Section 38
Original German
§ 38.
Wenn man die Eigenschaften des Cirkels betrachtet, dadurch diese Figur so manche willkürliche Bestimmungen des Raums in ihr sofort in einer allgemeinen Regel vereinigt, so kann man nicht umhin, diesem geometrischen Dinge eine Natur beizulegen. So theilen sich nämlich zwei Linien, die sich einander und zugleich den Cirkel schneiden, nach welchem Ungefähr sie auch gezogen werden, doch jederzeit so regelmäßig, daß das Rectangel aus den Stücken einer jeden Linie dem der andern gleich ist. Nun frage ich: „Liegt dieses Gesetz im Cirkel, oder liegt es im Verstande?“ d. i. enthält diese Figur unabhängig vom Verstande den Grund dieses Gesetzes in sich, oder legt der Verstand, indem er nach seinen Begriffen (nämlich der Gleichheit der Halbmesser) die Figur selbst construirt hat, zugleich das Gesetz der einander in geometrischer Proportion schneidenden Sehnen in dieselbe hinein? Man wird bald gewahr, wenn man den Beweisen dieses Gesetzes nachgeht, daß es allein von der Bedingung, die der Verstand der Construction dieser Figur zum Grunde legte, nämlich der Gleichheit der Halbmesser, könne abgeleitet werden. Erweitern wir diesen Begriff nun, die Einheit mannigfaltiger Eigenschaften geometrischer Figuren unter gemeinschaftlichen Gesetzen noch weiter zu verfolgen, und betrachten den Cirkel als einen Kegelschnitt, der also mit andern Kegelschnitten unter eben denselben Grundbedingungen der Construction steht, so finden wir, daß alle Sehnen, die sich innerhalb der letztern, der Ellipse, der Parabel und Hyperbel, schneiden, es jederzeit so thun, daß die Rectangel aus ihren Theilen zwar nicht gleich sind, aber doch immer in gleichen Verhältnissen gegen einander stehen. Gehen wir von da noch weiter, nämlich zu den Grundlehren der physischen Astronomie, so zeigt sich ein über die ganze materielle Natur verbreitetes physisches Gesetz der wechselseitigen Attraction, deren Regel ist, daß sie umgekehrt mit dem Quadrat der Entfernungen von jedem anziehenden Punkt eben so abnimmt, wie die Kugelflächen, in die sich diese Kraft verbreitet, zunehmen, welches als nothwendig in der Natur der Dinge selbst zu liegen scheint und daher auch als a priori erkennbar vorgetragen zu werden pflegt. So einfach nun auch die Quellen dieses Gesetzes sind, indem sie blos auf dem Verhältnisse der Kugelflächen von verschiedenen Halbmessern beruhen, so ist doch die Folge davon so vortrefflich in Ansehung der Mannigfaltigkeit ihrer Zusammenstimmung und Regelmäßigkeit derselben, daß nicht allein alle mögliche Bahnen der Himmelskörper in Kegelschnitten, sondern auch ein solches Verhältniß derselben unter einander erfolgt, daß kein ander Gesetz der Attraction als das des umgekehrten Quadratverhältnisses der Entfernungen zu einem Weltsystem als schicklich erdacht werden kann.
