however, if we consider it well, at all affect the present question. When things exist in God, they are not any thing distinct from him; they are represented in the Infinite Intelligence, which is, with all its representations, the infinite essence itself. To compare, therefore, the finite existence of things with their essence, as this is in God, is entirely to change the state of the question, and to seek the relation of things, not with their particular essences, but with the representations of the Divine understanding.

92. It may be objected that, if the existence of finite beings is the same as their essence, it will follow that existence will be essential to these beings; for, since nothing is more essential than essence itself, finite beings would exist of necessity, as all that pertains to essence is necessary. The radii of a circle are all equal, for equality is contained in the essence of the circle; and in like manner, if existence belong to the essence of things, they must exist, and non-existence would be a veritable contradiction.

This difficulty rests upon the ambiguous meaning of the word essence, and the want of exactness in joining the ideas of essential and necessary. The relation of essential properties is necessary, for we cannot destroy it without falling into contradiction. The radii of a circle are equal, because equality is involved in the very idea of the circle; consequently, if this be denied, it would be affirmed and denied at one and the same time. There is, however, no contradiction when some properties are not compared with others; but this comparison is not made when there is question of essence and existence, for in this case one thing is not compared with another, but with itself; if the distinction be introduced, it does not refer to two things, but to one and the same thing considered under two aspects, or in two different states, in the ideal order and in the real.

When we consider essence abstracted from existence, the object is the union of the properties which give to beings such or such a nature; we abstract their existence or non-existence, and attend only to what they would be were they to exist. The condition of existence is either expressly or impliedly involved in all that we affirm or deny of properties; but when we consider essence realized or existing, we do not compare property with property but the thing with itself. In this case, non-existence does not imply contradiction; for when existence disappears, the essence also disappears, with all that it included. There would be a contradiction were we to assert that essence implies existence, and to endeavor, while the former remains, to make the latter disappear, which is not verified in this supposition. The equality of the radii of a circle cannot fail, so long as the circle does not fail; and the contradiction would be to make the radii unequal while the circle continues to be a circle; but were the circle to cease to be a circle, there would be no reason why the radii should not be unequal. Essence is the same as existence; so long as there is essence, so long will there be existence; if the essence fail the existence will likewise fail; where, then, is the contradiction? Life is of the essence of man, and yet man dies; we may then say man is destroyed, and therefore there is in this no contradiction. If the essence cease to exist, it also will be destroyed, and existence, which is identified with it, may fail without any contradiction.

93. The scholastics taught that the being whose essence was the same as its existence would be infinite and absolutely immutable, because, since existence is the complement in the line of being or of act, it could receive nothing more. This difficulty also originates in the equivocal sense of words. What is meant by complement in the line of being or act? If it mean that nothing can supervene to essence identified with existence, here is a begging of the question, since what was to be proved is asserted. If it mean that existence is the complement in the line of being or act in the sense that, given it, nothing more is wanted to make the things, whose existence it is, really existing, an indubitable truth is advanced, but not one from which what was to be demonstrated can be inferred.

94. It would seem, therefore, that there is no real distinction in things corresponding to the distinction between essence and existence in our conceptions. Essence is not distinguished from existence, but it does not therefore cease to be finite, nor existence to be contingent. In God existence is identified with essence; but in such a manner, that his non-existence implies contradiction, and his essence is infinite.

[CHAPTER XIII.]

KANT'S OPINION OF REALITY AND NEGATION.

95. Kant numbers among his categories reality and negation, or existence and non-existence, and, conformably to his principles, defines them thus: "Reality is a pure conception of the understanding; it is what corresponds, in general, to any sensation whatever, consequently that whose conception denotes a being in itself, in time. Negation is that whose conception represents a not-being in time. The opposition of these two things consists in the difference of the same time, as full or void. Since then, time consists solely in the form of the intuition, and consequently in the form of the objects as phenomena, it follows that that which in them corresponds to the sensation, is the transcendental matter of all objects, as things in themselves, essential reality. Every sensation has a degree or intensity, by which it may fill more or less the same time, that is, the inward sense relatively to the representation of an object, until it be reduced to nothing = 0 = negation."

There is in this passage a fundamental error which ruins the whole basis of all intelligence: there is also much confusion in his application of the idea of time.

96. According to Kant, reality alone refers to sensations; therefore the idea of being will be the idea of the phenomena of sensibility in general; this idea will mean nothing, if applied to the non-sensible; the very principle of contradiction will necessarily be limited to the sphere of sensibility; and we neither shall know, or be able to know any thing without the sensible order. Such are the consequences of this doctrine; let us now examine the solidity of the principle from which they flow.

97. Were the idea of reality only the idea of the sensible in general, we could never apply it to non-sensible things, which, however, experience teaches we can do. We speak incessantly of the possibility and even of the existence of non-sensible beings, and we even distinguish the phenomena of our mind into those belonging to sensibility, and those which correspond to the purely intellectual order. The idea of being, therefore, for us, denotes a general conception non-circumscribed by the sensible order.

98. Kant will answer that the applications we make of this idea, extending it beyond the sphere of sensibility, are vain illusions expressed in unmeaning words. To this we reply.

I. There is now no question of ascertaining whether the applications of the idea of being or reality beyond the sensible order be founded or unfounded; there is question only of ascertaining what it is that this idea represents to us, whether the object represented be illusory or not. Kant, when defining reality, regards it as one of his categories, and consequently, as one of the pure conceptions of the understanding. To make his definition good, he ought to employ this conception in its greatest possible extent: but as he has demonstrated that conception, in itself, is not limited to the sphere of sensibility, it must follow that his definition is inadmissible. Had he said that the applications of the conception beyond the sensible order were unfounded, he would indeed have erred, but would not have destroyed conception itself; yet he equivocates not only in the uses of conception, but also in its nature, which he can only ruin, if he limit it to the sphere of sensibility.

II. The principle of contradiction is founded in the idea of being, and extends as well to the non-sensible as to the sensible. It would follow, were we to admit Kant's doctrine, that the principle of contradiction, "It is impossible for a thing to be and not to be at the same time," would be equivalent to this proposition; "It is impossible for a phenomenon of sensibility to appear and not to appear at the same time." Evidently neither philosophy nor common sense ever gave such a meaning to the principle of contradiction. When the impossibility of a thing's being and not being at the same time is affirmed, this is asserted in general, and abstraction is absolutely made of the things pertaining or not pertaining to the sensible order. Were it not thus, we should be obliged to say that non-sensible beings are absolutely impossible, which even Kant does not venture to maintain, or, supposing them to exist, to doubt whether the principle of contradiction is applicable to them. Who sees not the absurdity of such a doubt, and that, if it be admitted for a single instant, all intelligence is destroyed? If we limit the generality of the principle of contradiction, the impossibility is no longer absolute: and supposing it to fail in certain cases, who shall assure us that it does not in all?

III. Kant himself admits the distinction between the phenomena of sensibility and purely intellectual conceptions: with him, therefore, reality comprises something more than the sensible. Purely intellectual conceptions are a reality, are something at least as subjective phenomena of our mind, and yet are not sensible, as Kant himself confesses; he therefore falls into a contradiction, when he limits the idea of reality to the purely sensible.

99. Kant conceives reality and negation only as filling, or leaving void, time, which, in his opinion, is the primitive form of our intuitions, and a kind of back-ground upon which the mind sees all objects, even its own operations. According to this doctrine, the ideas of time precede those of reality and negation, since only in relation to it are the two latter conceivable. And now we see the singularity of a form, or whatever else it be called, to which the ideas of reality and negation are made to refer when nothing is conceivable without the idea of reality. Kant, scrupulous as he is in the analysis of the elements of our mind, and contemptuous as he is towards all metaphysicians who preceded him, ought to have explained to us the nature of this form in which we see reality, and which, nevertheless, is not contained in the idea of reality. If it is something, it will be a reality; and if it is not something, it will be a pure nothing; and consequently, it cannot be a form which can, by filling and becoming void, present to our mind the ideas of reality or negation. It would be easy to show, by an abundance of reason, the German philosopher's equivocation, when he so inexactly determines the relations between time and the idea of being; but as we propose to explain at length the idea of time, we will pass over here what belongs to another part of this work.

[CHAPTER XIV.]

RECAPITULATION AND CONSEQUENCES OF THE DOCTRINE CONCERNING THE IDEA OF BEING.

100. We wish now to recapitulate the doctrine brought out in the preceding chapters, so that it may be seen at a glance in all its bearings and connections.

The idea of being is so fruitful in results, that we must sound it under all its aspects, and never lose sight of it in investigating transcendental philosophy.

101. We have the idea of ens, or of being in general; reason and our inward sense both attest it.

102. This idea is simple, and cannot be resolved into other elements: it expresses a general reason of things, and its nature is in a certain manner destroyed if it be mingled with particular ideas. It is intuitive, but indeterminate to such a degree that, by itself alone, it affords us no idea of a real or possible being. We not only know that every being is, but that it is some thing which is its predicate: even the Infinite Being is not only a being, but is an intelligent and free being, and formally possesses all perfections which imply no imperfection.

103. The idea of being may express either simple existence, in which case it is substantive, or the relation of a predicate with a subject, and then it is copulative. In the proposition, "the sun is," being is substantive, that is, expresses existence; in the proposition, "the sun is luminous," being is copulative, that is, it denotes the relation of the predicate with a subject.

104. The ideas of identity and distinction originate in the ideas of being and of not-being; and thus the idea of copulative being, which affirms the identity of a predicate with a subject, flows also in a manner from the idea of substantive being.

105. Being, which is the principal object of the understanding, is not the possible inasmuch as possible. We conceive possibility only in order to actuality. Possibility flows from actuality, not actuality from possibility. We could not conceive pure possibility, that is, possibility without existence, did we not conceive finite beings in whose idea being is not of necessity involved, and of whose appearance and disappearance we are incessantly reminded by experience.

106. The understanding perceives being, and this is a condition indispensable to all its perceptions; but the idea of being is not the only one offered to it, since it knows different modes of being, which, by the very fact that they are modes, add something to the general and absolute idea of existence.

107. When we consider the essences of things, and abstract their reality, our cognitions always involve this condition,—if they exist. There can be only a conditional science of the purely possible, insomuch as it is not; that is, provided the object pass from possibility to reality. We must, in order to establish pure possibility so that it may have necessary relations, subject to the condition of existence, have recourse to a necessary being, origin of all truth.

108. The essences of things in the abstract mean nothing, nor can they become the object of affirmation or negation, unless we suppose a necessary being in which is the reason of the relations of things, and of the possibility of their existence.

109. Pure truth, independent of all understanding, of all being created or uncreated, is an illusion, or rather an absurdity. With pure nothing there is no truth. Truth cannot be atheistic; without God there is no truth.

110. We not only know being, but also not-being. We have an idea of negation, and it always refers to some being. Absolute nothing cannot be the object of intelligence. The idea of not-being has its own peculiar fecundity; combined with that of being, it gives the principle of contradiction, engenders the ideas of distinction and multiplicity, and makes negative judgments possible.

111. The idea of being does not flow from sensations; neither is it innate, in the sense that it pre-exists in our understanding as a type prior to all perceptions. There is no reason why it may not be called innate, if this mean only a condition sine qua non of all our intellectual acts, and consequently of the exercise of our innate faculties. The idea of being is mingled in every intellectual perception, but it is not offered to us with perfect clearness and distinctness until we separate it by reflection from the particular ideas which accompany it.

