The new transcendental exposition extends the above by two further statements: (_a_) that only through the intuition of time can any conception of change, and therewith of motion (as change of place), be formed; and (_b_) that it is because the intuition of time is an _a priori_ intuition that the synthetic _a priori_ propositions of the “general doctrine of motion” are possible. To take each in turn. (_a_) Save by reference to time the conception of motion is self-contradictory. It involves the ascription to one and the same thing of contradictory predicates, _e.g._ that an object both is and is not in a certain place. From this fact, that time makes possible what is not possible in pure conception, Kant, in his earlier rationalistic period, had derived a proof of the subjectivity of time.[504] (_b_) In 1786 in the _Metaphysical First Principles of Natural Science_ Kant had developed the fundamental principles of the general science of motion. He takes the opportunity of the second edition (1787) of the _Critique_ to assign this place to them in his general system. The implication is that the doctrine of motion stands to time in the relation in which geometry stands to space. Kant is probably here replying, as Vaihinger has suggested,[505] to an objection made by Garve to the first edition, that no science, corresponding to geometry, is based on the intuition of time. For two reasons, however, the analogy between mechanics and geometry breaks down. In the first place, the conception of motion is empirical; and in the second place, it presupposes space as well as time.[506] Kant elsewhere explicitly disavows this view that the science of motion is based on time. He had already done so in the preceding year (1786) in the _Metaphysical First Principles_. He there points out[507] that as time has only one dimension, mathematics is not applicable to the phenomena of inner sense. At most we can determine in regard to them (in addition, of course, to the two axioms already cited) only the law that all these changes are continuous. Also in Kant’s _Ueber Philosophie überhaupt_ (written some time between 1780 and 1790, and very probably in or about the year 1789) we find the following utterance: “The general doctrine of time, unlike the pure doctrine of space (geometry), does not yield sufficient material for a whole science.”[508] Why, then, should Kant in 1787 have so inconsistently departed from his own teaching? This is a question to which I can find no answer. Apparently without reason, and contrary to his more abiding judgment, he here repeats the suggestion which he had casually thrown out in the _Dissertation_[509] of 1770: “Pure mathematics treats of space in geometry and of time in pure mechanics.” But in the _Dissertation_ the point is only touched upon in passing. The context permits of the interpretation that while geometry deals with space, mechanics deals with time in addition to space.