Hier ist also Natur, die auf Gesetzen beruht, welche der Verstand a priori erkennt und zwar vornehmlich aus allgemeinen Principien der Bestimmung des Raums. Nun frage ich: liegen diese Naturgesetze im Raume, und lernt sie der Verstand, indem er den reichhaltigen Sinn, der in jenem liegt, blos zu erforschen sucht, oder liegen sie im Verstande und in der Art, wie dieser den Raum nach den Bedingungen der synthetischen Einheit, darauf seine Begriffe insgesammt auslaufen, bestimmt? Der Raum ist etwas so Gleichförmiges und in Ansehung aller besondern Eigenschaften so Unbestimmtes, daß man in ihm gewiß keinen Schatz von Naturgesetzen suchen wird. Dagegen ist das, was den Raum zur Cirkelgestalt, der Figur des Kegels und der Kugel bestimmt, der Verstand, so fern er den Grund der Einheit der Construction derselben enthält. Die bloße allgemeine Form der Anschauung, die Raum heißt, ist also wohl das Substratum aller auf besondere Objecte bestimmbaren Anschauungen, und in jenem liegt freilich die Bedingung der Möglichkeit und Mannigfaltigkeit der letztern; aber die Einheit der Objecte wird doch lediglich durch den Verstand bestimmt und zwar nach Bedingungen, die in seiner eigenen Natur liegen; und so ist der Verstand der Ursprung der allgemeinen Ordnung der Natur, indem er alle Erscheinungen unter seine eigene Gesetze faßt und dadurch allererst Erfahrung (ihrer Form nach) a priori zu Stande bringt, vermöge deren alles, was nur durch Erfahrung erkannt werden soll, seinen Gesetzen nothwendig unterworfen wird. Denn wir haben es nicht mit der Natur der Dinge an sich selbst zu thun, die ist sowohl von Bedingungen unserer Sinnlichkeit als des Verstandes unabhängig, sondern mit der Natur als einem Gegenstande möglicher Erfahrung, und da macht es der Verstand, indem er diese möglich macht, zugleich, daß Sinnenwelt entweder gar kein Gegenstand der Erfahrung oder eine Natur ist.
Musean translation
Mouseia’s complete machine-assisted Musean translation, made directly from the complete German of the Prolegomena (AA IV 253–383, all §§1–60 and the Appendix), for fidelity, the steps of Kant’s argument, clarity and structure.
§ 38.
If we consider the properties of the circle, through which this figure at once unites so many arbitrary determinations of space within itself under a universal rule, we cannot help ascribing a nature to this geometrical thing. Thus two lines that intersect one another and also the circle, however randomly they may be drawn, always divide each other with such regularity that the rectangle formed from the segments of either line is equal to that formed from the segments of the other. Now I ask: “Does this law lie in the circle, or does it lie in the understanding?” That is, does this figure contain the ground of this law within itself independently of the understanding, or does the understanding, having constructed the figure itself according to its concepts—namely, the equality of the radii—at the same time place in it the law of chords intersecting one another in geometrical proportion? If we follow the proofs of this law, we soon discover that it can be derived solely from the condition the understanding laid at the foundation of the construction of this figure: namely, the equality of the radii. If we now extend this concept, pursuing still further the unity of the manifold properties of geometrical figures under common laws, and consider the circle as a conic section, which therefore stands with other conic sections under the very same fundamental conditions of construction, we find that all chords intersecting within the latter—the ellipse, parabola, and hyperbola—always do so in such a way that the rectangles formed from their parts, though not equal, nevertheless always stand in equal ratios to one another. If we go still further, namely to the fundamental doctrines of physical astronomy, a physical law of reciprocal attraction appears, extending throughout all material nature. Its rule is that attraction decreases inversely as the square of the distance from each attracting point, just as the spherical surfaces over which this force spreads increase. This seems to lie necessarily in the nature of things themselves, and is therefore usually presented as cognizable a priori. Now simple as the sources of this law are, resting merely on the relation of spherical surfaces of different radii, its consequence is so excellent in the manifold harmony and regularity it produces that not only do all possible orbits of celestial bodies follow conic sections, but such a relation among them also results that no law of attraction other than that of the inverse square of the distances can be conceived as suitable for a world system.
Here, then, is nature resting on laws that the understanding cognizes a priori, chiefly from universal principles of the determination of space. Now I ask: do these laws of nature lie in space, and does the understanding learn them by merely seeking to explore the rich meaning lying within it? Or do they lie in the understanding and in the way it determines space according to the conditions of synthetic unity, toward which all its concepts converge? Space is something so uniform, and so undetermined with respect to all particular properties, that we shall certainly seek no treasure of natural laws within it. Rather, what determines space into the shape of a circle, or the figure of a cone and a sphere, is the understanding, insofar as it contains the ground of the unity of their construction. The mere universal form of intuition called space is indeed the substratum of all intuitions determinable with respect to particular objects, and in it certainly lies the condition of their possibility and manifoldness. But the unity of objects is determined solely by the understanding, and according to conditions that lie in its own nature. Thus the understanding is the source of the universal order of nature, by bringing all appearances under its own laws and thereby first producing experience, as to its form, a priori. By virtue of this, everything that is to be cognized only through experience is necessarily subjected to its laws. For we are not concerned with the nature of things in themselves, which is independent of the conditions both of our sensibility and of our understanding, but with nature as an object of possible experience. Here the understanding, in making experience possible, at the same time brings it about that the world of sense is either no object of experience at all, or a nature.
