That the understanding, therefore, cannot make of its à priori principles, or even of its conceptions, other than an empirical use, is a proposition which leads to the most important results. A transcendental use is made of a conception in a fundamental proposition or principle, when it is referred to things in general and considered as things in themselves; an empirical use, when it is referred merely to phenomena, that is, to objects of a possible experience. That the latter use of a conception is the only admissible one is evident from the reasons following. For every conception are requisite, firstly, the logical form of a conception (of thought) general; and, secondly, the possibility of presenting to this an object to which it may apply. Failing this latter, it has no sense, and utterly void of content, although it may contain the logical function for constructing a conception from certain data. Now, object cannot be given to a conception otherwise than by intuition, and, even if a pure intuition antecedent to the object is à priori possible, this pure intuition can itself obtain objective validity only from empirical intuition, of which it is itself but the form. All conceptions, therefore, and with them all principles, however high the degree of their à priori possibility, relate to empirical intuitions, that is, to data towards a possible experience. Without this they possess no objective validity, but are mere play of imagination or of understanding with images or notions. Let us take, for example, the conceptions of mathematics, and first in its pure intuitions. “Space has three dimensions”—“Between two points there can be only one straight line,” etc. Although all these principles, and the representation of the object with which this science occupies itself, are generated in the mind entirely à priori, they would nevertheless have no significance if we were not always able to exhibit their significance in and by means of phenomena (empirical objects). Hence it is requisite that an abstract conception be made sensuous, that is, that an object corresponding to it in intuition be forthcoming, otherwise the conception remains, as we say, without sense, that is, without meaning. Mathematics fulfils this requirement by the construction of the figure, which is a phenomenon evident to the senses. The same science finds support and significance in number; this in its turn finds it in the fingers, or in counters, or in lines and points. The conception itself is always produced à priori, together with the synthetical principles or formulas from such conceptions; but the proper employment of them, and their application to objects, can exist nowhere but in experience, the possibility of which, as regards its form, they contain à priori.