Section 10
Original German
§ 10.
Also ist es nur die Form der sinnlichen Anschauung, dadurch wir a priori Dinge anschauen können, wodurch wir aber auch die Objecte nur erkennen, wie sie uns (unsern Sinnen) erscheinen können, nicht wie sie an sich sein mögen; und diese Voraussetzung ist schlechterdings nothwendig, wenn synthetische Sätze a priori als möglich eingeräumt, oder, im Falle sie wirklich angetroffen werden, ihre Möglichkeit begriffen und zum voraus bestimmt werden soll.
Nun sind Raum und Zeit diejenigen Anschauungen, welche die reine Mathematik allen ihren Erkenntnissen und Urtheilen, die zugleich als apodiktisch und nothwendig auftreten, zum Grunde legt; denn Mathematik muß alle ihre Begriffe zuerst in der Anschauung und reine Mathematik in der reinen Anschauung darstellen, d. i. sie construiren, ohne welche (weil sie nicht analytisch, nämlich durch Zergliederung der Begriffe, sondern synthetisch verfahren kann) es ihr unmöglich ist, einen Schritt zu thun, so lange ihr nämlich reine Anschauung fehlt, in der allein der Stoff zu synthetischen Urtheilen a priori gegeben werden kann. Geometrie legt die reine Anschauung des Raums zum Grunde. Arithmetik bringt selbst ihre Zahlbegriffe durch successive Hinzusetzung der Einheiten in der Zeit zu Stande, vornehmlich aber reine Mechanik kann ihre Begriffe von Bewegung nur vermittelst der Vorstellung der Zeit zu Stande bringen. Beide Vorstellungen aber sind blos Anschauungen; denn wenn man von den empirischen Anschauungen der Körper und ihrer Veränderungen (Bewegung) alles Empirische, nämlich was zur Empfindung gehört, wegläßt, so bleiben noch Raum und Zeit übrig, welche also reine Anschauungen sind, die jenen a priori zum Grunde liegen und daher selbst niemals weggelassen werden können, aber eben dadurch, daß sie reine Anschauungen a priori sind, beweisen, daß sie bloße Formen unserer Sinnlichkeit sind, die vor aller empirischen Anschauung, d. i. der Wahrnehmung wirklicher Gegenstände, vorhergehen müssen, und denen gemäß Gegenstände a priori erkannt werden können, aber freilich nur, wie sie uns erscheinen.
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.
§ 10.
It is therefore only through the form of sensible intuition that we can intuit things a priori; but through it we cognize objects only as they can appear to us—to our senses—not as they may be in themselves. This presupposition is absolutely necessary if synthetic propositions a priori are to be admitted as possible or, where they are actually found, if their possibility is to be understood and determined in advance.
Now space and time are the intuitions on which pure mathematics bases all its cognitions and judgments, which at the same time present themselves as apodictic and necessary. For mathematics must first exhibit all its concepts in intuition, and pure mathematics in pure intuition—that is, it must construct them. Without this, it is impossible for mathematics to take a step, because it can proceed not analytically, by analyzing concepts, but synthetically: so long as it lacks pure intuition, it lacks the sole medium in which the material for synthetic judgments a priori can be given. Geometry takes the pure intuition of space as its foundation. Arithmetic itself produces its concepts of number by the successive addition of units in time; above all, pure mechanics can produce its concepts of motion only by means of the representation of time. Both representations, however, are merely intuitions. For if we leave out of the empirical intuitions of bodies and their alterations—motion—everything empirical, namely what belongs to sensation, space and time still remain. They are therefore pure intuitions, underlying those empirical intuitions a priori, and for this reason can never themselves be left out. But precisely because they are pure intuitions a priori, they prove that they are mere forms of our sensibility, which must precede all empirical intuition, that is, the perception of actual objects, and in accordance with which objects can be cognized a priori—though, to be sure, only as they appear to us.
Plain English translation
Mouseia’s complete Plain English edition, made independently and directly from the same complete German text.
§ 10.
It is therefore only through the form of sensible intuition that we can intuit things a priori. But through it we also know objects only as they can appear to us, to our senses, not as they may be in themselves. This assumption is absolutely necessary if synthetic a priori propositions are to be admitted as possible, or, where they actually occur, if their possibility is to be understood and determined in advance.
Now space and time are the intuitions that pure mathematics takes as the basis of all its cognitions and judgments, which it also presents as apodictic and necessary. Mathematics must first present all its concepts in intuition, and pure mathematics in pure intuition: that is, it must construct them. Without this, it cannot take a step as long as it lacks pure intuition, in which alone the material for synthetic a priori judgments can be given. For it cannot proceed analytically, by analyzing concepts, but only synthetically. Geometry takes the pure intuition of space as its basis. Arithmetic produces its concepts of number by successively adding units in time. Above all, pure mechanics can produce its concepts of motion only through the representation of time. Both representations, however, are simply intuitions. If we remove everything empirical—everything belonging to sensation—from empirical intuitions of bodies and their changes, or motion, space and time still remain. They are therefore pure intuitions that underlie those empirical intuitions a priori and so can never themselves be removed. But precisely because they are pure a priori intuitions, they prove that they are mere forms of our sensibility. They must precede all empirical intuition, that is, the perception of actual objects. Objects can be known a priori in conformity with them, but of course only as they appear to us.
About this section
Section 10 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 15 of 72 in the work, which is kept in the European tradition.
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