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Space is not a determination of things in themselves, because it is intuited a priori

Because space is intuited a priori, and no determination of things, absolute or relative, can be intuited before the existence of the things to which it belongs, space is not a determination of things in themselves.

The argument

Form

a space is intuited a priori
s space is a determination of things in themselves, absolute or relative, and so could be intuited only after the existence of the things to which it belongs, hence not a priori

P1a
P2(s → ¬a)
C¬s

Machine check, truth table: valid: the conclusion holds in all 1 assignments of a, s that satisfy the premises. The check says nothing about whether the premises are true or faithful to the passage; only a named human can (DISPUTES.md).

The argument is the one sentence of reason given for conclusion (a) at A 26 / B 42: space is no determination of things in themselves, "for neither absolute nor relative determinations can be intuited prior to the existence of the things to which they belong, hence not a priori" (AA 3:55.06–08). The first premise, that an a priori intuition of space underlies all concepts of it, is the conclusion of the third point of the metaphysical exposition (A 25 / B 39–40, AA 3:53.14–16).

What the form captures and what it leaves out: premise 2 is rendered as "if space were a determination of things in themselves, it would not be intuited a priori", which is the contrapositive use Kant makes of the general sentence at AA 3:55.06–08; the equation of "before the existence of the things" with "a priori" is Kant's "mithin" in that sentence and belongs to premise 2, not to premise 1. The form does not represent the generality of that sentence (every determination of things), only its application to space.

Depends on

c-kant-space-a-prioriSpace is a necessary a priori representation and a pure a priori intuition
c-kant-determinations-not-intuited-a-prioriNo determination of things can be intuited before the things exist

Supports

c-kant-space-not-of-things-in-themselvesSpace is not a property or relation of things in themselves

Permanent address: /a/kant-space-not-of-things-in-themselves/ · Produced by claude-fable-5-1, 2026-10-06 · Disputes: none

Kritik der reinen Vernunft A 26 / B 42, Transcendental Aesthetic §3, conclusions (a) (AA 3:55.02–08)korpora.org, AA III 55

a) Der Raum stellt gar keine Eigenschaft irgend einiger Dinge an sich, oder sie in ihrem Verhältniß auf einander vor, d. i. keine Bestimmung derselben, die an Gegenständen selbst haftete, und welche bliebe, wenn man auch von allen subjectiven Bedingungen der Anschauung abstrahirte. Denn weder absolute, noch relative Bestimmungen können vor dem Dasein der Dinge, welchen sie zukommen, mithin nicht a priori angeschaut werden.

a) Space represents no property at all of any things in themselves, nor them in their relation to one another; that is, no determination of them that would attach to the objects themselves and that would remain even if one abstracted from all subjective conditions of intuition. For neither absolute nor relative determinations can be intuited prior to the existence of the things to which they belong, hence not a priori. — the project

Kritik der reinen Vernunft A 24–25 / B 38–40, Transcendental Aesthetic §2, points 2 and 3 (AA 3:52.30–53.16)korpora.org, AA III 52–53

Der Raum ist eine nothwendige Vorstellung a priori, die allen äußeren Anschauungen zum Grunde liegt. Man kann sich niemals eine Vorstellung davon machen, daß kein Raum sei, ob man sich gleich ganz wohl denken kann, daß keine Gegenstände darin angetroffen werden. Er wird also als die Bedingung der Möglichkeit der Erscheinungen und nicht als eine von ihnen abhängende Bestimmung angesehen und ist eine Vorstellung a priori, die nothwendiger Weise äußeren Erscheinungen zum Grunde liegt. Der Raum ist kein discursiver oder, wie man sagt, allgemeiner Begriff von Verhältnissen der Dinge überhaupt, sondern eine reine Anschauung. Denn erstlich kann man sich nur einen einigen Raum vorstellen, und wenn man von vielen Räumen redet, so versteht man darunter nur Theile eines und desselben alleinigen Raumes. Diese Theile können auch nicht vor dem einigen allbefassenden Raume gleichsam als dessen Bestandtheile (daraus seine Zusammensetzung möglich sei) vorhergehen, sondern nur in ihm gedacht werden. Er ist wesentlich einig, das Mannigfaltige in ihm, mithin auch der allgemeine Begriff von Räumen überhaupt beruht lediglich auf Einschränkungen. Hieraus folgt, daß in Ansehung seiner eine Anschauung a priori (die nicht empirisch ist) allen Begriffen von demselben zum Grunde liegt.

Space is a necessary a priori representation that underlies all outer intuitions. One can never form a representation of there being no space, although one can quite well think that no objects are encountered in it. It is therefore regarded as the condition of the possibility of appearances, and not as a determination dependent on them, and is an a priori representation that necessarily underlies outer appearances. Space is not a discursive or, as one says, general concept of relations of things in general, but a pure intuition. For, first, one can represent only a single space, and when one speaks of many spaces one understands by that only parts of one and the same unique space. These parts cannot precede the single all-encompassing space as its constituents, as it were (out of which its composition would be possible), but can only be thought in it. It is essentially single; the manifold in it, and hence also the general concept of spaces in general, rests solely on limitations. From this it follows that, with respect to space, an a priori intuition (which is not empirical) underlies all concepts of it. — the project

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