Fundamental Philosophy, Vol. I (of 2)

127. I do not pretend that it is possible to explain why the representation of extension is found in our soul; we might as well ask why we are intelligent and sensible beings. The only reason a priori which we can give, is that God has so created us. This representation may be found in us, and it is so found, for we experience it; but this internal experience is the limit of philosophy; immediate observation can go no farther back. Reason raises us to the knowledge of a cause which created us, but not to a phenomenon which is the source of the phenomena of experience.

128. Why a simple being contains in itself the representation of multiplicity, and an unextended being the representation of extension, is the problem of intelligence, which, because it is intelligence, is one and simple, and capable of perceiving multiplicity and composition.

129. We pass from ideal to real extension by a natural and irresistible impulse, which is confirmed by the assent of reason. This has been demonstrated in the first book, and also in the second when treating of the objectiveness of sensations.

130. Of the five problems the last remains. We must determine how far we may apply to extension what is true of the other sensations, which are considered as phenomena of our soul, having no external object like them, and no other correspondence with the external world than the relation of effects to their cause.

131. The solution of this problem settles the question for or against the idealists. If we may apply to extension what is true of the other sensations, idealism triumphs, and the real world, if it exists, is a being which has no resemblance to the world which we think.

I have proved in treating of sensations49 that extension is something real, and independent of our sensations, and I have shown50 that it represents multiplicity and continuity. This is sufficient to overthrow idealism, and also to explain, to a certain extent, what extension consists in; but as the idea of space, which is closely connected with extension, had not then been examined, it was not possible for us to rise above the order of phenomena and regard extension under a transcendental aspect, examining it in itself, abstracted from all its relations with the world of appearances. This is what I propose to do in the following chapters.

132. We come now to a more cragged path; we have to distinguish the reality from appearance; our understanding, which is always accompanied by sensible representations, must now depart from them, and place itself in opposition to a condition to which it is naturally subjected in the exercise of its functions.

CHAPTER XIX.

EXTENSION ABSTRACTED FROM PHENOMENA

133. That which is extended is not one being only; it is a collection of beings. Extension necessarily contains parts, some outside of, and consequently distinct from, others. Their union is not identity; for, the very fact that they are united, supposes them distinct, since any thing is not united with itself.

It would seem from this that extension in itself and distinguished from the things extended, is nothing; to imagine extension as a being whose real nature can be investigated is to resign one's self to be the sport of one's fancy.

Extension is not identified in particular with any one of the beings which compose it, but it is the result of their union. This is equally true whether we consider extension composed of unextended points, or of points that are extended but infinitely divisible. If we suppose the points unextended, it is evident that they are not extension, because extended and unextended are contradictory. Neither are these points identified with extension, if we suppose them extended; for extension implies a whole, and a whole cannot be identified with any of its parts. If a line be four feet long, there cannot be identity between the whole line and one of its parts a foot long. We may suppose these parts, instead of a foot, to be only an inch in length, and we may divide them ad infinitum, but we shall never find any of these parts equal to any of its subdivisions. Therefore, extension is not identical with any of the particular beings which compose it.

134. The idea of multiplicity being involved in the idea of extension, it would seem that extension ought to be considered, not as a being in itself, but as the result of a union of many beings. This result is what we call continuity. We have already seen51 that multiplicity is not sufficient to constitute extension. It enters into the idea of number, and yet number does not represent any thing extended. We also conceive a union of acts, faculties, activities, substances, and beings of various classes, without conceiving extension, and yet multiplicity is a part of all these conceptions.

135. Therefore continuity is necessary, in order to complete the idea of extension. What, then, is continuity? It is the position of parts outside of, but joined to other parts. But what is the meaning of the terms, outside of, and joined to? Inside and outside, joined and separated, imply extension, they presuppose that which is to be explained; the thing to be defined enters into the definition in the same sense in which it is to be defined. Exactly; for, to explain the continuity of extension is the same as to show the meaning of the terms inside and outside, joined and separated.

136. We must not forget this observation, unless we wish to accept the explanations which are found in almost all the books on the subject. To define extension by the words inside and outside, is not to add any thing, under a philosophic aspect; it is merely to express the same thing in different words. Without doubt this language would be the simplest, if all we wanted was to establish the phenomenon only, but philosophy will not be satisfied with it. It is a practical, not a speculative, explanation. The same may be said of the definition of extension by space or places. What is extension? – the occupation of place: – but, what is a place? – a portion of space terminated by certain surfaces: – what is space? – the extension in which bodies are placed, or the capacity to receive them. But even admitting the existence of space as something absolute, what is the capacity of bodies to fill space? Who does not see that this is to define a thing by itself, a vicious circle? The extension of space is explained by the capacity of receiving; the extension of bodies by the capacity of filling. The idea of extension remains untouched; it is not defined, it is merely expressed in different words, but which mean the same thing.

