It is the aim of the Aesthetic to deal with the a priori knowledge which relates to the sensibility. This knowledge, according to Kant, is concerned with space and time. Hence he has to show firstly that our apprehension of space and time is a priori, i. e. that it is not derived from experience but originates in our apprehending nature; and secondly that within our apprehending nature this apprehension belongs to the sensibility and not to the understanding, or, in his language, that space and time are forms of perception or sensibility. Further, if his treatment is to be exhaustive, he should also show thirdly that space and time are the only forms of perception. This, however, he makes no attempt to do except in one passage,[1] where the argument fails. The first two points established, Kant is able to develop his main thesis, viz. that it is a condition of the validity of the a priori judgements which relate to space and time that these are characteristics of phenomena, and not of things in themselves.

It will be convenient to consider his treatment of space and time separately, and to begin with his treatment of space. It is necessary, however, first of all to refer to the term 'form of perception'. As Kant conceives a form of perception, it involves three antitheses.

(1) As a form of perception it is opposed, as a way or mode of perceiving, to particular perceptions.

(2) As a form or mode of perception it is opposed to a form or mode of conception.

(3) As a form of perception it is also opposed, as a way in which we apprehend things, to a way in which things are.

While we may defer consideration of the second and third antitheses, we should at once give attention to the nature of the first, because Kant confuses it with two other antitheses. There is no doubt that in general a form of perception means for Kant a general capacity of perceiving which, as such, is opposed to the actual perceptions in which it is manifested. For according to him our spatial perceptions are not foreign to us, but manifestations of our general perceiving nature; and this view finds expression in the assertion that space is a form of perception or of sensibility.[2]

Unfortunately, however, Kant frequently speaks of this form of perception as if it were the same thing as the actual perception of empty space.[3] In other words, he implies that such a perception is possible, and confuses it with a potentiality, i. e. the power of perceiving that which is spatial. The confusion is possible because it can be said with some plausibility that a perception of empty space—if its possibility be allowed—does not inform us about actual things, but only informs us what must be true of things, if there prove to be any; such a perception, therefore, can be thought of as a possibility of knowledge rather than as actual knowledge. The second confusion is closely related to the first, and arises from the fact that Kant speaks of space not only as a form of perception, but also as the form of phenomena in opposition to sensation as their matter. "That which in the phenomenon corresponds to[4] the sensation I term its matter; but that which effects that the manifold of the phenomenon can be arranged under certain relations I call the form of the phenomenon. Now that in which alone our sensations can be arranged and placed in a certain form cannot itself be sensation. Hence while the matter of all phenomena is only given to us a posteriori, their form [i. e. space] must lie ready for them all together a priori in the mind."[5] Here Kant is clearly under the influence of his theory of perception.[6] He is thinking that, given the origination of sensations in us by the thing in itself, it is the business of the mind to arrange these sensations spatially in order to attain knowledge of the spatial world.[7] Space being, as it were, a kind of empty vessel in which sensations are arranged, is said to be the form of phenomena.[8] Moreover, if we bear in mind that ultimately bodies in space are for Kant only spatial arrangements of sensations,[9] we see that the assertion that space is the form of phenomena is only Kant's way of saying that all bodies are spatial.[10] Now Kant, in thus asserting that space is the form of phenomena, is clearly confusing this assertion with the assertion that space is a form of perception, and he does so in consequence of the first confusion, viz. that between a capacity of perceiving and an actual perception of empty space. For in the passage last quoted he continues thus: "I call all representations[11] pure (in the transcendental sense) in which nothing is found which belongs to sensation. Accordingly there will be found a priori in the mind the pure form of sensuous perceptions in general, wherein all the manifold of phenomena is perceived in certain relations. This pure form of sensibility will also itself be called pure perception. Thus, if I abstract from the representation of a body that which the understanding thinks respecting it, such as substance, force, divisibility, &c., and also that which belongs to sensation, such as impenetrability, hardness, colour, &c., something is still left over for me from this empirical perception, viz. extension and shape. These belong to pure perception, which exists in the mind a priori, even without an actual object of the senses or a sensation, as a mere form of sensibility." Here Kant has passed, without any consciousness of a transition, from treating space as that in which the manifold of sensation is arranged to treating it as a capacity of perceiving. Moreover, since Kant in this passage speaks of space as a perception, and thereby identifies space with the perception of it,[12] the confusion may be explained thus. The form of phenomena is said to be the space in which all sensations are arranged, or in which all bodies are; space, apart from all sensations or bodies, i. e. empty, being the object of a pure perception, is treated as identical with a pure perception, viz. the perception of empty space; and the perception of empty space is treated as identical with a capacity of perceiving that which is spatial.[13]

