household stuff is.”
4 In contradistinction to the Metaphysic of Ethics. This work was never published.
Preface to the Second Edition, 1787
Whether the treatment of that portion of our knowledge which lies within the province of pure reason advances with that undeviating certainty which characterizes the progress of science, we shall be at no loss to determine. If we find those who are engaged in metaphysical pursuits, unable to come to an understanding as to the method which they ought to follow; if we find them, after the most elaborate preparations, invariably brought to a stand before the goal is reached, and compelled to retrace their steps and strike into fresh paths, we may then feel quite sure that they are far from having attained to the certainty of scientific progress and may rather be said to be merely groping about in the dark. In these circumstances we shall render an important service to reason if we succeed in simply indicating the path along which it must travel, in order to arrive at any results — even if it should be found necessary to abandon many of those aims which, without reflection, have been proposed for its attainment.
That logic has advanced in this sure course, even from the earliest times, is apparent from the fact that, since Aristotle, it has been unable to advance a step and, thus, to all appearance has reached its completion. For, if some of the moderns have thought to enlarge its domain by introducing psychological discussions on the mental faculties, such as imagination and wit, metaphysical discussions on the origin of knowledge and the different kinds of certitude, according to the difference of the objects (idealism, scepticism, and so on), or anthropological discussions on prejudices, their causes and remedies: this attempt, on the part of these authors, only shows their ignorance of the peculiar nature of logical science. We do not enlarge but disfigure the sciences when we lose sight of their respective limits and allow them to run into one another. Now logic is enclosed within limits which admit of perfectly clear definition; it is a science which has for its object nothing but the exposition and proof of the formal laws of all thought, whether it be a priori or empirical, whatever be its origin or its object, and whatever the difficulties — natural or accidental — which it encounters in the human mind.
The early success of logic must be attributed exclusively to the narrowness of its field, in which abstraction may, or rather must, be made of all the objects of cognition with their characteristic distinctions, and in which the understanding has only to deal with itself and with its own forms. It is, obviously, a much more difficult task for reason to strike into the sure path of science, where it has to deal not simply with itself, but with objects external to itself. Hence, logic is properly only a propaedeutic — forms, as it were, the vestibule of the sciences; and while it is necessary to enable us to form a correct judgement with regard to the various branches of knowledge, still the acquisition of real, substantive knowledge is to be sought only in the sciences properly so called, that is, in the objective sciences.
Now these sciences, if they can be termed rational at all, must contain elements of a priori cognition, and this cognition may stand in a twofold relation to its object. Either it may have to determine the conception of the object — which must be supplied extraneously, or it may have to establish its reality. The former is theoretical, the latter practical, rational cognition. In both, the pure or a priori element must be treated first, and must be carefully distinguished from that which is supplied from other sources. Any other method can only lead to irremediable confusion.
Mathematics and physics are the two theoretical sciences which have to determine their objects a priori. The former is purely a priori, the latter is partially so, but is also dependent on other sources of cognition.
In the earliest times of which history affords us any record, mathematics had already entered on the sure course of science, among that wonderful nation, the Greeks. Still it is not to be supposed that it was as easy for this science to strike into, or rather to construct for itself, that royal road, as it was for logic, in which reason has only to deal with itself. On the contrary, I believe that it must have remained long — chiefly among the Egyptians — in the stage of blind groping after its true aims and destination, and that it was revolutionized by the happy idea of one man, who struck out and determined for all time the path which this science must follow, and which admits of an indefinite advancement. The history of this intellectual revolution — much more important in its results than the discovery of the passage round the celebrated Cape of Good Hope — and of its author, has not been preserved. But Diogenes Laertius, in naming the supposed discoverer of some of the simplest elements of geometrical demonstration — elements which, according to the ordinary opinion, do not even require to be proved — makes it apparent that the change introduced by the first indication of this new path, must have seemed of the utmost importance to the mathematicians of that age, and it has thus been secured against the chance of oblivion. A new light must have flashed on the mind of the first man (Thales, or whatever may have been his name) who demonstrated the properties of the isosceles triangle. For he found that it was not sufficient to meditate on the figure, as it lay before his eyes, or the conception of it, as it existed in his mind, and thus endeavour to get at the knowledge of its properties, but that it was necessary to produce these properties, as it were, by a positive a priori construction; and that, in order to arrive with certainty at a priori cognition, he must not attribute to the object any other properties than those which necessarily followed from that which he had himself, in accordance with his conception, placed in the object.
A much longer period elapsed before physics entered on the highway of science. For it is only about a century and a half since the wise Bacon gave a new direction to physical studies, or rather — as others were already on the right track — imparted fresh vigour to the pursuit of this new direction. Here, too, as in the case of mathematics, we find evidence of a rapid intellectual revolution. In the remarks which follow I shall confine myself to the empirical side of natural science.
When Galilei experimented with balls of a definite weight on the inclined plane, when Torricelli caused the air to sustain a weight which he had calculated beforehand to be equal to that of a definite column of water, or when Stahl, at a later period, converted metals into lime, and reconverted lime into metal, by the addition and subtraction of certain elements;4 a light broke upon all natural philosophers. They learned that reason only perceives that which it produces after its own design; that it must not be content to follow, as it were, in the leading-strings of nature, but must proceed in advance with principles of judgement according to unvarying laws, and compel nature to reply its questions. For accidental observations, made according to no preconceived plan, cannot be united under a necessary law. But it is this that reason seeks for and requires. It is only the principles of reason which can give to concordant phenomena the validity of laws, and it is only when experiment is directed by these rational principles that it can have any real utility. Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose. To this single idea must the revolution be ascribed, by which, after groping in the dark for so many centuries, natural science was at length conducted into the path of certain progress.
We come now to metaphysics, a purely speculative science, which occupies a completely isolated position and is entirely independent of the teachings of experience. It deals with mere conceptions — not, like mathematics, with conceptions applied to intuition — and in it, reason is the pupil of itself alone. It is the oldest of the sciences, and would still survive, even if all the rest were swallowed up in the abyss of an all-destroying barbarism. But it has not yet had the good fortune