To suppose the existence of space as something absolute, does not help the question, and is, besides, an entirely gratuitous supposition. To take the extension of space as a term by relation to which we may explain the extension of bodies, is to suppose that to be found which we are looking for.

We run into the same error if we try to explain the words inside and outside, by referring them to distinct points in space, we should define a thing by itself; for, we have the same difficulty with respect to space to determine the meaning of inside and outside, joined and separated, and contiguous and distant. If we presuppose the extension of space as something absolute, and try to explain other extensions by relation to this, we only make the illusion more complete. We have to explain extension in itself, the extension of space must be explained as well as the rest; to presuppose it is to assume the question already solved, not to solve it.

137. Extension in relation to its dimensions seems to be independent of the thing extended in the same place. An extension may remain absolutely fixed with the same dimensions, notwithstanding the change of place of the thing extended. If we suppose a series of objects to pass over a fixed visual field, the things extended vary incessantly, but the extension remains the same. If we suppose a very large object to pass before a window, it changes continually; for the part which we see at the instant A is not the part which we see at the instant B, but the extension has not varied in its dimensions. This regards surfaces only, but the same doctrine may be applied to solids. A space may be successively filled with a variety of objects, but its capacity remains the same. There is no identity between the object and the extension which contains it; for any number of objects of the same size may occupy the same place; neither is the air, or any surrounding object, identified with the extension; for these, too, may change without affecting the extension in which the object is contained.

138. Though the dimensions remain fixed while the objects vary, it does not follow that extension is purely subjective, even though we suppose that the objects which vary cannot be distinguished. If the contrary were maintained, the change of the dimensions would prove them to be objective; and the argument might be retorted against our adversaries. That the dimensions are fixed shows that different objects may produce similar impressions; and therefore we can form an idea of a determinate dimension or figure, without reference to the particular object to which it does, or may correspond. No one will deny that we have the representation of dimensions, without necessarily referring them to any thing in particular; but what we wish to determine is, whether these dimensions exist in reality, and what is their nature, independently of their relations to us.

139. If we admit that continuity has no external object either in pure space or in bodies, what becomes of the corporeal world? It is indeed to a collection of beings which in one way or another, and in a certain order, act upon our being.

The difficulties against the realization of phenomenal continuity are not destroyed by appealing to the necessities of the corporeal organization of sensible beings. If any one should ask how external beings can act upon us, and affect our organs, if they have not in them the continuity with which they are presented to us; such a one would show that he does not understand the state of the question. For it is evident that if we should take from the external world all real continuity, leaving only the phenomenal, we should at the same time take it from our own organization, which is but a part of the universe. There is here a mutual relation and sort of parallelism of phenomena and realities which mutually complete and explain each other. If the universe is a collection of beings acting upon us in a certain order, our organization is another collection of beings, receiving their influence in the same order. Either both are inexplicable, or else the explanation of one involves the explanation of the other. If that order is fixed and constant, and its correspondence remains the same, nothing is changed, no matter what hypothesis is assumed in order to explain the phenomenon.

140. The object of our searches here, is the reality subject to the condition of explaining the phenomenon, and not contradicting the order of our ideas.

It might be objected to those who take from the external world the phenomenal or apparent qualities of continuity, that they destroy geometry, which is based on the idea of phenomenal continuity. But this objection cannot stand; for it supposes the idea of geometry to be phenomenal, whereas it is transcendental. We have already shown that the idea of extension is not a sensation, but a pure idea, and that the imaginary representations by which it is made sensible are not the idea, but only the forms with which the idea is clothed.

141. All phenomenal extension is presented to us with a certain magnitude; geometry abstracts all magnitude. Its theorems and problems relate to figures in general abstracted absolutely from their size, and when the size is taken into consideration it is only in so far as relative. Of two triangles of equal bases that which has greater altitude has the greater surface. Here the word greater relates to size, it is true; but to a relative, not to any absolute size; the question is not of the magnitudes themselves, but of their relation. Consequently, the theorem is equally true whether the triangles are immense, or infinitely small. Therefore, geometry abstracts absolutely all magnitudes considered as phenomena, and makes use of them only in order to assist the intellectual perception by the sensible representation.

