| In the latter, I proceed by geometrical construction, by means of which I collect, in a pure intuition, just as I would in an empirical intuition, all the various properties which belong to the schema of a triangle in general, and consequently to its conception, and thus construct synthetical propositions which possess the attribute of universality. |
| It would be vain to philosophize upon the triangle, that is, to reflect on it discursively; I should get no further than the definition with which I had been obliged to set out. |
| There are certainly transcendental synthetical propositions which are framed by means of pure conceptions, and which form the peculiar distinction of philosophy; but these do not relate to any particular thing, but to a thing in general, and enounce the conditions under which the perception of it may become a part of possible experience. |
| But the science of mathematics has nothing to do with such questions, nor with the question of existence in any fashion; it is concerned merely with the properties of objects in themselves, only in so far as these are connected with the conception of the objects. |
| In the above example, we merely attempted to show the great difference which exists between the discursive employment of reason in the sphere of conceptions, and its intuitive exercise by means of the construction of conceptions. |
| The question naturally arises; What is the cause which necessitates this twofold exercise of reason, and how are we to discover whether it is the philosophical or the mathematical method which reason is pursuing in an argument? |
| All our knowledge relates, finally, to possible intuitions, for it is these alone that present objects to the mind. |
| An a priori or non-empirical conception contains either a pure intuition--and in this case it can be constructed; or it contains nothing but the synthesis of possible intuitions, which are not given a priorI. In this latter case, it may help us to form synthetical a priori judgements, but only in the discursive method, by conceptions, not in the intuitive, by means of the construction of conceptions. |
| The only a priori intuition is that of the pure form of phenomena- space and time. |
| A conception of space and time as quanta may be presented a priori in intuition, that is, constructed, either alone with their quality (figure), or as pure quantity (the mere synthesis of the homogeneous), by means of number. |
| But the matter of phenomena, by which things are given in space and time, can be presented only in perception, a posteriorI. The only conception which represents a priori this empirical content of phenomena is the conception of a thing in general; and the a priori synthetical cognition of this conception can give us nothing more than the rule for the synthesis of that which may be contained in the corresponding a posteriori perception; it is utterly inadequate to present an a priori intuition of the real object, which must necessarily be empirical. |
| Synthetical propositions, which relate to things in general, an a priori intuition of which is impossible, are transcendental. |
| For this reason transcendental propositions cannot be framed by means of the construction of conceptions; they are a priori, and based entirely on conceptions themselves. |
| They contain merely the rule, by which we are to seek in the world of perception or experience the synthetical unity of that which cannot be intuited a priorI. But they are incompetent to present any of the conceptions which appear in them in an a priori intuition; these can be given only a posteriori, in experience, which, however, is itself possible only through these synthetical principles. |
| 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. |