112. Essence is not distinguished from existence even in finite beings. It is a distinction in conceptions, to which there is no real distinction corresponding.

113. The identity of essence with existence does not involve the necessity of finite things. The arguments by which some pretend to establish this consequence are founded upon an ambiguous meaning of words.

114. Kant's opinion, which limits the idea of reality, and that also of negation, to the purely sensible order, would destroy all intelligence, since it overthrows the very principle of contradiction. This doctrine of the German philosopher is also in opposition with what he himself taught concerning purely intellectual conceptions, distinct from sensible representations. When he refers the ideas of reality and negation to that of time, as the primitive form of the inward sense, he leaves out of the idea of reality what no less pertains to it, and presents the idea of time under a point of view wholly equivocal.

115. As sensible representation is based upon the finite intuition of extension, so the perceptive faculties of the pure understanding receive the idea of being as their foundation. In the same manner that extension is presented to sensibility as limitable, and from limitability results figurability, and consequently all the objects of geometrical science; so also does the idea of not-being, combined with that of being, fecundate in a manner the metaphysical sciences. The parallelism of the two ideas, extension and being, is not of such a nature as to render the former independent of the latter. So far as science is concerned, the idea of extension is sterile, if it be not combined with the general idea of being and not-being. This may be shown in many ways; but it will suffice to recollect that geometry cannot take a single step without the principle of contradiction, into which the ideas of being and of not-being enter.[24]

116. All our cognitions flow from the idea of being and not-being, combined with intuitive ideas. We shall have occasion in the following books to remark this admirable fecundity of an idea, which, although it cannot of itself teach any thing, can yet, when united with others, and modified itself in various ways, so illuminate the intellectual world as to merit to be called the object of understanding.

[BOOK SIXTH.]

UNITY AND NUMBER.

[CHAPTER I.]

PRELIMINARY CONSIDERATIONS ON THE IDEA OF UNITY.

1. Before analyzing the idea of number, let us examine its simplest element, unity. Number is a connection of unities. We cannot know what number is, if we do not know what unity is.[25]

2. What is unity? When is a thing one? We all seem to know what unity is, since upon it we found the fabric of all our arithmetic cognitions. We all know when a thing is one, and we never equivocate on the meaning of the word. In this the learned and the unlearned stand on the same footing. The word one, in our language, has only one meaning for all who understand it. The same may be said of the word which in other languages expresses the same idea. When we meet the figure 1, which corresponds to this idea, and expresses it in a general manner, abstracting the difference of idioms, all men understand and apply it in the same manner.

3. The idea of unity is the same in all men; it is a common patrimony of the human race. It is not bound to this or that object, nor to this or that act of the mind; it extends to all in the same manner. Even composite and multiple things are called one only, inasmuch as they participate in a general idea. The indivisible point is one. The line composed of many points could not be one were there not a contiguous enchainment of these points, and did they not all unite to form one object, which gives us one impression, and is submitted to one act of our understanding.

4. The idea of unity is not a particular sensation, since it applies to all; neither is it sensation in general, since it pertains to what is not sensation. The sensation of color is one; so, also, the consciousness of the me is one, although this is not a sensation. The size of the rectangle which I see is one, and the relation of the equality of its angles is also one, but is not a sensation.

5. The idea of unity is a simple idea, and accompanies our mind from its first steps; we find it everywhere, and understand it well, but cannot explain it as we would, because it is simple, and cannot be decomposed and expressed by various words. We do not mean to say, however, that we must abjure all explanation of it; we only propose to warn the reader of the kind of explanation he may expect, which can be no other than the analysis of the fact, inasmuch as it is an object, and of the phenomenon as presented to our mind.

[CHAPTER II.]

WHAT IS UNITY.

6. The scholastics were right in teaching that every being is one, and that whatever is one is being. Unity is a general attribute of every being, but is not distinct from it. However little we reflect, we cannot fail to perceive that unity and being are not distinguished: the unity of unity, by itself, offers us nothing real or even possible. What then would become of unity, if nothing but unity? This idea is involved in that of being; it is an aspect of it, a reason under which being is presented to the understanding.

7. But what is the conception of unity under which beings are presented to us? There is unity in the object when there is no distinction in the conception presenting it; and there is no distinction, when the perception of relative not-being is not combined in the object with that of being. We have unity whenever we perceive an object simply. Suppose that we perceive the object B. No matter what B is, it will to us be always one, unless we perceive it as composed of C, D, one of which is not the other. If we perceive in the object B, a distinction between C and D, unity disappears.

Evidently when we are aware of this composition we can abstract it and simply consider the result, the whole, B; and then unity appears anew.

8. We see by this that unity may be either real or fictitious. It is real and existing when there is no distinction in the thing either real or apparent; it is fictitious in those composites which of themselves include distinct things that may be offered to the understanding, inasmuch as they are subordinated to one unity of order, abstraction made of the real distinction contained in them.

9. The schoolmen sometimes defined what is one to be, "ens indivisum in se, et divisum ab aliis." The former part seems sufficiently exact if by indivisum is meant non-distinctum and not non-separatum; but the second part must be regarded at the best as superfluous. If there existed only one most simple and sole being, it would yet be one, although we could not say that it was divided from others, divisum ab aliis; for as there would be no others it could not be divided from them. This part of the definition is therefore superfluous.

10. It is no solution of the difficulty to say that this one being is divided from others, real or possible, and that in the supposition of one only being, others are possible although not real. The only being would be really one, and the division from others would be only possible; since there can be no real distinction between two terms when one of them is only possible. The division from others, divisis ab aliis, therefore is not a necessary element of unity, because unity is real, and this element is only possible.

11. However, in confirmation of this doctrine, we may remark, that in common parlance, unity is opposed to distinction, and there is no unity where there is no distinction. If the only being be not conceived as multiple there can be no distinction; and this is so independently of its being compared with the rest. The words, others, and the rest, suppose single beings; the idea of unity precedes that of distinction; beings are not considered as distinct between themselves until after they are conceived as individually single.

12. It seems, therefore, that a single being ought to be defined as ens indivisum in se, or a being which includes no division. Unity, then, will depend upon non-distinction. If non-division denote non-distinction, there will be real unity; but if it denote non-separation or re-union, we shall only have a fictitious unity. The molecules without extension, of which many suppose matter to be composed, would be really one, because there is no distinction in them. Bodies are fictitiously one because their composite parts though united are really distinct.

13. A difficulty may be raised by asking whether a being, indivisible in itself, but not divided from others, would be really one, for in case it would not be one, it might be inferred that we had unjustly censured the definition of the schoolmen, since whatever wants the second property required by the definition would not be one. We reply, then, a being that includes no distinction in itself, and is not distinguished from others, would indeed be one, but in such a case there would be no others, since they cannot be when there is no distinction. In such an hypothesis, there would be only one unity, the unity of pantheism, the great all, the absolute in which all things would be identified.

14. We have already said that the unity which is confounded with being, is not the unity which originates number. We here in fact encounter two different conceptions of unity, the one marking only want of distinction, and the other expressing the property of engendering number. But we are not thence to infer that the one which is identified with being is distinct from that which engenders number. All beings, one in themselves, but distinct from each other, no matter what they may be, may be conceived under the idea of number. The number three enters into the august mystery of the Trinity, and we say with all truth that in God there are three persons.

15. It is not necessary that the unity which engenders number should be real; it suffices if it be fictitious. When we take a foot measure for unity, we employ a fictitious unity, since the foot is composed of parts, but the number which results therefrom is, nevertheless, a true number.

[CHAPTER III.]

UNITY AND SIMPLICITY.

16. Real unity and simplicity are identical. What is really one has no distinction in itself; nor is it composed of parts, of which it can be said, this is not that. Evidently simplicity requires nothing more; the simple is opposed to the composite, to what is formed of many beings whereof one is not the other.

17. We meet this simplicity in none of the objects of our intuitions, excepting the acts of our own mind; so that even when we know, by discursion, that there are substances really one or simple, we do not see them in themselves.

Extension consists essentially of parts; whence it happens that we never encounter real unity or simplicity in the corporeal world as object of our sensibility. But as the composite must be resolved into the simple, as it is hard to proceed ad infinitum, we infer that the corporeal universe itself is a union of substances which, whether called points without extension, or any thing else, cannot be decomposed into others; for which reason they are really one, or simple.

18. Hence we conclude that substances may be said to be in a certain manner simple; and that things called composite are unions of substances, which in their turn form a third substance by virtue of a law presiding over them and giving them that unity which we call factitious.

19. We cannot, then, do less than to remark that the transcendental analysis refutes those who deny simplicity to thinking beings, since we have seen that simplicity is prior to composition, which can neither be nor be conceived if it be not presupposed. Simplicity is a necessary law of every being: a composite being ought to be called a union of beings, rather than a being.

20. We have said that simple substances are not objects of our intuition, which has none worthy to be called simple excepting the acts of our mind. The reason of this is, that the principal medium of our intuition is sensibility, which is founded upon representations, themselves based upon extension. There can be no doubt that the acts of our mind, given us by intuition, in the inward sense are perfectly simple; for who can decompose a perception, a judgment, an act of the reason or of the will?

21. The perception of a certain object requires preparatory acts; and the same may be said of judgments and ratiocinations; yet these operations are in themselves exceedingly simple, and cannot be divided into various parts. Simplicity is met with alike in the acts of the will, whether of the pure, intellectual, or sensible will. How shall we divide such acts as these into parts: I desire, I do not desire, I love, I abhor, I suffer, I rejoice?

22. We must take care not to confound the multiplicity of the acts with the acts themselves; there may be many acts, but in themselves they are simple. Thoughts, impressions and affections continually succeed one another in our mind; these phenomena are all distinct from each other, as is proved by their existing at different times, some at one time without the others, and by some being incompatible with others, because contradictory; but each individual phenomenon is by itself incapable of decomposition, and admits in itself no distinction into various parts; wherefore, it is simple.

23. True unity, therefore, is only found in simplicity; where there is no true simplicity, there may be factitious, but not real, unity; since even when there is no separation, there may be distinction between the various parts of which the composite is formed.

24. It may be inferred from this that indistinctum ought, perhaps, to take the place of indivisum in the definition of a one being; because distinction is opposed to unity of identity, and division to union. Absence of division is all that factitious unity requires; but real unity demands that there be no distinction. However closely united two things may be, if one is not the other they are distinct, and cannot, in strict metaphysical language, be called one.

25. The object of these observations is only to fix our ideas, not to modify our language. In common parlance, the idea of unity is used in a less rigorous sense, and, far from opposing this use, we readily accord it a reasonable foundation. There results from the union of two really distinct things, a conjunction, rightly called one so far as it also is subjected to a certain unity; and, were it not permitted to use this word in a sense less rigorous than that exacted by metaphysical analysis, we should be under the necessity of excluding unity from the great mass of objects. Simple substances, we have said, are not offered to us in immediate intuition, and we see compositions rather than their component elements. Could we apply unity only to simple elements, science would be greatly reduced, language would be impoverished, and literature and the fine arts would be despoiled of unity, one of their characteristic perfections.

[CHAPTER IV.]

ORIGIN OF THE TENDENCY OF OUR MIND TO UNITY.

26. Since we encounter multiplicity in all sensible objects, which are those chiefly demanding our attention, how does our mind acquire the idea of unity? In science, in literature, in the arts, and in every thing, we seek unity; and whence this irresistible tendency towards unity, which makes us seek a factitious when we cannot find a real unity, and this, too, notwithstanding the multiplicity presented by all the objects of our perception?

