| As we have taken upon us the task of determining, clearly and certainly, the limits of pure reason in the sphere of transcendentalism, and as the efforts of reason in this direction are persisted in, even after the plainest and most expressive warnings, hope still beckoning us past the limits of experience into the splendours of the intellectual world--it becomes necessary to cut away the last anchor of this fallacious and fantastic hope. |
| We shall, accordingly, show that the mathematical method is unattended in the sphere of philosophy by the least advantage--except, perhaps, that it more plainly exhibits its own inadequacy--that geometry and philosophy are two quite different things, although they go band in hand in hand in the field of natural science, and, consequently, that the procedure of the one can never be imitated by the other. |
| The evidence of mathematics rests upon definitions, axioms, and demonstrations. |
| I shall be satisfied with showing that none of these forms can be employed or imitated in philosophy in the sense in which they are understood by mathematicians; and that the geometrician, if he employs his method in philosophy, will succeed only in building card-castles, while the employment of the philosophical method in mathematics can result in nothing but mere verbiage. |
| The essential business of philosophy, indeed, is to mark out the limits of the science; and even the mathematician, unless his talent is naturally circumscribed and limited to this particular department of knowledge, cannot turn a deaf ear to the warnings of philosophy, or set himself above its direction. |
| I. Of Definitions. |
| A definition is, as the term itself indicates, the representation, upon primary grounds, of the complete conception of a thing within its own limits.* Accordingly, an empirical conception cannot be defined, it can only be explained. |
| For, as there are in such a conception only a certain number of marks or signs, which denote a certain class of sensuous objects, we can never be sure that we do not cogitate under the word which indicates the same object, at one time a greater, at another a smaller number of signs. |
| Thus, one person may cogitate in his conception of gold, in addition to its properties of weight, colour, malleability, that of resisting rust, while another person may be ignorant of this quality. |
| We employ certain signs only so long as we require them for the sake of distinction; new observations abstract some and add new ones, so that an empirical conception never remains within permanent limits. |
| It is, in fact, useless to define a conception of this kind. |
| If, for example, we are speaking of water and its properties, we do not stop at what we actually think by the word water, but proceed to observation and experiment; and the word, with the few signs attached to it, is more properly a designation than a conception of the thing. |
| A definition in this case would evidently be nothing more than a determination of the word. |
| In the second place, no a priori conception, such as those of substance, cause, right, fitness, and so on, can be defined. |
| For I can never be sure, that the clear representation of a given conception (which is given in a confused state) has been fully developed, until I know that the representation is adequate with its object. |
| But, inasmuch as the conception, as it is presented to the mind, may contain a number of obscure representations, which we do not observe in our analysis, although we employ them in our application of the conception, I can never be sure that my analysis is complete, while examples may make this probable, although they can never demonstrate the fact. |
| instead of the word definition, I should rather employ the term exposition- a more modest expression, which the critic may accept without surrendering his doubts as to the completeness of the analysis of any such conception. |
| As, therefore, neither empirical nor a priori conceptions are capable of definition, we have to see whether the only other kind of conceptions--arbitrary conceptions--can be subjected to this mental operation. |
| Such a conception can always be defined; for I must know thoroughly what I wished to cogitate in it, as it was I who created it, and it was not given to my mind either by the nature of my understanding or by experience. |
| At the same time, I cannot say that, by such a definition, I have defined a real object. |
| If the conception is based upon empirical conditions, if, for example, I have a conception of a clock for a ship, this arbitrary conception does not assure me of the existence or even of the possibility of the object. |