Those who assert the objective reality of time either conceive of it as a continuous flow in what exists, without, however, any existing thing, as is done especially by the English philosophers, an absurd fiction, or as something real abstracted from the succession of inner states, as it has been put by Leibnitz and his followers. The falsity of the latter opinion, besides obviously exposing it to the vicious circle in the definition of time, and, moreover, plainly neglecting simultaneity, the most important consequence of time, disturbs all sound reason, because it demands instead of the determining of the laws of motion by the measure of time, that time itself, as to its nature, be determined by what is observed in motion or some series of inner changes, whereby plainly all certitude of rules is abolished. That we can estimate the quantity of time only in the concrete, namely, either by motion or by a series of thoughts, arises from the concept of time resting only on an inherent mental law, it not being a connate intuition; whence the act of the mind co-ordinating the impressions is elicited only by the aid of the senses. So far from its being possible to deduce and explain the concept of time from some other source by force of reason, it is presupposed by the very principle of contradiction, it underlies it by way of condition. For a and not-a are not repugnant unless thought of the same thing simultaneously, that is, at the same time; they may belong to the same thing after each other, at different times. Hence the possibility of changes is not thinkable except in time. Time is not thinkable by changes, but reversely.[5]
6. But although time posited in itself and absolutely be an imaginary thing, yet as appertaining to the immutable law of sensible things as such, it is a perfectly true concept, and the patent condition of intuitive representation throughout all the infinite range of possible sense-objects. For since simultaneous things as such cannot be placed before the senses but by the aid of time, and since changes are unthinkable except by time, it is obvious that this concept contains the universal form of phenomena, and that, indeed, all events observable in the world, all motions, all internal changes, agree necessarily with the temporal axioms of cognition which we have partly expounded, since only under these conditions can they become sense-objects and be co-ordinated. It is, therefore, absurd to excite reason against the primary postulates of pure time, as, for example, continuity, etc., since they follow from laws prior and superior to which nothing is found, and since reason herself in the use of the principle of contradiction cannot dispense with the support of this concept, so primitive and original is it.
7. Time, then, is the absolutely first formal principle of the sensible world. For all sensible things of whatsoever description are unthinkable except as posited either simultaneously or one after another, and, indeed, as if involved and mutually related by determinate position in the tract of unique time, so that by this primary concept of everything sensuous originates necessarily that formal whole which is not a part of another, that is, the phenomenal World.
Paragraph 15 OF SPACE
A. The concept of space is not abstracted from external sensations. For I am unable to conceive of anything posited without me unless by representing it as in a place different from that in which I am, and of things as mutually outside of each other unless by locating them in different places in space. Therefore the possibility of external perceptions, as such, presupposes and does not create the concept of space, so that, although what is in space affects the senses, space cannot itself be derived from the senses.
B. The concept of space is a singular representation comprehending all things in itself, not an abstract and common notion containing them under itself. What are called several spaces are only parts of the same immense space mutually related by certain positions, nor can you conceive of a cubic foot except as being bounded in all directions by surrounding space.
C. The concept of space, therefore, is a pure intuition, being a singular concept, not made up by sensations, but itself the fundamental form of all external sensation. This pure intuition is in fact easily perceived in geometrical axioms, and any mental construction of postulates or even problems. That in space there are no more than three dimensions, that between two points there is but one straight line, that in a plane surface from a given point with a given right line a circle is describable, are not conclusions from some universal notion of space, but only discernible in space as in the concrete. Which things in a given space lie toward one side and which are turned toward the other can by no acuteness of reasoning be described discursively or reduced to intellectual marks. There being in perfectly similar and equal but incongruous solids, such as the right and the left hand, conceived of solely as to extent, or spherical triangles in opposite hemispheres, a difference rendering impossible the coincidence of their limits of extension, although for all that can be stated in marks intelligible to the mind by speech they are interchangeable, it is patent that only by pure intuition can the difference, namely, incongruity, be noticed. Geometry, therefore, uses principles not only undoubted and discursive but falling under the mental view, and the obviousness of its demonstrations—which means the clearness of certain cognition in as far as assimilated to sensual knowledge—is not only greatest, but the only one which is given in the pure sciences, and the exemplar and medium of all obviousness in the others. For, since geometry considers the relations of space, the concept of which contains the very form of all sensual intuition, nothing that is perceived by the external sense can be clear and perspicuous unless by means of that intuition which it is the business of geometry to contemplate. Besides, this science does not demonstrate its universal propositions by thinking the object through the universal concept, as is done in intellectual disquisition, but by submitting it to the eyes in a single intuition, as is done in matters of sense.[6]
D. Space is not something objective and real, neither substance, nor accident, nor relation; but subjective and ideal, arising by fixed law from the nature of the mind like an outline for the mutual co-ordination of all external sensations whatsoever. Those who defend the reality of space either conceive of it as an absolute and immense receptacle of possible things, an opinion which, besides the English, pleases most geometricians, or they contend for its being the relation of existing things itself, which clearly vanishes in the removal of things and is thinkable only in actual things, as besides Leibnitz, is maintained by most of our countrymen. The first inane fiction of the reason, imagining true infinite relation without any mutually related things, pertains to the world of fable. But the adherents of the second opinion fall into a much worse error. Whilst the former only cast an obstacle in the way of some rational or noumenal concepts, otherwise most recondite, such as questions concerning the spiritual world, omnipresence, etc., the latter place themselves in fiat opposition to the very phenomena, and to the most faithful interpreter of all phenomena, to geometry. For, not to enlarge upon the obvious circle in which they become involved in defining space, they cast forth geometry, thrown down from the pinnacle of certitude, into the number of those sciences whose principles are empirical. If we have obtained all the properties of space by experience from external relations only, geometrical axioms have only comparative universality, such as is acquired by induction. They have universality evident as far as observed, but neither necessity, except as far as the laws of nature may be established, nor precision, except what is arbitrarily made. There is hope, as in empirical sciences, that a space may some time be discovered endowed with other primary properties, perchance even a rectilinear figure of two lines.
E. Though the concept of space as an objective and real thing or quality is imaginary, it is nevertheless in respect to all sensible things not only perfectly true, it is the foundation of truth in external sensibility. Things cannot appear to the senses under any form but