A GLANCE AT THE IDEAS OF SPACE, NUMBER, AND TIME.
157. We may now mark out and determine with perfect exactness the necessary elements which form the object of the natural and exact sciences. This is not only curious, but highly important; for it presents under the simplest aspect, an immense field of knowledge, the limits of which expand, as we advance; so that, it is impossible to assign a limit to progress.
158. Space, number, and time, are the three elements of all the natural and exact sciences. All else contained in them pertains to mere experience, to the order of contingent facts, which involve no necessity, and cannot strictly be the objects of science.
159. Universal arithmetic is founded on the idea of numbers, geometry on that of space, and the idea of time places us in communication with the sensible world, so as to determine the relations of its phenomena. These phenomena are isolated contingent facts, and cannot become the objectof science, until subjected to the general ideas of space, number, and time.
160. Hence, there are two parts in every natural science; the theoretic, and the experimental. The former is founded on necessary ideas, the latter on contingent facts; the first without the second, would not come down to the real world; the second without the first, would not rise to the regions of science.
161. The natural sciences merit the name of science, in proportion to the quantity of necessary elements which they contain, and the closeness of the connection by which they unite with them contingent facts. But as no natural science can be conceived, without contingent facts, so there is none entirely free from the contingency which they communicate.
162. These observations reveal a great simplicity in the elements of science, and we may push this simplicity much farther, if we recollect what has been said when analyzing the ideas of number and time.
163. The idea of number arises from the idea of being and not-being: the same is also true of the idea of time; therefore, at bottom, these ideas are but one, though presented under different aspects.
164. Hence, all the natural and exact sciences may be reduced to two elements: the intuition of extension, and the general conception of being. Extension is the basis of all sensible intuitions: externally, it is a necessary condition of the relations which we conceive in the corporeal world; internally, it is a perception, without which the sensibility could not represent external objects. The conception of being, is the basis of all conceptions; developed in different ways, it generates the ideas of number and time; and these, combined with extension, constitute the necessary part of all the natural and exact sciences.
165. The ideas of space, number, and time are common to all men; the proof that they are identical to all is, that, in their application, all are led to the same results, and in speaking of them they all use the same expressions. All men measure space, and its various dimensions; they all count, they all conceive time: why, then, is there so great difficulty in explaining these ideas? why such difference of opinion among philosophers? Here we have a confirmation of what we have said[35]of the strength of direct perception, and the weakness of reflex. When we content ourselves with the direct perception of space, of number, and of time, our ideas are clear, and the understanding feels its strength and energy, it extends the sphere of its knowledge beyond all limits, and raises the edifice of the mathematical and exact sciences. But as soon as it turns upon itself, and, leaving the direct perception, passes to the reflex, endeavoring to perceive its perception, its strength fails, and it falls into a confusion which gives rise to interminable disputes. We scarce perceive that idea, which, a moment ago, we applied to every thing, which penetrated all our cognitions, and circulated, like our life, through all our perceptions; but in its isolation, and its purity, it continually escapes from us; mingled with all things, we see that it is something distinct from them; we separate it from one, and it unites with another; we make an effort to cut it off from all that is not itself, and the mind feels a kind of dizziness come over it, every thing vanishes from before it, and, unable to reach the reality, it is forced to be contented with names, which it pronounces and repeats a thousand times, turning over in them the little reality which they contain.
167. One of the causes of this weakness and of the errorswhich are its ordinary consequence, is, as I have before said, our mad desire of representing every idea as an internal form, or image, whereas we ought to consider that in many cases there is only a perception, a simple act in the lowest depth of our mind,—an act, which can be represented by nothing, which resembles nothing, and which cannot be explained in words, because it cannot be decomposed, and it is only present as a simple fact of consciousness. But this fact of consciousness is an active fact; by it we penetrate into things, and see what they have in common, and separate it from what is particular, establishing in our mind, as it were, a central, culminating point, from which we contemplate the internal and the external world, and roam through the boundless regions of possibility.