| Reason, when employed in the field of experience, does not stand in need of criticism, because its principles are subjected to the continual test of empirical observations. |
| Nor is criticism requisite in the sphere of mathematics, where the conceptions of reason must always be presented in concreto in pure intuition, and baseless or arbitrary assertions are discovered without difficulty. |
| But where reason is not held in a plain track by the influence of empirical or of pure intuition, that is, when it is employed in the transcendental sphere of pure conceptions, it stands in great need of discipline, to restrain its propensity to overstep the limits of possible experience and to keep it from wandering into error. |
| In fact, the utility of the philosophy of pure reason is entirely of this negative character. |
| Particular errors may be corrected by particular animadversions, and the causes of these errors may be eradicated by criticism. |
| But where we find, as in the case of pure reason, a complete system of illusions and fallacies, closely connected with each other and depending upon grand general principles, there seems to be required a peculiar and negative code of mental legislation, which, under the denomination of a discipline, and founded upon the nature of reason and the objects of its exercise, shall constitute a system of thorough examination and testing, which no fallacy will be able to withstand or escape from, under whatever disguise or concealment it may lurk. |
| But the reader must remark that, in this the second division of our transcendental Critique the discipline of pure reason is not directed to the content, but to the method of the cognition of pure reason. |
| The former task has been completed in the doctrine of elements. |
| But there is so much similarity in the mode of employing the faculty of reason, whatever be the object to which it is applied, while, at the same time, its employment in the transcendental sphere is so essentially different in kind from every other, that, without the warning negative influence of a discipline specially directed to that end, the errors are unavoidable which spring from the unskillful employment of the methods which are originated by reason but which are out of place in this sphere. |
| SECTION I. The Discipline of Pure Reason in the Sphere of Dogmatism. |
| The science of mathematics presents the most brilliant example of the extension of the sphere of pure reason without the aid of experience. |
| Examples are always contagious; and they exert an especial influence on the same faculty, which naturally flatters itself that it will have the same good fortune in other case as fell to its lot in one fortunate instance. |
| Hence pure reason hopes to be able to extend its empire in the transcendental sphere with equal success and security, especially when it applies the same method which was attended with such brilliant results in the science of mathematics. |
| It is, therefore, of the highest importance for us to know whether the method of arriving at demonstrative certainty, which is termed mathematical, be identical with that by which we endeavour to attain the same degree of certainty in philosophy, and which is termed in that science dogmatical. |
| Philosophical cognition is the cognition of reason by means of conceptions; mathematical cognition is cognition by means of the construction of conceptions. |
| The construction of a conception is the presentation a priori of the intuition which corresponds to the conception. |
| For this purpose a non-empirical intuition is requisite, which, as an intuition, is an individual object; while, as the construction of a conception (a general representation), it must be seen to be universally valid for all the possible intuitions which rank under that conception. |
| Thus I construct a triangle, by the presentation of the object which corresponds to this conception, either by mere imagination, in pure intuition, or upon paper, in empirical intuition, in both cases completely a priori, without borrowing the type of that figure from any experience. |
| The individual figure drawn upon paper is empirical; but it serves, notwithstanding, to indicate the conception, even in its universality, because in this empirical intuition we keep our eye merely on the act of the construction of the conception, and pay no attention to the various modes of determining it, for example, its size, the length of its sides, the size of its angles, these not in the least affecting the essential character of the conception. |
| Philosophical cognition, accordingly, regards the particular only in the general; mathematical the general in the particular, nay, in the individual. |
| This is done, however, entirely a priori and by means of pure reason, so that, as this individual figure is determined under certain universal conditions of construction, the object of the conception, to which this individual figure corresponds as its schema, must be cogitated as universally determined. |