Volume 1 / Book 3 — CHAPTER XXXIV.

CONCLUSION AND SUMMING UP.

262. Before passing to another subject, let us fix our attention for a few moments on the nature and origin of the idea of extension. We shall thus collect the fruit of the preceding investigations, and prepare the way for those which follow.

The scientific fruitfulness of this idea to our mind proves how distant sensible impressions are from intellectual perception. We cannot know whether this idea existed in our mind before the sensible impression; if it did exist we were not conscious of it, and in this respect it is affirming a gratuitous proposition to say that it is an innate idea. What we can safely say, is, that there are two distinct orders of internal phenomena, that sensation could not have produced the idea, that this idea is immeasurably superior to the external impression, or even the internal sensitive intuition, and that if it did not already exist in the mind, it was not produced by sensation as an effect is produced by its cause.

263. Here we make an important transition from the order of sensations, to the order of ideas, and discover in our mind a new class of facts. It matters little whether these facts exist before the impression, or result from its presence. In the first case, we see in the mind a deposit of germs which need only the warmth of life in order to be developed; in the second, we find in the mind a fertility which produces these germs. In either case we find a being of a privileged nature, a sublime being which by a single leap rises above the region of matter, and awakened by the external impression, arises to a new life which this world cannot contain.

264. In this sense there are innate ideas; ideas which sensation could not have produced. In this sense all general and necessary ideas are innate; for sensation could not produce them. Sensation is never any thing more than a phenomenon, a particular and contingent fact, and consequently incapable of producing general ideas, or the ideas of the necessary relations of being. Sight, or the imaginary representation of a triangle, is a contingent phenomenon which tells us nothing of the necessary relations of the sides and angles to each other. In order to perceive these relations, this necessity, something else is required. This something else, call it innate ideas, force, fecundity, or activity of the mind, or any thing you please, exists, and could not have been produced by sensation, but belongs to a higher order distinct from sensible phenomena.

265. After such long investigations of the phenomena of sensation, we at last find an idea; it is the idea of extension, the foundation of all the mathematical sciences and of their application to the laws of nature.

The human mind, in all its relations with the material world, seems to have one great idea, that of extension, which, modified in infinite ways, is the origin of all the sciences which relate to matter. The whole material world rests on this idea, and all knowledge of material objects proceeds from it. It is a pure idea in its necessary relations and in its necessary branches. It is a light given to the lord of creation that he may know and admire the prodigies of nature.

266. We find the same wonderful simplicity amidst so complicated a multiplicity in another order of ideas. Hence we infer that the whole edifice of the sciences and all human knowledge are founded on a small number of ideas, perhaps on two alone. These ideas are not sensible representations, they are the objects of pure intuitions; they cannot be decomposed, but they may be applied to an infinite variety of things; they are not explained by words, as a union including various conceptions; by them a mind acts on another mind, not to teach it any thing, but to make it concentrate its activity in order to note what it contains within itself, and learn, in a certain measure, what it already knows.

Try to explain extension, the idea by which we perceive this order which we cannot express in words, but on which we found sensible experience and geometrical science, and you can find no expression. Will you define it to be "parts outside of parts?" But what are parts, and what does outside mean, if you have not the idea of extension? Take any extended thing, make your mind concentrate itself and exercise its activity in generalization. Is this triangle a quadrilateral? No. Are they both extended? Yes. Is this surface a solid? No. Are they both extended? Yes. Are all triangles different from quadrilaterals? Yes. Have all surfaces and solids extension? Yes. How do you pass from one fact to all the facts of the same kind, from the contingent to the necessary? Have you explained what extension is? No. Have you shown what there is common to all these different things? No. All that you have done then is to arouse the activity of your mind, and to make it direct its attention to the general idea of extension, and the mind applies this idea to various things which are different, yet have something in common, it applies the different modifications of this idea to various things which have something in common, and finds them different. You have not taught the truths of geometry to the mind, but have awakened them in it, whether they already existed in it, or the mind had the faculty of producing them.

267. Let us now collect the result of the investigations we have made. I do not give an equal value to all the propositions which follow. I have explained my opinion of each in its proper place, but I consider it well to sum them all up here in order to assist the understanding and help the memory.

I. There is immediate certainty of our relations with beings distinct from us.

II. There is certainty of the existence of an external world.

III. The external world in relation to us, is only an extended being which affects us, and is subject to constant laws which we may determine.

IV. We have the idea of extension.

V. The idea of extension is excited by sensations, but it is not confounded with them.

VI. The idea of extension is the basis of all our cognitions of bodies.

VII. The idea of extension should not be confounded with the imaginary representation of extension.

VIII. An extended space which is nothing real, is an absurdity.

IX. Space is nothing real distinguished from the extension of bodies.

X. Where there are no bodies, there are no distances.

XI. Motion is the change of the positions of bodies among themselves.

XII. There is not and cannot be vacuum of any kind.

XIII. The idea of space is the idea of extension in the abstract.

XIV. The imagination of an unlimited space is only an attempt of the imagination to follow the understanding in the abstraction of extension. It also arises from our habit of seeing through transparent mediums, and moving in fluids whose resistance is not perceptible.

XV. As all that we know of bodies is, that they are extended and affect us, whatever has these two conditions is to us a body.

XVI. But as we do not know the essence of bodies, we do not know whether a body can exist without extension.

XVII. Neither do we know what modifications the extension of one body may be subject to, with respect to others.

XVIII. The elements of which bodies are composed are unknown to us.

XIX. The approximation of some bodies to others, and the gravitation which results from it, seem to be the necessary effect of their present relations.

XX. The necessity of approximation does not suffice to explain the laws of motion, or their beginning, or their continuation.

XXI. The idea of space is not an absolutely necessary condition of sensation.

XXII. The idea of extension has a real objectiveness.

XXIII. The transition from the subjective to the objective in relation to extension is a primitive fact of our nature.

XXIV. Therefore bodily phenomena have a real existence outside of us.

XXV. Therefore a real certainty, scientific as well as phenomenal, arises from the testimony of the senses.

XXVI. Reason justifies the instinct of nature when it examines the relation of subjectiveness with objectiveness in sensations.

XXVII. Geometry considers extension in the abstract; but with the certainty that when the principle exists in the real order, the consequences cannot fail to be produced, and that the consequences will be more or less exact in proportion as the principle is more or less exactly realized.

XXVIII. Notwithstanding our certainty of the existence of the external world we do not know its essence.

XXIX. We do not know what this world is when seen by a pure spirit.

XXX. Sensible intuition, to which our geometry relates, does not constitute the essence of scientific knowledge, and may be separated from it.

XXXI. A change in the relations of corporeal beings among themselves, and with our sensitive faculties, is not intrinsically impossible.