27. Two origins, if we mistake not, may be assigned to this tendency towards unity, the one objective, the other subjective. The former consists in the very character of unity in which the object of the understanding is mainly comprised; the other is the unity found in the intelligent being, and which it experiences in itself. We will explain these ideas more at length.

28. Unity is being; every being is one; and, properly speaking, being is not found without unity. Let us take a composite object: in it we discover two things; the simple component elements of it, and the union of them. The being, properly speaking, does not consist in the union, but in the united elements. The union is a mere relation, not even possible without the elements to be united. On the other hand, these elements in themselves, abstracted from their union, are true beings, existed before, and will exist after their union. What is an organized body? An aggregation of molecules united under a certain law, conformably to a principle presiding over their organization. The parts existed before their organization, and will continue to exist after its destruction. The being, therefore, properly consisted in the elements; and the organization was a relation of them among themselves.

29. Organization requires a principle to rule it, and subject its functions to determinate laws. Thus we see that even relation is subject to unity, to the unity of end and to the unity of a ruling and directing principle.

30. It is inconceivable how the union of distinct things can have any meaning, or lead to any result, if unity do not preside over it. In objects submitted to our experience, things are united in three ways: by juxtaposition in space; by co-existence in time; and by association in the exercise of their activity. The elements constitutive of extension are united in the first way; all objects belonging to the same time, in the second; and in the third all those which unite their forces and direct them to one and the same end.

31. The union consisting in the continuity of elements in space, has no value in the eyes of science, save inasmuch as there is an intelligent being who perceives the forms resulting from this continuity, by reducing them to unity under ideal types. Four lines of points, so disposed as to form a quadrilateral figure, have no scientific meaning until there comes an intelligence and perceives the form of a quadrilateral figure under the aspect of unity. We do not deny that the quadrilateral figure exists independently of intellectual perception: these lines will certainly exist, and be arranged in the same manner, although we prescind all intelligence; but this disposition in the quadrilateral form is a relation, not a being distinct from the aggregation of the elements disposed; and this relation, of itself alone, is no object of intelligence except inasmuch as presented to it under the unity of the quadrilateral form.

The intelligence in search of a true being, can find none, save in elements; and if it wishes to perceive their relation, it must recur to the unity of form.

32. Co-existence in time, is a relation, which, of itself alone, neither gives any thing to, nor takes any thing from objects. These exist independently of this relation; for they must, of necessity, exist, in order to co-exist. This relation denotes something perceptible to the understanding, only as it is presented to it under unity, which, in this case, is unity of time, as in the former it was unity of space.

33. Neither has the association of activities any meaning, except when it expresses the convergence of forces towards one and the same object. If unity be wanting to the point of their direction, their union will express nothing, and the intelligence will have for its object only scattered and unrelated activities.

34. We have then shown that unity is a law of our understanding, founded upon the very nature of things. Absolute being is never found in the composite, but only in the simple, and relative being is not even conceivable, if it be not submitted to unity.

35. We discover in the very nature of our mind, the second origin of its tendency to unity. It in itself is one, is simple, and therefore disposed to assimilate every thing to itself under this same unity and simplicity. It feels that it is one in the midst of multiplicity, permanent even in succession, and under all the immense variety of sensible phenomena, intellectual and moral, which it unceasingly experiences. The inward sense attests with irresistible certainty the identity of the me. This unity, this identity, is as certain, as evident to the child who begins to feel pleasure or pain, and is sure that he is one and the same that experiences both impressions, as they are to the philosopher who has spent long years in profoundly investigating the idea of the me and the unity of consciousness.

The unity and simplicity which we experience in ourselves force us to reduce the composite to the simple, the multiple to the one. The perception of things the most composite refers to a consciousness essentially one: even were we to perceive the whole complicated universe by a single act, this act would be most simple, since otherwise the me could not say, I perceive.

36. Two reasons, then, exist why our mind in all things seeks unity. Objects are unintelligible, except so far as subjected to a certain perceptible unity, to a form, under which the multiple is made one, and the composite simple. The object of the understanding is being, and being consists in the simple. The composite involves an aggregation of simple elements with the relation called union; but unless this be presented under a certain unity, it does not constitute a perceptible object.

Without the indivisible unity of consciousness, no intelligent subject is conceivable. Every intelligent being requires this link to unite the variety of phenomena of which it is the subject. If this unity fail, the phenomena become an informal aggregation, unrelated among themselves: intellectual acts without an intelligent being.

The tendency to unity originates in the perfection of our mind, and is itself a perfection; but it needs to be carefully watched, lest it go astray, and seek real unity there, where only a factitious unity can be found. This exaggeration is the cause of pantheism, the fatal error of our day. Our mind is one, so also is the infinite essence, cause of all finite beings; but the aggregation of these beings is not one, for even when united by many ties, they cease not to be distinct. There is in the world unity of order, of harmony, of origin, and of end; but there is no absolute unity. Number also enters into unity of harmony, but it is incompatible with absolute unity, as reason and experience both show.

[CHAPTER V.]

GENERATION OF THE IDEA OF NUMBER.

37. Unity is the first element of number, but does not of itself alone constitute number, which is not unity, but the collection of unities.

38. Two is a number. What is our idea of the number two? Evidently it is not confounded with its sign, for signs are many and very different, but it is one and always the same.

39. It would seem at first sight that the idea of two is independent of the mode of its generation, and that, being one, it may be formed by addition or subtraction, by adding one to one, or taking one from three: 1 + 1 = 2; 3 - 1 = 2. But if we reflect upon these two expressions, we shall see that the latter is impossible without the former. We should not know that 3 -1 = 2 if we did not previously know that two entered into the composition of three, and how it entered. We could know nothing of this had we not already the idea of two, and this idea is nothing else than the perception of this sum.

40. The idea of two is no sensation, for it extends alike to the sensible and the non-sensible, to the simultaneous and the successive. In itself it is simple, its object is composite.

41. Since the collection of objects is small in two, the imagination can easily figure to itself what the understanding perceives; and the idea seems clearer to us because made sensible by a representation. The idea of addition made, in facto, that is, the idea of the sum, enters into that of two, but not of addition in fieri. Our idea of this number is perfectly clear, and yet we do not continually think of one plus one.

42. The idea of two refers to the simultaneous as well as to the successive; but our mind does not discover it until after it has the idea of succession. The object of this perception is the relation of united things; the understanding perceives them as such, and then only has it the idea of two.

43. Neither the successive nor simultaneous perception of two objects unaccompanied by relation is the idea of two. Hence the saying: a man and a horse do not make two, but only one and one; and the reason of this is that the man and the horse are represented to the understanding by their difference, not by their resemblance; and things must be presented to the mind under a common idea in order to give number. Thus, if we abstract their difference, and consider them only as animals, or corporeal beings, or beings simply, or things, they will make two.

44. In objects, then, totally unlike, or not comprehended under some common idea, there can be no number. Abstract number is number by excellence; because it eliminates all that distinguishes the things numbered, and considers them only as beings, consequently as similar, as contained in the general idea of being. Concrete numbers are only numbers so far as they participate in this property. Two is applicable to one horse and another horse, but not to a horse and a man, unless we identify them under the idea of animal, and abstract rationality and irrationality. Concrete number requires a common denomination; otherwise it is not number.

45. The idea of distinction, that is, that the one is not the other, enters into the idea of two, so that this idea necessarily involves an affirmation and a negation. The affirmation is of the real, possible, or imaginary existence of the things counted; the negation is of the one with respect to the other. Affirmation without distinction or negation involves identity. The idea of two, as well as that of every other number, includes the ideas of identity and distinction. The identity is of each extreme with itself; the distinction is of the extremes among themselves. Identity in the thing is the thing itself: identity in the idea is the simple perception of the thing. Distinction in the thing is the negation of it with respect to others: distinction in the idea is the perception of negation. We always perceive a thing as identical, and consequently every perception includes the idea of unity. But we do not always, when we perceive a thing, observe its negation with respect to others, and consequently do not always perceive number. The idea of number originates in comparison, when we see an object which is not another.

46. The ideas of being, distinction, and similarity enter into that of two. The idea of being, because nothing cannot be counted: that of distinction, or negation of the one being the other, because the identical does not constitute number: that of similarity, because things are only numbered when abstraction is made of their difference. Being is the basis of perception; distinction, of comparison; and similarity, of union. Perception begins with unity, proceeds with distinction, and ends with similarity, which is a kind of unity. The perception of this similarity unites what is distinct; but the union need not always be of the things, but may be in the idea comprising them. There are two poles of the world, but they are not united. The perception of the number two requires something more than the simple perception of objects; they must be susceptible of comparison, and consequently united in a common idea. This perception, therefore, demands comparison and abstraction, and this is why animals cannot numerate; they can neither compare nor generalize.

47. The analysis of the idea of two is the analysis of all numbers; the difference is not of nature, but of more and less; in the repetition of the same perception.

48. If any one now ask whether number be in the things, or in the mind alone, we reply that it is in things as in its foundation, because both distinction and similarity are in the things; that is, the one is not the other, and both have something in common; but it is the mind that sees all this.

49. After having perceived the distinction and union of two objects, we can also perceive another object, which will be neither the one nor the other of them, and will yet be comprehended in one general idea with them. This is the perception or idea of the number three. No matter how many numbers be imagined, nothing will ever be discovered in any of them except a simultaneous perception of objects, distinction of objects, and similarity of objects. If these be determinate, we shall have concrete number; if they be comprised in the general idea of being, of thing, we shall have abstract number.

50. The limits of our mind prevent it from comparing many objects at one time, and from easily recollecting the comparisons it has already made. To assist the memory, and the perception of these relations, we make use of signs. When we pass beyond three or four, our power of simultaneous perception fails, and we divide the object into groups which serve us as new units, and are expressed by signs. Ten is clearly the general group in the decimal system; but before we reach the number ten we have already formed other subalternate groups; since to count ten, we do not say one and one and one, etc., but one and one, two; two and one, three; three and one, four, etc. Each unit added forms a new group, which, in its turn, serves to form another. With two, we form three; with three, four, and so on. This affords an idea of the relation of numbers with their signs; but, as this matter is too important to be here dismissed, we will further develop it in the following chapters.

[CHAPTER VI.]

CONNECTION OF THE IDEAS OF NUMBER WITH THEIR SIGNS.

51. The connection of ideas and impressions, in a sign, is a most wonderful intellectual phenomenon, and at the same time of the greatest help to our mind. Were it not for this connection, we could scarcely reflect at all upon objects somewhat complex, and above all our memory would be exceedingly limited.[26]

52. Condillac made some excellent remarks upon this matter: in his opinion, we cannot, unaided by signs, count more than three or four. If, indeed, we had no sign but that of unity, we could readily count two, saying one and one. Having only two ideas, we could easily satisfy ourselves that we had twice repeated one. But it is not so easy to be certain of the exactness of our repetition when we have to count three, by saying one and one and one; still, this is not difficult. It is more so to count four, and next to impossible to go as far as ten. If we undertake to abstract the signs, we shall find that it is impossible to form an idea of ten by repeating one; and that it will be alike impossible, if we employ no sign, to make sure that we have repeated one exactly ten times.

