Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

sible sensations, in so far as they belong to the unity of apperception (in a possible experience). As regards the former, we can determine a priori our concepts in intuition, by creating to ourselves in space and time, through a uniform synthesis, the objects themselves, considering them simply as quanta.

The former is called the use of reason according to concepts ; and here we can do nothing more than to bring phenomena under concepts, according to their real contents, which therefore can be determined empirically only, that is a posteriori (though in accordance with those concepts as rules of an empirical synthesis).

The latter is the use [p. 724] of reason through the construction of concepts, which, as they refer to an intuition a priori^ can for that reason be given a priori^ and defined in pure intuition, without any empirical data.

To consider everything which exists (everything in space or time) whether, and how far, it is a qitantum or not ; to consider that we must represent in it either existence, or absence of existence ; to consider how far this something which fills space or time is a primary substratum, or merely determination of it ; to consider again whether its existence is related to something else as cause or effect, or finally, whether it stands isolated or in reciprocal dependence on others, with reference to existence, — this and the possibility, reality, and necessity of its existence, or their opposites, all belong to that knowledge of reason, derived from concepts, which is called philosophical.

But to determine a priori an intuition in space (figure), to divide time (duration), or merely to know the general character of the synthesis of one and the same thing in time and space, and the quantity of an intuition in general which

582 Discipline of Pure Reason arises from it (number), all this is the work of reason bymeans of the construction of concepts, and is called mathematical.

The great success which attends reason in its mathematical use produces naturally the expectation that it, or rather its method, would have the same success outside the field of quantities also, by reducing all concepts to intuitions which may be given a priori, and by [p. 725] which the whole of nature might be conquered, while pure philosophy, with its discursive concepts a priori, does nothing but bungle in every part of nature, without being able to render the reality of those concepts intuitive a priori, and thereby legitimatised. Nor does there seem to be any lack of confidence on the part of those who are masters in the art of mathematics, or of high expectations - on the part of the public at large, as to their ability of achieving success, if only they would try it. For as they have hardly ever philosophised on mathematics (which is indeed no easy task), they never think of the specific difference between the two uses of reason which we have just explained. Current and empirical rules, borrowed from the ordinary operations of reason, are then accepted instead of axioms. From what quarter the concepts of space and time with which alone (as the original quanta) they have to deal, may have come to them, they do not care to enquire, nor do they see any use in investigating the origin of the pure concepts of the understanding, and with it the extent of their validity, being satisfied to use them as they are. In all this no blame would attach to them, if only they did not overstep their proper limits, namely, those of nature. But as it is, they lose themselves, without being aware of it, away from the field of

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sensibility on the uncertain ground of pure and even transcendental concepts {instabilis telhis, innabilis tmda) where they are neither able to stand nor to [p. 726] swim, taking only a few hasty steps, the vestiges of which are soon swept away, while their steps in mathematics become a highway, on which the latest posterity may march on with perfect confidence.

We have chosen it as our duty to determine with accuracy and certainty the limits of pure reason in its transcendental use. These transcendental efforts, however, have this peculiar character that, in spite of the strongest and clearest warnings, they continue to inspire us with new hopes, before the attempt is entirely surrendered at arriving beyond the liaiits of experience at the charming fields of an intellectual world. It is necessary therefore to cut away the last anchor of that fantastic hope, and to show that the employment of the mathematical method cannot be of the slightest use for this kind of knowledge, unless it be in displaying its own deficiencies ; and that the art of measuring and philosophy are two totally different things, though they are mutually useful to each other in natural science, and that the method of the one can never be imitated by the other.

The exactness of mathematics depends on definitions, axioms, and demonstrations. I shall content myself with showing that none of these can be achieved or imitated by the philosopher in the sense in which they are understood by the mathematician. I hope to show at the [p. 72^'] same time that the art of measuring, or geometry, will by its method produce nothing in philosophy but card-houses, while the philosopher with his method produces in mathematics nothing but vain babble. It is the very essence of