Plain English translation
Mouseia’s complete Plain English edition, made independently and directly from the same complete German text.
§ 38.
Consider the properties of a circle. This figure immediately unites so many arbitrary determinations of space within it under one universal rule that we cannot help attributing a nature to this geometrical thing. For example, take two lines that intersect each other and also cut the circle. No matter how randomly they are drawn, they always divide each other so regularly that the rectangle formed from the segments of either line equals the rectangle formed from those of the other. Now I ask: “Does this law lie in the circle, or does it lie in the understanding?” In other words, does the figure contain the ground of this law independently of the understanding? Or does the understanding, having itself constructed the figure according to its concepts, namely the equality of the radii, also put into it the law of chords intersecting in geometrical proportion? If we follow the proofs of this law, we soon see that it can be derived only from the condition the understanding made the basis of constructing this figure: the equality of the radii. Now let us extend this concept, to trace further the unity of the many properties of geometrical figures under common laws. We consider the circle as a conic section, which therefore stands under the same basic conditions of construction as other conic sections. We find that all chords intersecting inside these latter figures—the ellipse, parabola, and hyperbola—always do so in such a way that the rectangles formed from their segments, though not equal, always stand in equal ratios to one another. Let us go still further, to the basic teachings of physical astronomy. We find a physical law of mutual attraction extending throughout material nature. Its rule is that attraction decreases inversely as the square of the distances from each attracting point, just as the spherical surfaces over which this force spreads increase. This seems to lie necessarily in the nature of things themselves, and is therefore usually presented as knowable a priori. The sources of this law are simple: they rest only on the ratio of spherical surfaces with different radii. Yet its consequence is remarkable for the variety of the agreement it produces and for its regularity. It yields not only all possible paths of heavenly bodies in conic sections, but also such a relation of those paths to one another that no law of attraction other than the inverse-square law of distances can be conceived as suitable for a system of the world.
Here, then, is nature resting on laws that the understanding knows a priori, chiefly from universal principles for determining space. Now I ask: do these laws of nature lie in space? Does the understanding learn them simply by trying to investigate the rich meaning contained in space? Or do they lie in the understanding and in the way it determines space according to the conditions of synthetic unity, toward which all its concepts are directed? Space is so uniform, and so undetermined with respect to all particular properties, that we certainly will not look in it for a treasure of natural laws. Instead, it is the understanding that determines space into the shape of a circle, a cone, or a sphere, insofar as it contains the ground of the unity of their construction. So the mere universal form of intuition called space is indeed the underlying basis of all intuitions that can be determined with respect to particular objects. And this basis certainly contains the condition of their possibility and variety. But the unity of objects is determined solely by the understanding, according to conditions that lie in its own nature. So the understanding is the source of the universal order of nature. It brings all appearances under its own laws and thereby first produces experience a priori as far as its form is concerned. Through this experience, everything that is to be known only through experience is necessarily subjected to the understanding's laws. For we are not dealing with the nature of things in themselves. That is independent of the conditions both of our sensibility and of our understanding. We are dealing with nature as an object of possible experience. Here the understanding, by making experience possible, also ensures that the world of sense is either no object of experience at all, or a nature.
About this section
Section 38 is part of Prolegomena to Any Future Metaphysics by Immanuel Kant. This page sets the German original beside 2 direct-source translations, so any line can be checked against the source. It is section 45 of 72 in the work, which is kept in the European tradition.
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