53. Suppose the sign two, and one half of the difficulty is obviated; thus it will be much easier to say two and one, than one and one and one. In this supposition four will be no more difficult than was two, since, just as we before said, one and one, two; we now say, two and two, four. The attention before divided four times by the repetition of one, is now only divided twice. Six was before a hard number to count, but, in the present supposition, it is as easy as three was before; for, if we repeat two and two and two, we shall have six. The attention before distracted by six signs, is now distracted only by three. Evidently, if we continue to form the numbers three, four, and so on, expressive of distinct collections, we shall gradually facilitate numeration, until we attain the decimal simplicity now in use.

54. It may here be asked if the actual system be the most perfect possible? And if facility depend upon the distribution of collections in signs, can there be any thing more perfect than this distribution? Either there is question of new signs to denote new collections, or of the combination of signs. There can be no number which we cannot express with our present system, and consequently there is no need of inventing any thing to denote new collections. New signs might perhaps be invented for these collections, and these collections might possibly be distributed in a simpler and more convenient manner. In this case we admit an amelioration to be possible, though very difficult; but none in the former. In a word, the only possible progress would be in expressing better, not in expressing more.

55. The sign connects many ideas which, without it, would be isolated; hence its necessity in many cases, its utility in all cases. With the word hundred, or its numerical representative, 100, we know that we have one repeated a hundred times. Were this help to fail, we could not speak of a hundred, base calculations upon it, or even form it. It is, however, well said that we do not succeed in forming it except by tens, by repeating the calculation ten ten times.

56. Let it not, therefore, be thought that the idea of the number is the idea of the sign; for evidently the same idea of ten corresponds to the word ten, whether written, spoken, or numerically represented by the figures 10, although these three signs are very different. Every language has a word of its own to express ten, and all people have the same idea of it.

57. This last remark creates a difficulty as to what the idea of ten consists in. We cannot say that it is the recollection of the repetition of one ten times; first, because we do not think of this recollection when thinking of ten; and second, because, according to what has already been said, a clear recollection of this repetition is impossible. Neither is it the idea of the sign, for the idea signified existed before the sign was invented, otherwise the invention would have had no object, and would even have been impossible. There can be no sign where there is nothing to signify.

The idea of number includes more difficulties than Condillac ever imagined; who, if he had, after his close analysis of what facilitates numeration, profoundly meditated upon the idea itself, would not so readily have censured St. Augustine, Malebranche, and the whole Platonic school, for having said that numbers perceived by the pure understanding are something superior to those perceived by the senses.

[CHAPTER VII.]

ANALYSIS OF THE IDEA OF NUMBER IN ITSELF AND IN ITS RELATIONS WITH SIGNS.

58. In order clearly to conceive the idea of number, and the way it is engendered in our mind, let us study its formation in a deaf and dumb person.

We have no better way of giving such a one an idea of unity than by presenting an object to him. Now, if we would convey to him the idea of two, we show him two fingers, then two oranges, then two books, and in each of these operations make a sign which must be always the same. If we repeat this operation a number of times, the deaf and dumb person will associate the idea of two with that of the sign, and one will suggest the others; and he will endeavor to show us that he has seen two objects of some kind, by uniting the expression of the object with the sign of two. The same will take place with three, or four. When we reach higher numbers, the sign becomes more indispensable; since the less easily the idea of number is represented, the more necessary is the sign to secure it. But what we do to convey an idea of number to the deaf and dumb person, what he himself must do to express the number which he conceives, we must all do if we would obtain the idea.

59. Numeration is a repetition of operations; and the art of facilitating it consists in instituting signs which recall to our memory what we have done. It is an exceedingly complicated labyrinth, and we cannot trust ourselves to its windings with any expectation of finding our way out again, if we do not take care to mark the path we have followed.

It is to the admirable simplicity of the decimal system, united to its inexhaustible variety, that the facility and fecundity of our arithmetic are due. Algebra, going a step beyond, expresses without determining numbers, and presents the results of its operations without effacing its footsteps on the road travelled, is far superior to arithmetic, and has made the human mind take gigantic strides. But how? Solely by aiding the memory. Thus, the very principle that enables the child to say four and one, five, instead of adding unity five times to unity, the dumb man to express five by a hand, a hundred by a grain, enables the algebraist to express the result of his longest operations by a formula easy of retention by the memory. Both attain their object simply by aiding the memory. A grain of wheat denotes to the dumb man the idea of hundred, and this he applies to all similar collections; a few letters combined in a simple manner designate to the mathematician a property of certain quantities, and this he applies to all which are found in the same case.

60. Numeration is only an aggregation of formulas; and the more easy these are of mutual transformation with a slight modification, the more perfect will be the numeration. The better one knows the relations of these formulas and the manner of transforming them, the better will he know how to count. The greater a person's intellectual power of fixing simultaneously the attention upon many formulas, and of composing them, the more perfect arithmetician will he be, because the simultaneous comparison of many, leads to the perception of new relations.

61. What is our idea of hundred? The union of the units composing it, a union which we have made more or less frequently when learning to count. But how do we know that it is the same union? Because we have a formula called a hundred, expressed by a sign 100. This formula is so easily recollected that we have no difficulty in recollecting the idea of hundred and all the properties connected with it. We may be asked if a hundred is more than ninety. Were we under the necessity counting one and one and one, we should be bewildered, and never succeed in distinguishing the greater; but knowing as we do that to reach the formula hundred, we must pass by another formula ninety, and that this was in ascending, we know, once for all, that hundred expresses ninety and something more, that is, a hundred is more than ninety. And if it be further inquired what is the excess, we shall not undertake to ascertain this by adding units, but by the two formulas ninety and ten which compose the formula hundred.

62. By generalization we unite many similar things in one idea. The general idea is a kind of formula. Numeration unites in one sign many things contained in a general idea, but this sign has, at the same time, its own distinctive character. Thus the general idea belongs as a predicate to each of its particular objects; number belongs to no one in particular, but to all joined. We perceive in abstraction a common property, and lay aside all the particular objects which it presents; in numeration, we perceive similarity, but always with distinction. Abstraction is the result of comparison, but not comparison. Numeration implies a permanent comparison, or the recollection of it.

63. The idea of number is not conventional; a hundred is always a hundred with all its properties and relations, and this, too, prior to all convention and even to all human perception. The sign, and the sign only, is conventional. Were there no intellectual creature, and a hundred beings distinct among themselves were to exist, there would really be this number. The number three exists in the august mystery of the Trinity, from all eternity, and of absolute necessity. Number requires only the existence of distinct things; since, however unlike they may be, they always have something in common being, which may be included in a general idea, and consequently they fulfil the two conditions necessary to number.

64. The perception of being and of distinction, that is, of substantive being and of relative not-being, is the perception of number. The science of the relations of every collection, with its measure, which is unity, is the science of numbers.

[BOOK SEVENTH.]

ON TIME.

[CHAPTER I.]

IMPORTANCE AND DIFFICULTY OF THE SUBJECT.

1. The explanation of the idea of time is not a matter of mere curiosity, but of the highest importance. To convince ourselves of this we have only to consider that the explanation of the whole edifice of human cognitions is based upon it. The most fundamental and indispensable principle which supports all others, includes the idea of time. A thing cannot be and not be at the same time: "impossibile est idem simul esse et non esse." The impossibility of being and of not-being regards only the simul, the same time. Therefore, the idea of time necessarily enters into the very principle of contradiction.

2. The idea of time is involved in all our perceptions; it extends to many more objects than does the idea of space. We estimate not only the movements of bodies by time, but also the operations of the mind. We know that a series of thoughts may be measured by time the same as a series of corporal movements.

3. The idea of succession necessarily enters into that of time, and vice versa, the idea of time into that of succession. We may conceive that one thing succeeds another; but this would be impossible without succession, without a before and after, that is, without time. This reasoning, apparently vicious, shows, perhaps, that we must not explain the ideas of time and succession, the one by the other, since they are identical.

4. Time does not seem to be distinct from things; for who can imagine duration without that which lasts, or a succession without that which succeeds? Is it a substance? Is it a modification inherent in things, or distinct from them? Whatever is something exists; and yet we nowhere meet time existing. Its nature is composed of instants divisible to infinity, essentially successive, and consequently incapable of simultaneousness. Imagine the minutest instant you can, and it does not exist, for it is composed of others infinitely minute, which cannot exist united. To conceive an existing time, we must conceive it as actual, and in order to do this, we must surprise it in an indivisible instant; but even this is not time; it involves no succession; it is not duration, containing a before and an after.

5. Nothing is easier than to calculate time, and nothing more difficult than to conceive it in its essence. As to the former the learned and the ignorant are on the same footing; both have equally clear ideas; the latter is excessively difficult even to the most eminent men. The passage in the Confessiones of St. Augustine, in which the Holy Doctor endeavors to penetrate this mystery is well known.

[CHAPTER II.]

IS TIME THE MEASURE OF MOVEMENT?

6. Time is said by many philosophers to be the measure of movement. This idea is fruitful, but it needs to be illustrated.

When we measure movement we refer to something fixed. Thus we measure the rapidity with which we have traversed a certain space by noticing the time denoted by a watch. But how do we measure time by a watch? By the space passed over by the hand on the dial. If we reflect carefully, we shall see that this is purely conventional, or rather, that it depends upon an arbitrary condition. For if we suppose the time marked to be an hour, the space passed over by the minute hand, that is, the circumference of the dial, has no relation with the hour except what the artificer gave it by so constructing the watch that the minute hand would make one revolution every hour. If the watchmaker had constructed it differently, as he did the hour hand, the time would be the same, but the space passed over is very different.

7. The time, therefore, indicated by the watch is no measure, save as itself is subject to another measure; consequently it is not the primitive measure. The same can evidently be said of all other watches which must have been regulated one after another, until we come to the first of all watches. There was no other watch to regulate this; it follows, therefore, that no one of the measures furnished by art is the primitive measure.

8. Not finding this measure in the works of man, we must seek it in nature; and here we discover fixed measures. If we regard the course of the sun, and take for unity the time it requires from the time it leaves the meridian until it returns, we shall have the day; this divided into twenty-four parts gives us the hours. Here we have a great watch which will serve to regulate all others.

9. Nevertheless, however lightly we reflect upon this, we cannot help seeing that the solution is not so satisfactory as it seems at first sight.

Solar time and sidereal time do not agree. Thus, if we note the moment when a star is in the meridian conjointly with the sun, we shall the next day see that the star reaches the meridian a little before the sun. Which is right? Has the star taken just twenty-four hours, or the sun? If time be a fixed thing independently of movement, neither of these measures corresponds exactly to time.

10. This argument, which may be called practical, is corroborated by another purely theoretical. If we take celestial movement for the measure of time, will it be true that whenever the movement, which serves as the rule, shall be verified, that there has passed a fixed and determinate time? If we be answered in the affirmative, we must infer, that even were this movement to be accelerated or retarded, as, for instance, if a solar revolution were to be made with a half, or with twice its ordinary velocity, it would continue to mark the same time, which, however, is absurd. If it be said that the movement is supposed to be uniform, we reply, that this is a begging of the question. Uniformity of movement consists in equal times recurring after equal intervals. Did time, then, in its nature depend upon the movement of the sun, or of any star, as primitive measure, neither uniformity nor variety would have any meaning. If the space of twenty-four hours depended upon a revolution's being made, no matter in what manner whether at a snail's pace, or with the velocity of light, we should never have more or less than twenty-four hours. But if these depend upon another measure, if prior to them, there was a time which measured the velocity of movement, and determined whether it had been accelerated or retarded, then the movement of the stars is not the primitive measure; they are in the same category as our watches, they marked the time passed, but time has not passed because they mark it. Time is the measure of their movement, not their movement the measure of time. Movement is in time, not time in movement.

