I may now summarise this general discussion. Though Kant in the first edition of the Critique had spoken of the mathematical sciences as based upon the intuition of space and time, he had not, despite his constant tendency to conceive space and time as parallel forms of existence, based any separate mathematical discipline upon time. His definition of number, in the chapter on Schematism, had recognised the essentially conceptual character of arithmetic, and had connected it with time only in a quite indirect manner. A passage in the Prolegomena is the one place in all Kant’s writings in which he would seem to assert, though in brief and quite indefinite terms, that arithmetic is related to time as geometry is related to space. No such view of arithmetic is to be found in the second edition of the Critique. In the transcendental exposition of time, added in the second edition, only pure mechanics is mentioned. This would seem to indicate that Kant had made the above statement carelessly, without due thought, and that on further reflection he found himself unable to stand by it. The omission is the more significant in that Kant refers to arithmetic in the passages added in the second edition Introduction. The teaching of these passages, apart from the asserted necessity of appealing to fingers or points,[526] harmonises with the view so briefly outlined in the Analytic. Arithmetic is a conceptual science; though it finds in ordered sequence its intuitional material, it cannot be adequately defined as being the science of time.
CONCLUSIONS FROM THE PRECEDING CONCEPTS[527]
These Conclusions do not run parallel with the corresponding Conclusions in regard to space. In the first paragraph there are two differences. (a) Kant takes account of a view not considered under space, viz. that time is a self-existing substance. He rejects it on a ground which is difficult to reconcile with his recognition of a manifold of intuition as well as a manifold of sense, namely that it would then be something real without being a real object. In A 39 = B 57 and B 70 Kant describes space and time, so conceived, as unendliche Undinge. (b) Kant introduces into his first Conclusion the argument[528] that only by conceiving time as the form of inner intuition can we justify a priori synthetic judgments in regard to objects.
Second Paragraph (Conclusion b).—This latter statement is repeated at the opening of the second Conclusion. The emphasis is no longer, however, upon the term “form” but upon the term “inner”; and Kant proceeds to make assertions which by no means follow from the five arguments, and which must be counted amongst the most difficult and controversial tenets of the whole Critique. (a) Time is not a determination of outer appearances. For it belongs neither to their shape nor to their position—and prudently at this point the property of motion is smuggled out of view under cover of an etc. Time does not determine the relation of appearances to one another, but only the relation of representations in our inner state.[529] It is the form only of the intuition of ourselves and of our inner state.[530] Obviously these are assertions which Kant cannot possibly hold to in this unqualified form. In the very next paragraph they are modified and restated. (b) As this inner intuition supplies no shape (Gestalt), we seek to make good this deficiency by means of analogies. We represent the time-sequence through a line progressing to infinity in which the manifold constitutes a series of only one dimension. From the properties of this line, with the one exception that its parts are simultaneous whereas those of time are always successive, we conclude to all the properties of time.
The wording of the passage seems to imply that such symbolisation of time through space is helpful but not indispensably necessary for its apprehension. That it is indispensably necessary is, however, the view to which Kant finally settled down.[531] But he has not yet come to clearness on this point. The passage has all the signs of having been written prior to the Analytic. Though Kant seems to have held consistently to the view that time has, in or by itself, only one dimension,[532] the difficulties involved drove him to recognise that this is true only of time as the order of our representations. It is not true of the objective time apprehended in and through our representations. When later Kant came to hold that consciousness of time is conditioned by consciousness of space, he apparently also adopted the view that, by reference to space, time indirectly acquires simultaneity as an additional mode. The objective spatial world is in time, but in a time which shows simultaneity as well as succession. In the Dissertation[533] Kant had criticised Leibniz and his followers for neglecting simultaneity, “the most important consequence of time.”
“Though time has only one dimension, yet the ubiquity of time (to employ Newton’s term), through which all things sensuously thinkable are at some time, adds another dimension to the quantity of actual things, in so far as they hang, as it were, upon the same point of time. For if we represent time by a straight line extended to infinity, and simultaneous things at any point of time by lines successively erected [perpendicular to the first line], the surface thus generated will represent the phenomenal world both as to substance and as to accidents.”
Similarly in A 182 = B 226 of the Critique Kant states that simultaneity is not a mode of time,[534] since none of the parts of time can be simultaneous, and yet also teaches in A 177 = B 219 that, as the order of appearances, time possesses in addition to succession the two modes, duration and simultaneity. The significance of this distinction between time as the order of our inner states, and time as the order of objective appearances, we shall consider immediately.
A connected question is as to whether or not Kant teaches the possibility of simultaneous apprehension. In the Aesthetic and Dialectic he certainly does so. Space is given as containing coexisting parts, and[535] can be intuited as such without successive synthesis of its parts. In the Analytic, on the other hand, the opposite would seem to be implied.[536] The apprehension of a manifold can only be obtained through the successive addition or generation of its parts.
(c) Lastly, Kant argues that the fact that all the relations of time can be expressed in an outer intuition is proof that the representation of time is itself intuition. But surely if, as Kant later taught, time can be apprehended at all only in and through space, that, taken alone, would rather be a reason for denying it to be itself intuition. In any case it is difficult to follow Kant in his contention that the intuition of time is similar in general character to that of space.[537]
Third Paragraph (Conclusion c).—Kant now reopens the question as to the relation in which time stands to outer appearances. As already noted, he has argued in the beginning of the previous paragraph that it cannot be a determination of outer appearances, but only of representations in our inner state. External appearances, however, as Kant recognises, can be known only in and through representations. To that extent they belong to inner sense, and consequently (such is Kant’s argument) are themselves subject to time. Time, as the immediate condition of our representations, is also the mediate condition of appearances. Therefore, Kant concludes, “all appearances, i.e. all objects of the senses, are in time, and necessarily stand in time-relations.”