142. This is an important truth, and I shall explain it further when combating Condillac's system in the treatise on ideas, where I shall show that even the ideas which we have of bodies neither are, nor can be, a transformed sensation. According to these principles, geometry is a science which makes its pure ideas sensible by a phenomenal representation. This representation is necessary so long as geometry is a human science, and man is subject to phenomena; but geometry in itself and in all its purity has no need of such representations.

143. In order that this doctrine may seem less strange, and may be more readily accepted, I will ask, whether pure spirits possess the science of geometry? We must answer in the affirmative; for, otherwise we should be forced to conclude that God, the author of the universe and greatest of geometricians, does not know geometry. Does God, then, have these representations, by the aid of which we imagine extension? No; these representations are a sort of continuation of sensibility which God has not; they are the exercise of the internal sense, which is not found in God. St. Thomas calls them phantasmata, and says they are not found in God, or in pure spirits, nor even in the soul separated from the body. Therefore, the science of geometry is possible, and does really exist without sensible representations, and, consequently, we may distinguish two extensions, the one phenomenal, and the other real, without thereby destroying either the phenomenon or the reality, so long as we admit the correspondence between them; so long as we do not break the thread which unites our being with those around us; so long as the conditions of our being harmonize with those of the external world.(32)

CHAPTER XX.

ARE THERE ABSOLUTE MAGNITUDES?

144. The preceding doctrine will seem much more probable if we reflect that all purely intellectual perceptions of extension may be reduced to the knowledge of order and relation. There is nothing absolute in the eyes of science, not even of mathematical science. The absolute, in relation to extension, is an ignorant fancy which the observation of the phenomena is sufficient to dissipate.

In the order of appearances there are no absolute magnitudes; all are relations. We can not even form an idea of a magnitude, unless with reference to another which serves for a measure. The absolute is found only in number, and never in extension; a magnitude is absolute, not in itself, but only by being numbered. A surface two feet square, presents two distinct ideas; the number of its parts, and the kind of parts. The number is a fixed idea, but the kind is purely relative. I will try to make this clearer.

145. When I speak of a surface four feet square, the number four is a simple, fixed, and unchangeable idea; but I can explain a square foot only by relations. If I am asked what is a square foot, I can answer only by comparison with a square rod or a square inch; but if I am again asked what is a square rod or a square inch, I am again forced to recur to other measures which are greater or smaller; I can nowhere find a fixed magnitude.

146. If there were some fixed measure it might be some dimension of the body, my hand, or foot, or arm. But who does not see that the dimensions of my body are not a universal measure, and that the hands, or feet, or arms, of all men are not equal? And even in the same individual they are subject to a thousand changes more or less perceptible. Shall we take for our fixed measure the radius of the earth, or of a heavenly body? But one has no claim to preference before the other. Every one knows that astronomers take sometimes the radius of the earth, and sometimes the radius of its orbit as the unity of measure. If we suppose these radii to be greater or smaller, can we not equally in either case take them as the measure? They are preferred because they do not change.

But even astronomers regard these magnitudes as purely relative, and at one time consider them infinitely large, at another infinitely small, according to the point of view from which they look at them. The radius of the earth's orbit is considered infinite in comparison with a small inequality on the earth's surface, and infinitely small when compared with the distance of the fixed stars.

We can form no idea of these measures except by comparison with those in constant use. What idea should we have of the magnitude of the radius of the earth if we did not know how many million measures it is equal to? What idea should we have in turn of these measures if we had nothing constant to which we could refer them?

147. There is something absolute in magnitudes, it may be objected; for a foot is a certain length which we both see and touch, and cannot be greater or smaller; the surface of a square yard is in like manner something definite which we see and which we touch; and the same may be applied to solids. There is no necessity of going farther to find that which is so clearly presented to us in sensible intuition. This objection supposes that there is something fixed and constant in intuition; this is false. I appeal to experience.

It is probable that men see the same magnitudes very differently according to the disposition of their eyes. No one is ignorant that this happens when the objects are at a distance; for, then, one sees clearly what another cannot even distinguish; to one it is a surface, while to another it is not even so much as a point. We all know what a great variety there is in the size of objects when looked at through differently graduated glasses. From all this we conclude that there is nothing fixed in phenomenal magnitude; but that every thing is subject to continual changes.

When we look through a microscope objects which were before invisible, take large dimensions; and as the microscope may be infinitely perfected, it is not absurd to suppose that there are animals to whom what is invisible to us appears larger than the whole earth. The construction of the eye may also be considered in an inverse sense, and as infinite perfection is also possible in this case, it is possible that magnitudes which to us are immense may be invisible to other beings. To this eye of colossal vision the terrestrial globe would perhaps be an imperceptible atom. This is no more than what happens by the interposition of distance; immense masses in the firmament seem to us to be only small specks of light.