11. To appeal to the movement of the superior heavens, is evidently no solution of this difficulty, for what has been said of the sun, may also be said of the remotest star in the firmament. Whether we appeal to annual, solar, or sidereal movements, the same difficulty remains. Would sidereal years be the same, if the movement be made with greater or less velocity. If they would, an absurdity would follow; if not, this is not the primitive measure.

12. Moreover, we perceive, when considering movement, that we seem to conceive of greater and less velocity; and thus the idea of time, of necessity, enters into that of velocity, since velocity is the relation of space passed over in a given time. The idea of time is therefore prior to, consequently independent of, every particular measure.

13. We measure time by movement, and in order to measure the velocity of movement we need that of time. Here then, perhaps, is a vicious circle; but possibly this only shows that these are correlative ideas, the one explanatory of the other; or, rather, they are different aspects of one and the same idea. The difficulty of separating them, and the intimate union which unites them on the one hand as much as it divides them on the other, confirms this conjecture. To show this, we ask, what time has passed? Two hours. How do we know this? By our time-piece. But what if it be too fast or too slow? The measure fails. This time is thus to us as a fixed measure, prior to that of the watch by which we undertake to measure it. But what are these two hours, if we abstract the measure of the watch, that also of the stars, and every other measure? Two hours, in the abstract, can be found in no category of real or possible beings; and we cannot, without a measure, give any idea of them, nor form one for ourselves. The idea of hour refers to a determinate movement of known bodies; and this in its turn refers to others; and finally, we come to one in which we can discover no reason why it should be exempted from the general law to which the others are subject. No farther reference being possible, all measure fails; and this failing, time, by the force of analysis, vanishes.

14. Therefore, the referring of time to movement, explains nothing; it only expresses a thing known, and that is, the mutual relation between time and movement, a relation known to the unlearned, and of constant and common use; but the philosophic idea stands intact; the same difficulty remains; what is time?

[CHAPTER III.]

SIMILARITIES AND DIFFERENCES BETWEEN TIME AND SPACE.

15. Time seems to us to be something fixed. An hour is neither more nor less than an hour, no matter how our time-pieces go, or the world itself; just as a cubic foot of space is always a cubic foot, neither more nor less, whether occupied or not occupied by bodies.

16. Time exists independent of all movement, of all succession; if it is something absolute, has a determinate value of its own, is applicable to all that changes without itself changing, the measure of all succession without itself being measured, what is it? That it is something accidental cannot be reconciled with its immutability and universality. Every thing lives in it, but it lives in nothing; every thing dies in it, but death has no power over it. When the substance perishes, the accident perishes; but time continues the same although no substance exist. Before all created beings, we conceive ages and ages, that is, time; and after the destruction, the annihilation of all beings, we still conceive a successive although unending succession, which is time. The idea, then, of time, does not demand that of the universe; it existed before it, and will survive it: but without time the universe is inconceivable.

17. The idea of time seems to be independent of the idea of any being; of all duration in it; every thing may endure in it; but it does not begin or end with what endures in itself; it is applicable to all that endures, but it is not itself an endurable thing. We imagine it to be one in the multiple, uniform in the various, fixed in the movable, eternal in the perishable; and it even seems to contain some features of the attributes of Divinity; but it is, on the other hand, essentially despoiled of every property excepting that of succession in its abstractest signification. It is essentially sterile, has no power of its own, no condition of being or action, and consequently leads to the highest imaginations of what a pure idea really is, an abstraction, which, like space, we have imagined in the presence of things.

18. The points of similarity between time and space are worthy of our attention. Both are infinite, immovable; both are a general measure; both essentially composed of continuous and inseparable parts. Limit them you cannot, determine any limit you chose, and beyond it you will see an ocean extended. Your powers are impotent; beyond the highest heaven are unbounded abysses of space; before the beginning of things there was a long chain of interminable ages.

In vain would you undertake to move space; you can only move yourself in it, or survey its various points. Its points are all fixed; you may mark out distances and directions with respect to them, but you cannot change them. The result will be analogous if you attempt to move time. The present instant is not the one just past, nor the one next to succeed; they are of necessity distinct, and of necessity exclude each other. Their very nature is to succeed each other. If their place be changed with respect to time, it ceases to be the same. Imagine, if you can, that to-morrow is to-day, that to-day is yesterday. It is impossible for that which was at a certain time not to have then been; but this would not be impossible if time could be moved; for in order that what was yesterday may not be, it is necessary to convert yesterday into to-morrow; but this would be an absurdity. The past, the present, and the future, are essentially distinct things.

A simple space, a space without parts, is no space at all, it is a contradiction; neither is a simple time, a time without parts, a time, but is a contradiction.

A space whose parts are not continuous, is not a space; neither is a time whose parts are not continuous, a time. The parts of space are inseparable; you may distinguish them one from another, count them one after the other, compare them one with another, and consider them one after another, but you cannot separate them. All imaginable bodies may exist in the apartment where we write, one or many, at rest or in motion; but the space which we conceive is one, fixed, and always the same; we can estimate its extent in cubic feet, if we choose, but these feet are fixed and inseparable; we cannot separate one cubic foot from another, even if we would; for even while we annihilate it, it is present to us, and in the same distance that we need in order to conceive separation. We cannot conceive separation, if we do not conceive distance; nor conceive distance, if we do not conceive space. We separate bodies from each other, but not one space from another. Space remains with the same continuity when bodies are separated, and it is by this continuity remaining unalterable that we measure the extent of their separation. The same happens with time; it is a chain which cannot be broken. Can we conceive three successive, immediate instants, A, B, C, and then suppress B? Certainly not; such a suppression would be impossible, or it would be a poor diversion. We destroy B in our caprice, and A and C are continuous; since being only separated by B, when it disappears the extremes meet. But in this case it is no longer A, but B, for B is the instant which precedes C. We have no other distinction than that of priority with respect to C, and continuity with A. When, then, by the imaginary disappearance of B, A is brought into contact with C, it is converted into B. Moreover, A is not only connected with C, but is preceded by others; if, then, by the disappearance of B, it makes a step, so also must the whole infinite chain which precedes it. Each one is then a soldier, or rather no soldiery is possible, for we have taken an instant from the infinite chain, and so rendered it finite. Or, more distinctly; can we conceive yesterday or to-morrow without to-day, a future or a past without the present? Evidently we cannot. Time, then, is essentially composed of inseparable parts.

19. This similarity between time and space naturally leads us to believe that time is an abstract idea just as space is. What we have said of space is applicable to time, only with a few modifications exacted by the very nature of the thing. It can in no case be without utility, in scientific investigations, to approximate and compare these great ideas, which are as immense receptacles wherein our mind deposits its treasures. The actual corporeal universe, and all possible universes, are included in the idea of space; and all finite beings, corporeal or incorporeal, are included in that of time.

20. We may well suspect that these ideas, so intimately united to our perceptions, are formed in a similar manner; for it is probable that they belong to the order of those primitive laws which govern the development of our intellect.

21. The similarity between space and time must not make us ignore the differences which distinguish them.

I. All the parts of space are co-existent; otherwise, that continuity which is essential to them, would be inconceivable. Time is composed of successive parts; to imagine them co-existent, is to destroy the essence of time.

II. Space refers solely to the corporeal world, under only one aspect, that of continuity. Time extends to all that is successive, corporeal or incorporeal.

III. Consequently, the idea of space exists only in the geometrical order, of which it is the basis. The idea of time is mingled with every thing, and more especially with our own acts.

IV. Our soul, when reflecting upon itself, can totally prescind space, and forget all its relations with extended objects; but it cannot prescind time, which it finds necessary even to its own operations.

This last difference is a great help to the understanding in what the idea of time consists; and we venture to recommend it to the attention and memory of the reader.

[CHAPTER IV.]

DEFINITION OF TIME.

22. Time is duration; but duration without something which endures, is an absurdity. There can then be no time without something existing. The duration which we conceive, after reducing every thing to nihility, is a vain imagination; it is not an idea, but is rather in contradiction with ideas.

An important consequence flows from this; it is, that time in itself, cannot be defined with absolute elimination of every thing to which it refers. Time, then, has no proper existence; and separated from beings is annihilated.

23. Hence, also, it follows that that infinity which we attribute to time, has no rational foundation. We have no other reason to affirm this infinity than a vague conception, which presents it as such; but we cannot fail to perceive that this conception also exists, even if we suppose all to be reduced to nothing. If, then, there is in this supposition a vain diversion of the imagination, it is not an idea, but a contradiction with ideas; and what has once deceived us, no longer deserves any credit. Those infinite ages of time which we conceive prior to the creation, are not nothing; they are an imaginary time, similar to an imaginary space.

24. Time has no necessary relation with movement, since if nothing were to move, or even no bodies to exist, we should nevertheless conceive time in the succession of operations of our soul. This last is indispensable; we must have some succession of things in order to conceive time. If we suppose nothing to change or to be altered, a being subject to no external or internal change, having one single thought always the same, one single will always the same, having no succession of ideas or acts of any kind whatever, we conceive nothing to which the idea of time is applicable.

Time is a measure; but what is it to measure in a being of this kind? Succession? But there is no succession. Duration? But what is there to measure in a duration always the same, which is only the same being? Duration must have parts given to it before it can be measured; but what parts has it? Those of time? But this would be a begging of the question, since time is applied to it when we are inquiring whether time is applicable to it. When theologians say that the existence of God cannot be measured by time, that there is no succession in eternity, but that all is united in a single point, they utter a profound truth; and Clarke, before ridiculing it, should have studied to understand it.

25. Time commences with mutable things; if they perish, it perishes with them. There is no succession without mutation; and consequently, no time.

26. What, then, is time? The succession of things considered in the abstract.

What is succession? Being and not-being. A thing exists; it ceases to exist; here we have succession. Whenever time can be calculated, there is succession; and whenever succession can be calculated a being and a not-being are considered. The perception of this relation, of this being and not-being, is the idea of time.

27. Time cannot exist without being and not-being; because in this, succession consists; wherever there is succession, there is some mutation; and there is no mutation without something being in another manner, and this other manner is not possible unless the prior manner ceases to be.

Substances, modifications, and appearances have no succession without this being and not-being. What is motion? The succession of the positions of a body with respect to various points; and this succession is verified by occupying some of these positions and destroying others. What is the succession of thoughts or affections of our mind? The not-being of some which were, and the being of others which were not.

28. Time, then, in things, is their succession, their being and not-being. Time in the understanding, is the perception of this mutation, this being and not-being.

[CHAPTER V.]

TIME IS NOTHING ABSOLUTE.

29. Is time something absolute? The definition given in the last chapter shows clearly enough that it is not. Time in things is not being only, nor not-being only, but the relation of being and not-being. Time in the understanding, is the perception of this relation.

The measure of time is nothing else than the comparison of mutations among themselves. To us, those mutations which seem to be unalterably uniform serve as the primitive measure. For this we have taken the movement of the sun. This movement varies when compared with that of the stars, and ceases to be the primitive measure when referred to this: and it was upon this the scholastics rested when they taught that the movement of the first heavens was the primitive measure of time.