The existence of the confusion, however, is most easily realized by asking, 'How did Kant come to think of space and time as the only forms of perception?' It would seem obvious that the perception of anything implies a form of perception in the sense of a mode or capacity of perceiving. To perceive colours implies a capacity for seeing; to hear noises implies a capacity for hearing. And these capacities may fairly be called forms of perception. As soon as this is realized, the conclusion is inevitable that Kant was led to think of space and time as the only forms of perception, because in this connexion he was thinking of each as a form of phenomena, i. e. as something in which all bodies or their states are, or, from the point of view of our knowledge, as that in which sensuous material is to be arranged; for there is nothing except space and time in which such arrangement could plausibly be said to be carried out.

As has been pointed out, Kant's argument falls into two main parts, one of which prepares the way for the other. The aim of the former is to show firstly that our apprehension of space is a priori, and secondly that it belongs to perception and not to conception. The aim of the latter is to conclude from these characteristics of our apprehension of space that space is a property not of things in themselves but only of phenomena. These arguments may be considered in turn.

The really valid argument adduced by Kant for the a priori character of our apprehension of space is based on the nature of geometrical judgements. The universality of our judgements in geometry is not based upon experience, i. e. upon the observation of individual things in space. The necessity of geometrical relations is apprehended directly in virtue of the mind's own apprehending nature. Unfortunately in the present context Kant ignores this argument and substitutes two others, both of which are invalid.

1. "Space is no empirical conception[14] which has been derived from external[15] experiences. For in order that certain sensations may be related to something external to me (that is, to something in a different part of space from that in which I am), in like manner, in order that I may represent them as external to and next to each other, and consequently as not merely different but as in different places, the representation of space must already exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phenomena through experience; but, on the contrary, this external experience is itself first possible only through the said representation."[16] Here Kant is thinking that in order to apprehend, for example, that A is to the right of B we must first apprehend empty space. He concludes that our apprehension of space is a priori, because we apprehend empty space before we become aware of the spatial relations of individual objects in it.

To this the following reply may be made. (a) The term a priori applied to an apprehension should mean, not that it arises prior to experience, but that its validity is independent of experience. (b) That to which the term a priori should be applied is not the apprehension of empty space, which is individual, but the apprehension of the nature of space in general, which is universal. (c) We do not apprehend empty space before we apprehend individual spatial relations of individual bodies or, indeed, at any time. (d) Though we come to apprehend a priori the nature of space in general, the apprehension is not prior but posterior in time to the apprehension of individual spatial relations. (e) It does not follow from the temporal priority of our apprehension of individual spatial relations that our apprehension of the nature of space in general is 'borrowed from experience', and is therefore not a priori.

2. "We can never represent to ourselves that there is no space, though we can quite well think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and not as a determination dependent upon them, and it is an a priori representation, which necessarily underlies external phenomena."[17]

Here the premise is simply false. If 'represent' or 'think' means 'believe', we can no more represent or think that there are no objects in space than that there is no space. If, on the other hand, 'represent' or 'think' means 'make a mental picture of', the assertion is equally false. Kant is thinking of empty space as a kind of receptacle for objects, and the a priori character of our apprehension of space lies, as before, in the supposed fact that in order to apprehend objects in space we must begin with the apprehension of empty space.