148. It must now be very evident that there is nothing absolute in magnitudes of sight; but that all is relative, and that objects appear to us greater or less, according to habit, the construction of our organs, and other circumstances. The variety of appearances is in accordance with philosophy; since no necessary relation can be discovered between the size of the organ and the object. What connection is there between a narrow surface like the retina of our eye and the immense surfaces which are painted on it?

149. From sight we may pass to touch, but we find no reason of the fixity of phenomenal magnitude. The sense of touch gives us the ideas of magnitudes by relation to the time it takes to pass over them, and to the velocity of our motion. The ideas of time and velocity are also relative; they refer to the space passed over. When we measure velocity we say that it is the space divided by the time; in measuring time we say that it is the space divided by the velocity; and we measure space by multiplying the velocity by the time. All these ideas are correlative, and are measured by each other, and by their mutual relations. This shows that these ideas have nothing absolute; their whole character is that of a relation which is incomplete, or rather does not exist, if one of the terms is wanting.

150. We shall find it equally impossible to determine these measures by the impressions which the motion causes in us. If for example we propose to measure the degree of velocity, by the agitation which we feel in our body, we shall find that the measure varies with the agitation, but this agitation depends on the degree of force exerted, and still more on the strength of the subject. Thus a little child is obliged to run till he is almost out of breath, to keep up with his father who is walking fast.

The impossibility of any fixed measure by means of impressions will be still more apparent if we compare the motion of a horse with the motion of a microscopic animal. The distance which a horse would pass over almost without any sensible motion, would require the microscopic animal to display its whole activity, and run perhaps a whole day. The horse would scarce believe he had changed his place, whereas the poor animalcule would at night be overcome by fatigue like one who has travelled a long journey. Compare now the motion of the horse with the motion of those fabulous giants who piled up mountains to scale the heavens; a single step of one of those giants would be a long distance for the horse to travel.

151. Art seems to be in accordance with science on this point. In art, size is nothing, the only thing which is regarded is the proportion or relation. A skilful miniature represents a person as clearly as a painting the size of life. The same principle is applied to all the objects embraced by art, the artistic thought never refers directly to the size; proportion, the relative is all that is attended to; the absolute counts for nothing. We see the system of relations transferred to the order of appearances, inasmuch as they affect the faculties susceptible of pleasure; reason is thus admirably harmonized with sentiment, in the same manner as we have found intellect harmonized with the senses.

CHAPTER XXI.

PURE INTELLIGIBILITY OF THE EXTENDED WORLD

152. Objects in themselves do not change their nature, by the variety of appearances which they produce in us. A polygon turning with rapidity has the appearance of a circle; the stars appear like small points; and considering the various classes of objects, we may observe that there is a great variety of appearances depending on circumstances. The nature of a being does not consist in what it appears, but in what it is. Suppose there were no sensitive being in the world, the present order of sensibility would disappear; for without sensitive beings there would be no representations. What would the world be in that case? This is a great problem of metaphysics.

153. A pure spirit, – the existence of which we must always suppose; for, though all finite beings were annihilated, there would still remain the infinite being which is God, – a pure spirit would know the extended world just as it is in itself, and would not have the sensible representations either external or internal, which we have. This is certain, unless we mean to attribute imagination and sensibility to pure spirits, and even to God himself.

On this supposition I ask, what would a pure spirit know of the external world? or, to speak more properly, since the existence of such a spirit is certain and its intelligence infinite, what does this spirit know of the external world?

154. That which this spirit knows of the world is the world, because he cannot be deceived. But this spirit does not know the world under any sensible form. Therefore the world may be known without any of the forms of sensibility, and consequently may be the object of a pure intelligence.

There is no difficulty on this point in what regards sensations. It is only necessary that we should say that the pure spirit knows perfectly the principle of causality which resides in the object, and produces the impressions which we experience. There is no need of attributing to the intelligent spirit any sensation of the thing understood.

This question is more difficult when we come to explain what relates to extension. For, if we say that the spirit only knows the principle of causality of the subjective representation of the extended, it follows that there is no true extension in the objects, because the spirit sees all that there is, and if the spirit does not see it, it is because it is not. We fall into Berkeley's idealism; an external world without extension is not the world of common sense, but the world of the idealists. If, on the other hand, we say that this pure spirit does know extension, we seem to attribute to the spirit sensible representation; because the extension represented seems to involve sensible representation. What is an extension with lines, surfaces, and figures? And these objects, as we understand them, are sensible; if, however, they be taken in another sense, the extension of the world will be of another nature, it will be something of which we have no idea; and here again we fall into idealism.