30. But what if the velocity of the sun were augmented, and it should make its revolution in one half of its time? Would the hours continue the same? We distinguish. If this alteration should be verified solely in the solar movement, we should perceive the discordance between this and all other movements; and perceiving this alteration in the sun, we should continue to refer our hours as things fixed to other measures, to our own movements, to our time-pieces, or to other heavenly bodies.

But if we suppose every thing to be changed at one and the same time, and in the same proportion; the movement of all the heavens and of every thing terrestrial to be doubly accelerated, but in such a way as not to increase the rapidity of our thoughts; we should indeed discover an alteration, but we should not know whether to attribute it to the world or to ourselves; we should perceive a discrepancy between our thoughts and these movements, but should not know whether these were accelerated or our thoughts retarded.

If this rapidity be also communicated to us, so that such or such a series of thoughts formerly corresponding to so many minutes is now made in one half the number, we should then witness a perfect correspondence in all things; we could perceive no mutation. An hour, for example, is to us only the perception of the relation of certain mutations: so long as this relation continues the same, there will be no alteration in the hour.

31. To take away from time every idea of absolute, seems an absurdity to the imagination, but not to reason. This case will make this evident. Not the man, the best skilled in perceiving the succession of time, can, if he look at no time-piece, nor refer to any measure for twelve hours, say whether eleven hours and a half or twelve hours have passed. If he live long in this way, he will become totally incapable of estimating time; if locked up in a dark dungeon for several months, he will believe he has spent years there. The idea, therefore, of the measure of time, is nothing absolute; it is essentially relative; it is the perception of the relations between various mutations. So long as these relations remain whole and intact, time will be to us the same.

[CHAPTER VI.]

DIFFICULTIES IN THE EXPLANATION OF VELOCITY.

32. Here arises a serious difficulty: if time be nothing absolute, greater or less velocity is inexplicable. This seems to result even from what we have said, that if the relation of movements be not changed, any augmentation or diminution of velocity is impossible; because, if velocity be in necessary relation to time, and time itself be nothing but the relation of mutations, it is inconceivable how time, and consequently how velocity, can be changed without changing the relation of mutations. Thus it would be impossible for the velocity of the whole mechanism of the universe to be changed, just as it would be absurd to say that the stars and every thing that exists may now experience the same changes of velocity. This would destroy the very idea of velocity; at least if taken as something absolute, wherein different grades may be considered.

33. Let us now examine this difficulty, which indeed deserves to be examined, for it seems to contradict our most common ideas.

First of all, we must premise that velocity is not something absolute, but a relation. Physicists and mathematicians express it by a fraction whose numerator is the space run over and whose denominator is the time consumed. Making V the velocity, S the space, and T the time, we shall have V = S/T. This shows the velocity to be essentially a relation; for it cannot be otherwise expressed than by the ratio of the space to the time.

34. This mathematic formula expresses the idea we all have of velocity; it expresses in three letters what the unlettered man repeatedly says to himself. The velocity of two horses is ascertained not solely by the space they have passed over, nor solely by the time they have consumed in their career, but by the greater or less space passed over in a given time; or by the longer or shorter time required to pass over a given space.

To deny, then, to velocity an absolute nature, is nothing new; for we all of us make it essentially consist in a relation.

35. In the expression V = S/T two terms enter, space and time. Viewing the former in the real order, abstraction made of that of phenomena, we more easily come to regard it as something fixed; and we comprehend it in a given case without any relation. A foot is at all times a foot; and a yard, a yard. These are quantities existing in reality; and if we refer them to other quantities, it is only to make sure that they are so; not because their reality depends upon the relation. A cubic foot of water is not a cubic foot because the measure so says, but on the contrary, the measure so says because there is a cubit foot. The measure itself is also an absolute quantity; and in general, all extensions are absolute, for otherwise, we should be obliged to seek measure of measure, and so on to infinity. True, to call things large or small depends upon comparison; but this does not change their own quantity. The diameter of the earth, compared with an inch measure, is immense; but it is an almost imperceptible point compared with the distance of the fixed stars; yet this does not prevent the inch measure, the diameter of the earth, and the distance to the fixed stars, from being values in themselves determinate, and independent of each other.[27]

If the denominator in S/T were a quantity of the same kind as space, that is, having determinate values, existing and conceivable by themselves alone, the velocity, although still a relation, might also have determinate values, not indeed, wholly absolute, but only in the supposition that the two terms, S and T, having fixed values, are compared. Thus, if we require a velocity of 4, we have only to take a fixed quantity of space, and another fixed quantity of time, having the relation to each other of 4 to 1; and this is quite easy, when S and T are both absolute quantities. If, in this supposition, an acceleration or delay be required in the whole universe, nothing more would be required than to augment or diminish the time in which each part would have to traverse its respective space. But from the difficulties which we have on the one hand seen presented to the consideration of time as an absolute thing, and from the fact that, on the other hand, no solid proof can be adduced to show such a property to have any foundation, it follows that we know not how to consider velocity as absolute, even in the sense above explained.

36. Hence a consequence not less important than striking, as to the possibility of a universal acceleration or retardation. If we would have an acceleration or retardation of the whole machine of the universe, and should abandon all motion to which we might refer time, should at once change all, not excluding the operations of our own soul, we should have a problem proposed to us that appears insolvable, nothing less than the realization of an impossibility; the relation of many terms would have to be changed without undergoing any change. If velocity be only the relation of space and time, and time only the relation of spaces traversed, it is the same thing to change them all in the same proportion, and not to change them at all; it is to leave every thing as it is.

37. The singularity of such consequences ought not to be a sufficient excuse for abandoning them. We must not forget that we are examining the common ideas of time and velocity in their most transcendental aspect, and that it is by no means astonishing that our mind finds itself, as it leaves its ordinary walks, in an entirely new atmosphere, wherein it seems to discover contradictions. When we examine the ideas of time and velocity, we unwittingly fall into the error of uniting them in the same explanation. We would prescind them; but this we do only with great difficulty, and we often fall into a vicious circle. Hence it is that when, by a great effort, we succeed in really prescinding, the consequences that follow seem contradictory; but this apparent contradiction arises solely from our not having persevered with due firmness in our prescision; and as, in this case, the understanding starts from two different suppositions, whereas it believes that it starts from one alone, the results seem to it contradictory, which in reality they may not be. The same thing occurs in the examination of the idea of space.[28]

[CHAPTER VII.]

FUNDAMENTAL EXPLANATION OF SUCCESSION.

38. The reasons that destroy the absolute nature of time, inasmuch as it is subject to measure, do not seem fully to obviate another difficulty, arising from the consideration of time in itself. If indeed time be succession, what is this succession? It is evident that things succeed each other; but if there be no before or after, that is, time existing before succession, since succession consists in some things coming after others, what is the meaning of succeeding each other? Thus, time is explained by succession, and succession by time. What is afterwards but a part of time that is in relation with a heretofore?

39. What we said in the fourth chapter does not seem completely to solve the difficulty; for being and not-being do not form succession, save only inasmuch as one comes after the other, that is, inasmuch as it presupposes the time to be explained already to exist. There may be a simultaneous being and not-being of distinct things; and there is in one and the same thing no repugnance between being and not-being, if not referred to the same time. In such a case, therefore, this is always presupposed so to be; since in one and the same thing, being and not-being are inconceivable unless at different instants of time. Hence it follows that being and not-being do not sufficiently explain time.

40. This difficulty is indeed grave; and we must, in order to solve it, elaborate a fundamental explanation of succession. This we shall endeavor to do, and without in any sense supposing the idea of time.

41. There are things which exclude, and things which do not exclude each other. When we have existence of things which exclude each other, we have succession. If in a line a————b————c, a body be at a, it cannot pass to b, without ceasing to be at a. The situation at b excludes that at a; and so also that at c excludes that at b. When we see things exist notwithstanding this reciprocal exclusion, we find succession.

42. Succession is, in reality, the existence of things mentally exclusive of each other. What each involves is the being of that which excludes, and the not-being of that which is excluded.

43. This exclusion prevails in all variations; and therefore, we find succession in every variation. Variation is the mutation of states; the loss of one, and the acquisition of another; therefore, there is exclusion, for being excludes not-being, and not-being, being.

44. When we perceive these distinctions, these exclusions realized, we perceive succession, time. When we compute these exclusions, these distinctions in which distinct and exclusive things are offered to us, such as being and not-being, we compute time.

45. Here arises a difficulty. If succession involves exclusion, and there is no succession without exclusion, it follows that things which do not exclude each other are simultaneous; and from this we infer the absurdity of saying, that the things happening in the time of Adam, which do not exclude those of our own time, are simultaneous. The motion of the plants of Paradise excludes not that of plants in gardens now existing; this motion, then, is simultaneous with that; the motion that was then is the present; and the present motion was then; which is inconceivably absurd.

This difficulty is serious: it seems to be based upon a reason founded in evident truths; but it is not impossible to give a solution of it.

46. Were there to exist one thing which excluded nothing, and was excluded by nothing, it would be simultaneous with every thing. Know you what this thing is? There is but one, God. It is therefore that the theologians say, with great truth, and with a profoundness which has not, perhaps, been at all times understood even by those who have made the remark, that God is present to all times; that to him there is no succession, no before or after; that to him every thing is present, is now.

47. Of God alone is this true; in all else there is some exclusion, being and not-being, and therefore succession. Let us now, for example, examine how the motion of the plants in our gardens is excluded by that of the garden of Eden. How are those of our gardens moved? By existing, and also by being subject to conditions necessary to motion. How do they exist? By a development of the germs they themselves contain. What is this development? A series of motions, of being and of not-being, and consequently of things that exclude each other. There is, then, no simultaneousness between those of the garden of Eden and those of our own gardens; for between the former and the first germ, there was no mediation other than the movement of the first development; whereas, between the movements of those of our gardens and the first germ, many others have intervened. Here we have exclusion, being and not-being. The number of exclusions necessary to existence is very different in the two cases; therefore, there is no simultaneousness. Considering all the developments, and all the changes of the orb, as a dilated series of terms interlaced by a mutual dependence, as in fact they are by the laws of nature; and calling these terms A, B, C, D, E,—N, the plants of the garden of Eden belong to the term A, and those of ours, to the term N.

48. The non-simultaneousness of motion is proved in the same manner as the non-simultaneousness of existence, for motion is a manner of existing. Moreover, the air which agitates the plants of our gardens has been moved by another, and this other by yet another; and these motions, subject to all the fixed and constant laws of nature, are all interlinked from the very first motion, just as the wheels are interlocked in a system of machinery. But as the curvature of one wheel is not that of the other, so these motions are different, and exclude one another down to the last, which is the air which moves the present plants.

49. This explanation of succession and time, throws much light on the idea of eternity; and shows that eternity, or the simultaneousness of all existence, belongs only to the immutable being. All mutable beings, which necessarily imply a transition from not-being to being, and from being to not-being, involve a succession, if not in their substance, at least in their modifications.

50. This explains how the idea of time is found in almost all our conceptions, and is expressed in all languages. Man continually perceives being and not-being in all around him. He perceives it within him, in the multitude of his thoughts and affections; at one time agreeing, at another disagreeing; sometimes connected, and sometimes separated; but always distinguished from one another, always producing different modifications in the mind: they therefore exclude each other, and cannot co-exist; because the existence of one excludes the existence of the other.

[CHAPTER VIII.]

WHAT IS CO-EXISTENCE?

