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

That logic should in this respect have been so successful, is due entirely to its limitation, whereby it has not only the right, but the duty, to make abstraction of all the objects of knowledge and their differences, so that the understanding has to deal with nothing beyond itself and its own forms. It was, of course, far more difficult for reason to enter on the secure method of science, when it has to deal not with itself only, but also with objects. Logic, therefore, as a kind of preparation {propaedeutic^ forms, as it were, the vestibule of the sciences only, and where real knowledge is concerned, is presupposed for critical purposes only, while the acquisition of knowledge must be sought for in the sciences themselves, properly and objectively so called.

If there is to be in those sciences an element of reason, something in them must be known a priori, and knowledge may stand in a twofold relation to its object, by eithe t simply deter- [p. x] mining it and its concept (which must be supphed from elsewhere), or by making it 7'eal also. The former is theoretical, the latter practical knowledge of reason. In both the pui'e part, namely, that in which reason determines its object entirely a priori (whether it contain much or little), must be treated first, without mixing up with it what comes from other sources ; for it is bad economy to spend blindly whatever comes in, and not to be able to determine, when there is a stoppage, which part of the income can bear the expenditure, and where reductions must be made.

Mathematics and physics are the two theoretical sciences of reason, which have to determine their objects a priori ; the

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690 Suppleniejit II former quite purely, the latter partially so, and partially from other sources of knowledge besides reason.

Mathematics, from the earHest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of a science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road.

I believe, on the contrary, that there was a long period of tentative work (chiefly [p. xi] still among the Egyptians), and that the change is to be ascribed to a revolution., produced by the happy thought of a single man, whose experiment pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science.

The history of that intellectual revolution, which was far more important than the discovery of the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us.

But the story preserved by Diogenes Laertius, who names the reputed author of the smallest elements of ordinary geometrical demonstration, even of such as, according to general opinion, do not require to be proved, shows, at all events, that the memory of the revolution, produced by the very first traces of the discovery of a new method, appeared extremely important to the mathematicians, and thus remained unforgotten.

A new light flashed on the first man who demonstrated the properties of the isosceles triangle^ (whether his name was Thales or any other name), for he found that he had not to investigate what [p. xii] he saw in the figure, or the mere concept of that figure, and thus to learn its properties ; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that

1 Kant himself in a letter to Schlitz (Darstellung seines Lebens von seinem Sohn, Halle, 1835, B^ind. 11. S. 208) pointed out the mistake which appears in the preface to the 2nd edition, namely, gleichseitig (equilateral), instead of gleichschenkelig (isosceles).

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figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.

It took a much longer time before physics entered on the high way of science : for no more than a century and a half has elapsed, since Bacon's ingenious proposal partly initiated that discovery, pardy, as others were already on the right track, gave a new impetus to it, — a discovery which, Hke the former, can only be explained by a rapid intellectual revolution. In what I have to say, I shall confine myself to natural science, so far as it is founded on empirical principles.