The examination of Kant's arguments for the perceptive character of our apprehension of space is a more complicated matter. By way of preliminary it should be noticed that they presuppose the possibility in general of distinguishing features of objects which belong to the perception of them from others which belong to the conception of them. In particular, Kant holds that our apprehension of a body as a substance, as exercising force and as divisible, is due to our understanding as conceiving it, while our apprehension of it as extended and as having a shape is due to our sensibility as perceiving it.[18] The distinction, however, will be found untenable in principle; and if this be granted, Kant's attempt to distinguish in this way the extension and shape of an object from its other features can be ruled out on general grounds. In any case, it must be conceded that the arguments fail by which he seeks to show that space in particular belongs to perception. There appears to be no way of distinguishing perception and conception as the apprehension of different realities[19] except as the apprehension of the individual and of the universal respectively. Distinguished in this way, the faculty of perception is that in virtue of which we apprehend the individual, and the faculty of conception is that power of reflection in virtue of which a universal is made the explicit object of thought.[20] If this be granted, the only test for what is perceived is that it is individual, and the only test for what is conceived is that it is universal. These are in fact the tests which Kant uses. But if this be so, it follows that the various characteristics of objects cannot be divided into those which are perceived and those which are conceived. For the distinction between universal and individual is quite general, and applies to all characteristics of objects alike. Thus, in the case of colour, we can distinguish colour in general and the individual colours of individual objects; or, to take a less ambiguous instance, we can distinguish a particular shade of redness and its individual instances. Further, it may be said that perception is of the individual shade of red of the individual object, and that the faculty by which we become explicitly aware of the particular shade of red in general is that of conception. The same distinction can be drawn with respect to hardness, or shape, or any other characteristic of objects. The distinction, then, between perception and conception can be drawn with respect to any characteristic of objects, and does not serve to distinguish one from another.

Kant's arguments to show that our apprehension of space belongs to perception are two in number, and both are directed to show not, as they should, that space is a form of perception, but that it is a perception.[21] The first runs thus: "Space is no discursive, or, as we say, general conception of relations of things in general, but a pure perception. For, in the first place, we can represent to ourselves only one space, and if we speak of many spaces we mean thereby only parts of one and the same unique space. Again, these parts cannot precede the one all-embracing space as the component parts, as it were, out of which it can be composed, but can be thought only in it. Space is essentially one; the manifold in it, and consequently the general conception of spaces in general, rests solely upon limitations."[22]

Here Kant is clearly taking the proper test of perception. Its object, as being an individual, is unique; there is only one of it, whereas any conception has a plurality of instances. But he reaches his conclusion by supposing that we first perceive empty space and then become aware of its parts by dividing it. Parts of space are essentially limitations of the one space; therefore to apprehend them we must first apprehend space. And since space is one, it must be object of perception; in other words, space, in the sense of the one all-embracing space, i. e. the totality of individual spaces, is something perceived. The argument appears open to two objections. In the first place, we do not perceive space as a whole, and then, by dividing it, come to apprehend individual spaces. We perceive individual spaces, or, rather, individual bodies occupying individual spaces.[23] We then apprehend that these spaces, as spaces, involve an infinity of other spaces. In other words, it is reflection on the general nature of space, the apprehension of which is involved in our apprehension of individual spaces or rather of bodies in space, which gives rise to the apprehension of the totality[24] of spaces, the apprehension being an act, not of perception, but of thought or conception. It is necessary, then, to distinguish (a) individual spaces, which we perceive; (b) the nature of space in general, of which we become aware by reflecting upon the character of perceived individual spaces, and which we conceive; (c) the totality of individual spaces, the thought of which we reach by considering the nature of space in general.

In the second place, the distinctions just drawn afford no ground for distinguishing space as something perceived from any other characteristic of objects as something conceived; for any other characteristic admits of corresponding distinctions. Thus, with respect to colour it is possible to distinguish (a) individual colours which we perceive; (b) colouredness in general, which we conceive by reflecting on the common character exhibited by individual colours and which involves various kinds or species of colouredness; (c) the totality of individual colours, the thought of which is reached by considering the nature of colouredness in general.[25]

Both in the case of colour and in that of space there is to be found the distinction between universal and individual, and therefore also that between conception and perception. It may be objected that after all, as Kant points out, there is only one space, whereas there are many individual colours. But the assertion that there is only one space simply means that all individual bodies in space are related spatially. This will be admitted, if the attempt be made to think of two bodies as in different spaces and therefore as not related spatially. Moreover, there is a parallel in the case of colour, since individual coloured bodies are related by way of colour, e. g. as brighter and duller; and though such a relation is different from a relation of bodies in respect of space, the difference is due to the special nature of the universals conceived, and does not imply a difference between space and colour in respect of perception and conception. In any case, space as a whole is not object of perception, which it must be if Kant is to show that space, as being one, is perceived; for space in this context must mean the totality of individual spaces.

