A Commentary to Kant's 'Critique of Pure Reason'

by Norman Kemp Smith

The argument, more freely stated, is that what is empirically given from without can be thought away, and that since space cannot be thus eliminated, it must be grounded in our subjective organisation, i.e. must be psychologically a priori. The argument, as stated by Kant, emphasises the apriority, not the subjectivity, of space, but none the less the asserted apriority is psychological, not logical in character. For the criterion employed is not the impossibility of thinking otherwise, but our incapacity to represent this specific element as absent. The ground upon which the whole argument is made to rest is the merely brute fact (asserted by Kant) of our incapacity to think except in terms of space.

The argument is, however, complicated by the drawing of a further consequence, which follows as a corollary from the main conclusion. From the subjective necessity of space follows its objective necessity. Space being necessary a priori, objects can only be apprehended in and through it. Consequently it is not dependent upon the objects apprehended, but itself underlies outer appearances as the condition of their possibility. This corollary is closely akin to the first argument on space, and differs from it only in orientation. The first argument has a psychological purpose. It maintains that the representation of space precedes external experience, causally conditioning it. The corollary has a more objective aim. It concludes that space is a necessary constituent of the external experience thus generated. The one proves that space is a necessary subjective antecedent; the other that it is a necessary objective ingredient.[439]

To consider the proof in detail. The exact words which Kant employs in stating the nervus probandi of the argument are that we can never represent (eine Vorstellung davon machen) space as non-existent, though we can very well think (denken) it as being empty of objects. The terms Vorstellung and denken are vague and misleading. Kant himself recognises that it is possible to conceive that there are beings who intuit objects in some other manner than in space. He cannot therefore mean that we are unable to think or conceive space as non-existent. He must mean that we cannot in imagination intuit it as absent. It is the necessary form of all our intuitions, and therefore also of imagination, which is intuitive in character. Our consciousness is dependent upon given intuitions for its whole content, and to that extent space is a form with which the mind can never by any possibility dispense. Pure thought enables it to realise this de facto limitation, but not to break free from it. Even in admitting the possibility of other beings who are not thus constituted, the mind still recognises its own ineluctable limitations.

Kant offers no proof of his assertion that space can be intuited in image as empty of all sensible content; and as a matter of fact the assertion is false. Doubtless the use of the vague term Vorstellung is in great part responsible for Kant’s mistaken position. So long as imagination and thought are not clearly distinguished, the assertion is correspondingly indefinite. Pure space may possibly be conceived, but it can also be conceived as altogether non-existent. If, on the other hand, our imaginative power is alone in question, the asserted fact must be categorically denied. With the elimination of all sensible content space itself ceases to be a possible image. Kant’s proof thus rests upon a misstatement of fact.

In a second respect Kant’s proof is open to criticism. He takes the impossibility of imagining space as absent as proof that it originates from within. The argument is valid only if no other psychological explanation can be given of this necessity, as for instance through indissoluble association or through its being an invariable element in the given sensations. Kant’s ignoring of these possibilities is due to his unquestioning belief that sensations are non-spatial, purely qualitative. That is a presupposition whose truth is necessary to the cogency of the argument.

Third Argument.—This argument, which was omitted in the second edition, will be considered in its connection with the transcendental exposition into which it was then merged.

Fourth (in second edition, Third) Argument.—The next two arguments seek to show that space is not a discursive or general concept but an intuition. The first proof falls into two parts, (a) We can represent only a single space. For though we speak of many spaces, we mean only parts of one and the same single space. Space must therefore be an intuition. For only intuition is thus directly related to a single individual. A concept always refers indirectly, per notas communes, to a plurality of individuals. (b) The parts of space cannot precede the one all-comprehensive space. They can be thought only in and through it. They arise through limitation of it. Now the parts (i.e. the attributes) which compose a concept precede it in thought. Through combination of them the concept is formed. Space cannot, therefore, be a concept. Consequently it must, as the only remaining alternative, be an intuition. Only in an intuition does the whole precede the parts. In a concept the parts always precede the whole. Intuition stands for multiplicity in unity, conception for unity in multiplicity.

The first part of the argument refers to the extension, the second part to the intension of the space representation. In both aspects it appears as intuitional.[440]

Kant, in repeating his thesis as a conclusion from the above grounds, confuses the reader by an addition which is not strictly relevant to the argument, viz. by the statement that this intuition must be non-empirical and a priori. This is simply a recapitulation of what has been established in the preceding proofs. It is not, as might at first sight appear, part of the conclusion established by the argument under consideration. The reader is the more apt to be misled owing to the fact that very obviously arguments for the non-empirical and for the a priori character of space can be derived from proof (b). That space is non-empirical would follow from the fact that representation of space as a whole is necessary for the apprehension of any part of it. Empirical intuition can only yield the apprehension of a limited space. The apprehension of the comprehensive space within which it falls must therefore be non-empirical.

“As we intuitively apprehend (anschauend erkennen) not only the space of the object which affects our senses, but the whole space, space cannot arise out of the actual affection of the senses, but must precede it in time (vor ihr vorhergehen).”[441]