51. If the succession of time involves exclusion, there must be co-existence where there is no exclusion: therefore, supposing that God has created other worlds, they must necessarily be contemporaneous with the present; for it is evident that they would not be excluded; and as they have not the mutual relation of cause and effect like the phenomena of the present world, we cannot apply to them the explanation which we gave to show that the motion of the plants of Paradise was not contemporaneous with the motion of the plants in our gardens. We must, therefore, hold that it would have been impossible for another world to exist before the present world; and that though God might create as many beings as he pleased, yet, so long as they do not exclude each other, they must be contemporaneous.

52. This difficulty is not easy to solve, unless we have perfectly understood the meaning of the word exclusion. By exclusion is meant, not only the intrinsical repugnance of one being to another, but that, for one reason or another, whether intrinsical or extrinsical, the existence of one implies the negation of the existence of the other. This explanation solves the difficulty.

53. Two worlds, entirely independent of one another, could have been subjected to this exclusion by the will of God. God can create one without creating the other; in this case, we find the existence of the first and the negation of the existence of the other. God can cease to preserve the first, and create the second; we then find the existence of the second and the negation of the first. In both these cases, there is before and after, a succession in existence. God can create both; we can conceive the existence of both without the negation of the existence of either; this is co-existence.

54. We shall understand the whole question much better, if we examine for a moment the meaning of co-existence. Two beings co-exist, or exist at the same time, when there is no succession of one to the other, when both exist, when there is not the existence of one and the negation of the other. In order to conceive co-existence, we need only conceive the existence of two beings: we form the idea of succession, by combining with the idea of the existence of one the idea of the negation of the other. The co-existence of two beings is their existence; their succession is the being of one, and the not-being of the other. Being refers only to the present; the past and the future are not being. That only is which is, not that which was, or which will be. There is a profound truth, a sound philosophy, and an admirable ontology in those words of the sacred text: "I am who am. He who is, hath sent me to you."

55. Without being and not-being, there is no succession, there is no time, there is only the present, there is eternity. To a being immutable in itself, and in all its acts, one in its intelligence, one in its will, always its own object, unchangeable, in the plenitude of its being, without any kind of negation,—to such a being there is neither before nor after; there is only now. If you give to it the succession of instants, you apply to it, without any ground, the work of your imagination. Reflect well on the meaning of before and after, in that which can change in nothing, by nothing, and for nothing, and you will see that succession is in this case a word without any meaning. We attribute to it succession because we judge the object by our perceptions, and our perceptions are successive; they have an alternative of being and not-being, even when applied to an immutable object.

56. Every one may experience this in his own mind. Conceive two beings to exist; add to this thought nothing accessory, neither the negation of being, nor of time, nor of any thing else,—merely conceive the existence of two beings, and see if any thing is wanting to complete your idea of their co-existence. If, on the contrary, you wish to perceive succession, or difference of instants, you must perceive the existence of one, and the negation of the existence of the other. Therefore, the idea of co-existence is simple, and implies only the existence of the beings, but the idea of succession is composed of the combination of being with not-being.

57. I must here call attention to the fruitfulness of the idea of being, which, combined with the idea of not-being, furnishes the idea of time. We have before seen, that the ideas of unity and number were favored in the same manner, and we shall soon have occasion to observe, how, from the ideas of being and not-being, spring others, which, although secondary in respect to these, are the most important of all the ideas which the human mind possesses. I call attention to this, from a desire that the reader may become accustomed to refer all ideas to a few points where they are united, not by a factitious chain imposed by arbitrary methods, but by the internal nature of things themselves. What extension is, in relation to sensible intuitions, the idea of being is, in relation to conceptions. The intuition of extension, and the idea of being, are the two fundamental points in all ideological and ontological science; they are two primitive data possessed by the mind, by means of which it can solve all problems, either in the sensible order, or in the purely intellectual. Regarded from this point of view, every thing becomes clear, and is arranged in the most logical order, because it is the order of nature.

58. I wish to make one observation on the method which I have followed in this work. I did not think it well to explain separately my opinion of these general connections of all ideas; for then it would have been necessary to treat philosophy in a systematic order, placing at the beginning what ought to be at the end, and trying to establish as a preliminary doctrine, what ought only to be the result of a collection of doctrines. To attain my object, it was necessary to go on analyzing in succession facts and ideas, without reference to system, without doing violence to them, in order to make them conform to a system, but only examining them, in order to ascertain their result. This, undoubtedly, is the best method. We thus obtain the knowledge of truth as a fruit of our labors on facts, and are not obliged to alter objects for the sake of forcing them to bend to the author's opinion. After the application which we have been making of the ideas of being, and not-being, to one of the most abstruse points of metaphysics, it is not out of place to call the reader's attention to this for a moment, so that he may be able to see the connection of doctrines.

[CHAPTER IX.]

PRESENT, PAST, AND FUTURE.

59. After explaining the idea of co-existence, we came to the definition of the various relations which time presents. They are principally three: present, past, and future. All others are combinations of these.

60. The present is the only absolute time: by this I mean, that it needs no relation, in order to be conceived. The present is conceived without relation to the past or to the future. Neither the past nor the future can be conceived without relation to the present.

61. The past is an essentially relative idea. When we speak of the past, we have to take some point to which it refers, and in respect to which we say it is past. This point is the present, either in reality, or in the ideal order; that is to say, that by the understanding, we place ourselves in that point, and make it present to us, and in reference to it, we speak of the past.

To prove that the idea of past is essentially relative, we may observe, that by varying the points of reference, the past may cease to be considered as such, and may be presented as present or future. Speaking of the events of the time of Alexander, they are presented to us as past, because we consider them in relation to the present moment; but if we are speaking of the empire of Sesostris, the epoch of Alexander ceases to be past, and is converted into future. If we were relating events contemporary with the deeds of Alexander, this epoch would cease to be past or future, and would become present.

The past, therefore, is always in reference to a present point, taken in the course of time, and it is only in respect to this, that any thing is said to have been, to be past; without this relation, the idea of past is absurd, and it is impossible to conceive it.

62. What is the relation of past? According to the definition which we have given of time, when we perceive the being of any thing, and then its not-being, and the being of something else, we say the first is past in relation to the second.

63. What would take place, then, if we should perceive the being of something, and then its not-being, without relation to any other being? This hypothesis is absurd; for we must always have this other being, if we perceive being and not-being.

But it may be replied that we may suppose the disappearance of ourselves, and then the objection would be good. Even though we should disappear, there would still remain intelligences capable of perceiving being and not-being. If there were no finite intelligence, there would still be the infinite intelligence.

64. Here arises a new difficulty; for it may be asked whether the thing would be passed with relation to the infinite intelligence. If we admit that it would be, we seem to introduce time with the duration of God, by which we destroy his eternity, which excludes all succession. If we say that to the eyes of the infinite intelligence the thing would not be past, then it would not be past in reality; for things are as God knows them. Then there would be the idea of being and of not-being, and still there would not be the idea of past. This difficulty arises from a confusion of terms.

Let us suppose that God had created only one being, and this being had ceased to exist; and let us see what would be the result of this hypothesis. God knows the existence and the non-existence of the object. This intellectual act is most simple; there can be no succession in it. There is properly no past with respect to God, and applied to the object this idea can only mean its non-existence in relation to its existence which is destroyed. When the ideas are presented in this light it is easy to understand that there is no past in God, but that there is the knowledge of past things.

65. On this hypothesis, how can the time of only one creature be measured? By its changes. But if it has none? On this imaginary supposition there would be no time.

This conclusion is absolutely necessary, although it may at first sight seem strange. We must either abandon our definition of time, or else admit that there is no time where there is no change.

66. Whatever conclusions we form on questions founded on imaginary suppositions, this, at least, is certain—that the idea of past is essentially relative, and that on no supposition can we conceive the past, if we take from it all relation. The expression has been implies both being and not-being,—the succession which constitutes time. In this relation the order is such that not-being is perceived after being, and this is why it is called past.

67. The idea of the future is also relative to the present. The future is inconceivable without this relation. The future is that which is to come,—that which is to be with respect to a real or hypothetical now; for we may apply to the future what we said of the past, that it is changed by changing the point of its reference. The future for us will be past to those who come after us; that which was future to those past, is present or past to us.

The point of reference of the future is always a present moment; it cannot be referred to the past as its ultimate term; for it is in itself referred equally to the present.

68. Therefore all that we find in the idea of time that is absolute is the present. The present needs no relation. It not only needs none, but it admits none. We can neither refer it to the past nor to the future, because these two times both presuppose the idea of the present, without which they cannot even be conceived.

69. Time is a chain whose links are infinitely divisible. There is no time which we cannot divide into other times. The indivisible instant represents something analogous to the indivisible point; a limit which we approach without ever reaching, an unextended element producing extension. A geometrical point must be moved in order to generate a line; but no motion is conceived as possible unless we presuppose space in which the point moves; or in other words, when we treat of the generation of extension, we commence by presupposing it. A similar thing happens in relation to time. We imagine an indivisible instant, from the fluxion of which results the continuity of duration which we call time. But this fluxion is impossible, unless we suppose a time in which it flows. We wish to examine the generation of time, and we suppose it already existing, prolonged infinitely, as an immense line on which the fluxion of the instant takes place. What are we to infer from these apparent contradictions? Nothing but a strong confirmation of the doctrine which we have established.

Time distinguished from things is nothing. Duration in the abstract, distinguished from that which endures, is a being of reason,—a work which our understanding produces from the materials furnished by reality. All being is present. That which is not present is not-being. The present instant, the now, is the reality of the thing; it is not sufficient to constitute time, but it is necessary to time. There can be present without either past or future; but there can be neither past nor future without the present. When besides being there is not-being, and this relation is perceived, time begins. To conceive past and future without the alternation of being and not-being, as a sort of line infinitely produced in two opposite directions, is to take an empty play of the phantasy for a philosophical idea, and to apply to time the illusion of imaginary space.

70. Therefore, if there is only being, there is only absolute, present duration; therefore no past nor future, and, consequently, no time. Time is in its essence a successive, flowing quantity; it cannot be seized in its actuality; for it is always divisible, and every division in time constitutes past and future. This is a demonstration that time is a mere relation, and in so far as it is in things, it only expresses being and not-being.

[CHAPTER X.]

APPLICATION OF THE PRECEDING DOCTRINE TO SEVERAL IMPORTANT QUESTIONS.

71. This theory will be much better understood by its application to the solution of several questions.

I. How long a time had passed before the creation? None. As there was no succession, there was only the present, the eternity of God. All else that we imagine is a mere illusion, contrary to sound philosophy.

II. Was it possible for another world to have existed when this world's existence began? Undoubtedly it was; this would only require that God had created it, without creating this world; it would only require the being of the one and the not-being of the other. And as there was not-being because there was no creation, it follows that if God had created the one without creating the other, and had ceased to preserve the first when he created the second, there would have been succession and priority of time.

III. Here is another question which is somewhat strange, and at first seems very difficult. Was the existence of a world prior to this possible in any time? or, in other words, could another world have ceased to exist some time before the beginning of the existence of this world? This question implies a contradiction. It supposes an interval of time, that is, of succession, without any thing to succeed. If a world had ceased to exist, and no new world should exist, there would be nothing but God; there would then be no succession, there would be only eternity. To ask, therefore, how long a time they were apart, is to suppose that there is time, where there is none. The proper answer is, that the question is absurd.

