If we are to form a synthetical judgement regarding a conception, we must go beyond it, to the intuition in which it is given.If we keep to what is contained in the conception, the judgement is merely analytical- it is merely an explanation of what we have cogitated in the conception.But I can pass from the conception to the pure or empirical intuition which corresponds to it.I can proceed to examine my conception in concreto, and to cognize, either a priori or a posterio, what I find in the object of the conception.The former- a priori cognition- is rational-mathematical cognition by means of the construction of the conception; the latter- a posteriori cognition- is purely empirical cognition, which does not possess the attributes of necessity and universality.Thus I may analyse the conception I have of gold; but I gain no new information from this analysis, I merely enumerate the different properties which I had connected with the notion indicated by the word.My knowledge has gained in logical clearness and arrangement, but no addition has been made to it.But if I take the matter which is indicated by this name, and submit it to the examination of my senses, I am enabled to form several synthetical- although still empirical-propositions.The mathematical conception of a ******** I should construct, that is, present a priori in intuition, and in this way attain to rational-synthetical cognition.But when the transcendental conception of reality, or substance, or power is presented to my mind, I find that it does not relate to or indicate either an empirical or pure intuition, but that it indicates merely the synthesis of empirical intuitions, which cannot of course be given a priori.The synthesis in such a conception cannot proceed a priori- without the aid of experience- to the intuition which corresponds to the conception; and, for this reason, none of these conceptions can produce a determinative synthetical proposition, they can never present more than a principle of the synthesis* of possible empirical intuitions.A transcendental proposition is, therefore, a synthetical cognition of reason by means of pure conceptions and the discursive method, and it renders possible all synthetical unity in empirical cognition, though it cannot present us with any intuition a priori.
*In the case of the conception of cause, I do really go beyond the empirical conception of an event- but not to the intuition which presents this conception in concreto, but only to the time-conditions, which may be found in experience to correspond to the conception.My procedure is, therefore, strictly according to conceptions; I cannot in a case of this kind employ the construction of conceptions, because the conception is merely a rule for the synthesis of perceptions, which are not pure intuitions, and which, therefore, cannot be given a priori.
There is thus a twofold exercise of reason.Both modes have the properties of universality and an a priori origin in common, but are, in their procedure, of widely different character.The reason of this is that in the world of phenomena, in which alone objects are presented to our minds, there are two main elements- the form of intuition (space and time), which can be cognized and determined completely a priori, and the matter or content- that which is presented in space and time, and which, consequently, contains a something- an existence corresponding to our powers of sensation.As regards the latter, which can never be given in a determinate mode except by experience, there are no a priori notions which relate to it, except the undetermined conceptions of the synthesis of possible sensations, in so far as these belong (in a possible experience) to the unity of consciousness.As regards the former, we can determine our conceptions a priori in intuition, inasmuch as we are ourselves the creators of the objects of the conceptions in space and time-these objects being regarded simply as quanta.In the one case, reason proceeds according to conceptions and can do nothing more than subject phenomena to these- which can only be determined empirically, that is, a posteriori- in conformity, however, with those conceptions as the rules of all empirical synthesis.In the other case, reason proceeds by the construction of conceptions; and, as these conceptions relate to an a priori intuition, they may be given and determined in pure intuition a priori, and without the aid of empirical data.The examination and consideration of everything that exists in space or time- whether it is a quantum or not, in how far the particular something (which fills space or time) is a primary substratum, or a mere determination of some other existence, whether it relates to anything else- either as cause or effect, whether its existence is isolated or in reciprocal connection with and dependence upon others, the possibility of this existence, its reality and necessity or opposites- all these form part of the cognition of reason on the ground of conceptions, and this cognition is termed philosophical.But to determine a priori an intuition in space (its figure), to divide time into periods, or merely to cognize the quantity of an intuition in space and time, and to determine it by number- all this is an operation of reason by means of the construction of conceptions, and is called mathematical.