Kant's second argument is stated as follows: "Space is represented as an infinite given magnitude. Now every conception must indeed be considered as a representation which is contained in an infinite number of different possible representations (as their common mark), and which therefore contains these under itself, but no conception can, as such, be thought of as though it contained in itself an infinite number of representations. Nevertheless, space is so conceived, for all parts of space ad infinitum exist simultaneously. Consequently the original representation of space is an a priori perception and not a conception." In other words, while a conception implies an infinity of individuals which come under it, the elements which constitute the conception itself (e. g. that of triangularity or redness) are not infinite; but the elements which go to constitute space are infinite, and therefore space is not a conception but a perception.

Though, however, space in the sense of the infinity of spaces may be said to contain an infinite number of spaces if it be meant that it is these infinite spaces, it does not follow, nor is it true, that space in this sense is object of perception.

The aim of the arguments just considered, and stated in § 2 of the Aesthetic, is to establish the two characteristics of our apprehension of space,[26] from which it is to follow that space is a property of things only as they appear to us and not as they are in themselves. This conclusion is drawn in § 4. §§ 2 and 4 therefore complete the argument. § 3, a passage added in the second edition of the Critique, interrupts the thought, for ignoring § 2, it once more establishes the a priori and perceptive character of our apprehension of space, and independently draws the conclusion drawn in § 4. Since, however, Kant draws the final conclusion in the same way in § 3 and in § 4, and since a passage in the Prolegomena,[27] of which § 3 is only a summary, gives a more detailed account of Kant's thought, attention should be concentrated on § 3, together with the passage in the Prolegomena.

It might seem at the outset that since the arguments upon which Kant bases the premises for his final argument have turned out invalid, the final argument itself need not be considered. The argument, however, of § 3 ignores the preceding arguments for the a priori and perceptive character of our apprehension of space. It returns to the a priori synthetic character of geometrical judgements, upon which stress is laid in the Introduction, and appeals to this as the justification of the a priori and perceptive character of our apprehension of space.

The argument of § 3 runs as follows: "Geometry is a science which determines the properties of space synthetically and yet a priori. What, then, must be the representation of space, in order that such a knowledge of it may be possible? It must be originally perception, for from a mere conception no propositions can be deduced which go beyond the conception, and yet this happens in geometry. But this perception must be a priori, i. e. it must occur in us before all sense-perception of an object, and therefore must be pure, not empirical perception. For geometrical propositions are always apodeictic, i. e. bound up with the consciousness of their necessity (e. g. space has only three dimensions), and such propositions cannot be empirical judgements nor conclusions from them."

"Now how can there exist in the mind an external perception[28] which precedes[29] the objects themselves, and in which the conception of them can be determined a priori? Obviously not otherwise than in so far as it has its seat in the subject only, as the formal nature of the subject to be affected by objects and thereby to obtain immediate representation, i. e. perception of them, and consequently only as the form of the external sense in general."[30]

Here three steps are taken. From the synthetic character of geometrical judgements it is concluded that space is not something which we conceive, but something which we perceive. From their a priori character, i. e. from the consciousness of necessity involved, it is concluded that the perception of space must be a priori in a new sense, that of taking place before the perception of objects in it.[31] From the fact that we perceive space before we perceive objects in it, and thereby are able to anticipate the spatial relations which condition these objects, it is concluded that space is only a characteristic of our perceiving nature, and consequently that space is a property not of things in themselves, but only of things as perceived by us.[32]

