Kant Lexicon

Space: Raum (German)

In his 1768 essay “Concerning the Ultimate Ground of the Differentiation of Directions in Space,” Kant argued for the claim that there is an “absolute and original space” which is the only basis for the possibility of the the relation of physical things to one another (Ak 2:383). This view is generally in accord with that of Newton and is opposed to the view of Leibniz, who held that “space simply consists in the external relation of the parts of matter which exist alongside one another” (Ak 2:383).

As proof of this thesis, Kant appealed to the phenomenon of an “incongruent counterpart,” which is “a body which is exactly equal and similar to another, but which cannot be enclosed in the same limits as that other” (Ak 2:382). For example a human right hand is an incongruent counterpart of a human left hand, and a mirror-image is an incongruent counterpart of what it reflects. If space consists in the external relation of the parts of matter that exist along side one another, then the relations of the parts of, say, a right hand would define its space. But the relation of the parts of a left hand would define its space as well. Since the relations are the same in both cases, the two spaces would be the same. But they are not, as the right hand cannot be enclosed in the limits of the left hand. So, the position of the parts of matter does not determine its space. Rather, it is absolute and original space that determines the space of material things.

Kant concluded further that space cannot be perceived by the senses. It is instead a “fundamental concept which first makes possible all outer perception” (Ak 2:383).

This conception of space is expanded in the 1770 Inaugural Dissertation, On the Form and Principles of the Sensible and the Intelligible World. Kant begins by defining the matter of a world as its parts, which “are taken to be substances” (Ak 2:389). The form is what co-ordinates the substances. He held that a world necessarily has “a certain constant and invariable form, which, as the perennial principle of each contingent and transitory form belonging to the state of that world, must be regarded as belonging to its nature” (Ak 2:391).

The distinction between the form and matter of a world is then carried over to the presentation of the world through sense, which presents things “as they appear” as opposed to “as they are” (Ak 2:392). The matter of presentation is sensation, and its form is “a certain law, which is inherent in the mind and by means of which it co-ordinates for itself that which is sensed from the presence of an object” (Ak 2:393). What is sensed is termed “phenomenon” or “appearance.”

Kant claims that there are two principles of the form of the sensible or phenomenal world: time and space. These are the products of laws of the mind and serve to co-ordinate what is sensed.

These formal principles of the phenomenal universe are absolutely primary and universal; they are, so the speak, the schemata and conditions of everything sensitive in human cognition.” (Ak 2:398)
Here we shall restrict our remarks to space.

Kant proceeds to develop an account of space which is in several ways the same as that in the Critique.

Kant argues against the “reality of space” by attacking its two chief forms. The absolute space of the Newtonians is a “fable” in that it allows the existence of spatial relations which relate no objects to one another. The relative space of the Leibnizians is more seriously in error, both because of its being “in headlong conflict with with the phenomena themselves” (presumably because of incongruent counterparts) and because it would degrade geometry to an empirical science (Ak 2:404).

The concept of space is innate only in the sense that it is the product of a law of the mind. It is acquired only in the sense that the law is triggered only upon the occasion of sense-perception, though it is not abstracted from sense-perception. (Ak 2:405)

In the second edition of the Critique, there are two “expositions” of the concept of space, followed by conclusions from them and (after the treatment of time) general comments about both space and time. The “metaphysical exposition“ “exhibits the concept as given a priori” (A23/B38). The “transcendental exposition” explicates the concept of space as “a principle that permits insight into the possibility of other synthetic a priori cognitions” (A25/B41). The material in the transcendental exposition is included in the metaphysical exposition in the first edition.

Four points are made in the metaphysical exposition.

  1. Space is not an empirical concept that is abstracted from experience.
  2. Space is an a priori cognition, and it underlies all outer intuitions
  3. Space is a pure intuition, and not a discursive concept.
  4. Space is presented as an infinite given magnitude.
The transcendental exposition explains how space as a pure intuition underlies and makes comprehensible the synthetic a priori principles of geometry.

Two conclusions are then drawn.

Space is “transcendentally ideal, i.e., . . . nothing as soon as we omit the condition of the possibility of all experience and suppose space to be something underlying things in themselves” (A28/B44). On the other hand, space is “empirically real,” in the sense that all objects of experience are subject to space as a condition.

After the exposition of time, there is an “Elucidation” which is marked in the second edition as §7. Here, Kant considers a dilemma for those who would maintain the transcendental reality of space. Space is either subsistent (the Newtonian view) or inherent (the Leibnizian view). If the former, “they must assume two eternal and infinite self-subsistent nonentitied (space and time), which exist (yet without there being anything actual) only in order to encompass anything actual” (A39/B56). This view does have the advantage of making intelligible the a priori application of geometry to the world, but its disadvantage is that space creates confusion when it is applied to the world beyond experience. If the latter, then space is an empirical concept, in which case it cannot be explained how geometry can be applied a priori to the world. However, there is the advantage that space does not “get in the way” of their accounts of reality beyond appearances.

In the second edition, the general comments make four points, only the first of which is found in the first edition. The first is an elaboration of the points made earlier, specifically attacking the standpoint of Leibniz and his followers that sensibility is merely a confused way of presenting things that are presented clearly by the understanding. Then a reductio argument is given against space being a condition for the possibility of things in themselves. Second, a confirmation of the earlier view is given, based on the relational nature of the properties of physical objects. Third, a distinction is made between appearances and illusion. Fourth, if space is an objective form, it would have to be a condition for God’s existence, which is an undesirable outcome that is avoided if space is subjective. (This may be an instance of the “confusion” introduced into metaphysics by making spacee self-subsistent.)

Further criticism of the Leibnizian view of space is found in the “Amphiboly of the Concepts of Reflection.” The claim there is that the relational view of space is the result of trying to understand objects merely by a comparison of concepts. Conceptually, matter is prior to form, while for the spatial objects of sensibility, form is prior to matter.

See the lecture on time for a detailed analysis of the account of space in the Transcendental Aesthetic in the Critique)

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