But we shall be asked, were they distant, or were they not? There is no distance of time where there is no time; this distance is a mere illusion, by which we imagine time, while, by the state of the question, we suppose that there is no time.

Then it may be objected, that the two successive worlds must be necessarily immediate, that is to say, that the first instant of one must be immediately connected with the last instant of the other. I deny it. For immediateness of instants supposes the succession of beings mutually connected in a certain order; the two worlds in question would have no mutual relation; consequently, there would be neither distance nor immediateness between them.

But, it may be replied, there is no medium between being and not-being, and distance being the negation of immediateness, and immediateness the negation of distance, by denying one, we affirm the other; they must, therefore, either be distant or immediate. This reply also supposes something which we deny. It speaks of distance and immediateness, that is, of time, as though it were something positive, distinct from the beings themselves. The principle, that every thing is, or is not, quodlibet est vel non est, is applicable only when there is something; but when there is nothing, there is no disjunctive. The time of the two worlds is nothing, as distinguished from them; it is the succession of their respective phenomena; the succession of the two worlds, the one to the other, is nothing distinguished from them; it is the being of the one, and the negation of the other, and the being of the second and the negation of the first. God sees this; an intelligent creature would also see it, if he could survive the annihilation of the first world. To the eyes of God, who sees the reality, succession would be simply the respective existence and non-existence of the two objects. The intelligent creature would say, that the two worlds are immediate, if to the perception of the last instant of the annihilated world, the perception of a new existing world had followed without another intermediate perception; and he would say, that there is distance, if he had experienced various perceptions between the annihilation of the old and the perception of the new creation. The measure of this time would be taken from the changes of perceptions of this creature, and would be longer or shorter, according to the number of these perceptions.

72. The idea of time is essentially relative, as it is the ordered perception of being and not-being. The mere perception of one of the two extremes, would not be sufficient to produce the idea of time in our mind; for this idea necessarily implies comparison. The same is true of the idea of space, which has always a great resemblance to time. We cannot conceive space, or extension of any kind, without juxtaposition; that is to say, without relations of various objects. Multiplicity necessarily enters into the ideas of both space and time. Hence, we may say, that if we conceive a being, absolutely simple, with no multiplicity, either in its essence, or in its acts, but in which all is identified with its essence, there is no room for the ideas of space and time; and, consequently, they are mere fictions of the imagination, when we attribute to them any thing real, beyond the corporeal world, and before the existence of the created.

[CHAPTER XI.]

THE ANALYSIS OF THE IDEA OF TIME CONFIRMS ITS RESEMBLANCE TO THE IDEA OF SPACE.

73. Having explained the idea of time, and applied it to the most difficult questions, we may explain this doctrine still farther, by examining what we have already intimated concerning the resemblance between time and space.[29] There is analogy in the difficulties; analogy in the definitions of both ideas; analogy in the illusions which hinder the knowledge of the truth. What we announced before with respect to these two ideas, considering the idea of time as only what it appeared at first sight, we may now assert as the secure result of analytical investigations. I call attention in particular to the following parallel, because it greatly explains the ideas of both.

74. Space is nothing in itself, distinguished from bodies; it is only the extension of bodies: time is nothing in itself, distinguished from things. It is only the succession of things.

75. The idea of space is the idea of extension in general; the idea of time is the idea of succession in general.

76. Where there are no bodies, there is no space: where there are no things which succeed each other, there is no time.

77. An infinite space, before the existence of bodies, or outside of bodies, is an illusion of the imagination: an infinite time before the existence of things, or outside of them, is also an illusion.

78. Space is continuous: so is time.

79. One part of space excludes all others; one part of time also excludes all others.

80. A pure space, in which bodies are situated, is imaginary: a succession, a time, in which things succeed, is also imaginary.

81. That which is entirely simple has no need of space, and can exist without it: that which is immutable has no need of time, and can exist without it.

82. The simple and infinite is present to all points of space, without losing its infinity: the immutable and infinite is present to all instants of time, without altering its eternity.

83. Two things are distant in space, because there are bodies placed between them; this distance is only the extension of the bodies themselves: two beings are distant in time, because there are other beings placed between them; this distance is the existence of the beings which are placed between.

84. Extension needs no other extension, in which to be placed, otherwise we should have a processus in infinitum: the succession of things, for the same reason, needs no other succession in which to succeed.

85. Just as we form the idea of continued succession in space by distinguishing different parts of extension, and perceiving that one excludes the others, so we also form the idea of continued succession of time by distinguishing different facts and perceiving that one excludes the others.

86. In order to form determinate ideas of the parts of space, we must take a measure and refer to it: to form an idea of the parts of time we also need a measure. The measure of space is the extension of some body which we know: the measure of time is some series of changes which we know. To measure space we seek for fixed things, as far as possible; for the want of something better, men have recourse to the parts of the body, the hand, the foot, the yard, and the pace, which give an approximate, if not an exact measure. The exact sciences having advanced, they have taken for their measure the forty-millionth part of the meridian of the earth: time is measured by the motion of the celestial bodies, by the diurnal motion, the lunar, solar, and sidereal year.

87. The idea of number is necessary in order to determine space and compare its different parts: the same idea is necessary in the same manner to time. The discrete quantity explains the continuous.

[CHAPTER XII.]

RELATIONS OF THE IDEA OF TIME TO EXPERIENCE.

88. If time is nothing distinct from things, how does it happen that we conceive it in the abstract, independently of things themselves? How does it happen that it presents itself to us as an absolute being, subject to no transformation or motion, while within it every thing is moved and transformed? If it is a subjective fact, why do we apply it to things? If it is objective, why is it mingled with all our perceptions? Because it contains a necessity sufficient to be the object of science.

The idea of time, whatever it may be, seems prior to all perception of transformation, the consciousness of all internal acts included. It is impossible for us to know any of these things, unless time serves as a receptacle in which we may place our own changes and those of others.

89. The idea of time is not the result of observation; for in that case it would be the expression of a contingent fact, and could not be the principle of science. We measure time with the same exactness as we do space, and it is one of the most fundamental ideas of the exact sciences, in so far as they have any application to the objects of nature.

90. It might seem to follow from this that the idea of time is innate in our mind; and that it is prior to all ideas, and even sensations; for both are necessarily involved in successive duration.

91. The necessity of the idea of time seems to prove that time is independent of transitory things; in this case we are obliged to convert it into a purely subjective fact, or else to grant it an objective reality, independent of that which is changeable. By the former we destroy it; by the latter we make it an attribute of the divinity. To deny time is to deny the light of the sun; to raise it to the rank of an attribute of divinity is to admit change in an immutable being. If we make it purely subjective, we deny it; if objective, we make it divine: is there no middle way?

92. I agree that the idea of time is not derived from mere experience; for experience could not furnish an element so solid and so fixed, on which we may with perfect security rest all the observations of science. Still less can it be maintained, that the idea of time is derived from purely sensible experience, or that it is in itself a sensation.

93. The idea of time is not a sensation; for it is relative, and sensation is an affection of our being, without any reference to or comparison with any thing. When we experience sensations, if we had only the sensitive faculty, we should be limited to pure sensation, without any consideration of before or after, or any relation of any kind. Sensation, being limited to certain objects, cannot, like the idea of time, extend to all objects. By time, we measure not only the external world, but also the internal; not only the affections of the body, but also the most concealed and abstract actions of our mind. Time is, in itself, succession, and, in our mind, it is the perception of this succession; it cannot, therefore, present any object to the mind; even when time refers to objects, and is, as it were, the link between them, it is not itself either these objects themselves, nor the intuition of them. The idea of the time which measures the succession of a sound or of a sight, clearly is not either the sound or the sight, but the perception of their succession, of their connection. If it were the sight alone, or the sound alone, either the sight or the sound would alone be sufficient in order to perceive time, which is absurd; for there is no time without succession, and consequently there can be no time which measures two sensations without these sensations. The idea of time is independent of either of the two; it is superior to them; it is a sort of universal form, independent of this or that matter; so that, if after the sound, instead of the sight, another sound should be perceived by us, the measure of the succession would be the same, and this measure is nothing more than the idea of time. Sensations being mere contingent facts, cannot be the foundation of necessary and universal truths, they cannot serve as the basis of a science. But the idea of time is one of the principal ideas in all the physical sciences, and, like extension, is subjected to a very rigorous calculation; therefore, it is not a sensation, and it is not derived from sensation.

94. Purely experimental cognitions are confined to the sphere of experience; the idea of time extends to the whole real and possible order, it teaches us not only what is, but what may, and what must be; its relations are of absolute necessity, and may be subjected to the strictest calculation; therefore it contains something more than the elements furnished by sensible or insensible experience. It is not otherwise possible to explain the necessity which it involves, or to pass beyond a collection of contingent facts to arrive at the possession of an element of science.

95. Let us observe, as we pass, that here is found another proof that the system of Condillac is neither true nor subsistent. His system has been found insufficient to explain any fundamental idea, and it does not explain the idea of time, any more than the rest, although it seems as though this idea must have the most intimate relations to the sensible order.

96. If the idea of time is not merely experimental, how explain the priority and necessity of time?

[CHAPTER XIII.]

KANT'S OPINION.

97. Kant uses the same theory to explain time that he used to explain space. Time, according to him, is nothing in itself, neither is it any thing in things; it is a subjective condition of intuition, a form of the internal sense, by means of which phenomena are presented to us as successive, just as space was the form by which they are presented as continuous. To speak frankly, it seems to me that this is saying nothing; it affirms a well-known fact, but does not explain it. Who does not know that what we perceive we perceive in succession—that we perceive even our own perceptions in succession? But what is succession? This is what he ought to have explained.

98. Kant says that time is only in us; but I should like to ask him, if succession is only in us. He pretends that we know nothing of the external world, but that we perceive certain appearances, or phenomena; but he does not deny that beyond the appearance there may be a reality. If this reality is possible, changes are possible in it; and change cannot be conceived without succession, nor succession without time.

99. According to Kant, the ideas of space and time are à priori, they cannot be empirical, or experimental; for in that case they could not be the basis of science; we could only affirm what we had experienced, and this only with respect to the cases in which we have experienced it. This is true, and I have demonstrated it in the last chapter; but, conceding this priority, it proves nothing in favor of Kant's system. The ideas of space and time, although à priori, may nevertheless correspond to something in reality, as follows from the theory by which I have explained them.

100. Time is not any thing which subsists by itself, but it is not equally certain that it does not belong, as an objective determination, to things, and that nothing remains of it, if we abstract it from all the subjective impressions of intuition. I have demonstrated that time does not subsist by itself, and that a duration without any thing which endures, is an absurdity; but it does not follow from this that the order represented by the idea of time is not something real in the objects. Abstracting it from our intuition, there still remains something which verifies the propositions by which we express the properties of time.

101. The German philosopher makes time purely subjective, and relies on the following argument: "If time were a condition belonging to the things themselves, or an order, it could not precede the objects as a condition of them, and be known and perceived à priori by synthetical judgments. This last is easily explained if time is nothing but the subjective condition under which all intuitions are possible in us. For then this form of the internal intuition can be represented before the objects, and consequently à priori....

"If we abstract our manner of perceiving ourselves internally, and of embracing, by means of this intuition, all external intuitions in the faculty of representation, and consequently take objects just as they may be in themselves, time is nothing....

"I can say that my representations are successive, but this only means that we are conscious of them in a succession,—that is, in a form of the internal sense. Time would not therefore be any thing in itself, nor a determination inherent in things."[30]