Two points in this argument are, even on the face of it, paradoxical. Firstly, the term a priori, as applied not to geometrical judgements but to the perception of space, is given a temporal sense; it means not something whose validity is independent of experience and which is the manifestation of the nature of the mind, but something which takes place before experience. Secondly, the conclusion is not that the perception of space is the manifestation of the mind's perceiving nature, but that it is the mind's perceiving nature. For the conclusion is that space[33] is the formal nature of the subject to be affected by objects, and therefore the form of the external sense in general. Plainly, then, Kant here confuses an actual perception and a form or way of perceiving. These points, however, are more explicit in the corresponding passage in the Prolegomena.[34]

It begins thus: "Mathematics carries with it thoroughly apodeictic certainty, that is, absolute necessity, and, therefore, rests on no empirical grounds, and consequently is a pure product of reason, and, besides, is thoroughly synthetical. How, then, is it possible for human reason to accomplish such knowledge entirely a priori?... But we find that all mathematical knowledge has this peculiarity, that it must represent its conception previously in perception, and indeed a priori, consequently in a perception which is not empirical but pure, and that otherwise it cannot take a single step. Hence its judgements are always intuitive.... This observation on the nature of mathematics at once gives us a clue to the first and highest condition of its possibility, viz. that there must underlie it a pure perception in which it can exhibit or, as we say, construct all its conceptions in the concrete and yet a priori. If we can discover this pure perception and its possibility, we may thence easily explain how a priori synthetical propositions in pure mathematics are possible, and consequently also how the science itself is possible. For just as empirical perception enables us without difficulty to enlarge synthetically in experience the conception which we frame of an object of perception through new predicates which perception itself offers us, so pure perception also will do the same, only with the difference that in this case the synthetical judgement will be a priori certain and apodeictic, while in the former case it will be only a posteriori and empirically certain; for the latter [i. e. the empirical perception on which the a posteriori synthetic judgement is based] contains only that which is to be found in contingent empirical perception, while the former [i. e. the pure perception on which the a priori synthetic judgement is based] contains that which is bound to be found in pure perception, since, as a priori perception, it is inseparably connected with the conception before all experience or individual sense-perception."

This passage is evidently based upon the account which Kant gives in the Doctrine of Method of the method of geometry.[35] According to this account, in order to apprehend, for instance, that a three-sided figure must have three angles, we must draw in imagination or on paper an individual figure corresponding to the conception of a three-sided figure. We then see that the very nature of the act of construction involves that the figure constructed must possess three angles as well as three sides. Hence, perception being that by which we apprehend the individual, a perception is involved in the act by which we form a geometrical judgement, and the perception can be called a priori, in that it is guided by our a priori apprehension of the necessary nature of the act of construction, and therefore of the figure constructed.

The account in the Prolegomena, however, differs from that of the Doctrine of Method in one important respect. It asserts that the perception involved in a mathematical judgement not only may, but must, be pure, i. e. must be a perception in which no spatial object is present, and it implies that the perception must take place before all experience of actual objects.[36] Hence a priori, applied to perception, has here primarily, if not exclusively, the temporal meaning that the perception takes place antecedently to all experience.[37]

The thought of the passage quoted from the Prolegomena can be stated thus: 'A mathematical judgement implies the perception of an individual figure antecedently to all experience. This may be said to be the first condition of the possibility of mathematical judgements which is revealed by reflection. There is, however, a prior or higher condition. The perception of an individual figure involves as its basis another pure perception. For we can only construct and therefore perceive an individual figure in empty space. Space is that in which it must be constructed and perceived. A perception[38] of empty space is, therefore, necessary. If, then, we can discover how this perception is possible, we shall be able to explain the possibility of a priori synthetical judgements of mathematics.'

Kant continues as follows: "But with this step the difficulty seems to increase rather than to lessen. For henceforward the question is 'How is it possible to perceive anything a priori?' A perception is such a representation as would immediately depend upon the presence of the object. Hence it seems impossible originally to perceive a priori, because perception would in that case have to take place without an object to which it might refer, present either formerly or at the moment, and accordingly could not be perception.... How can perception of the object precede the object itself?"[39] Kant here finds himself face to face with the difficulty created by the preceding section. Perception, as such, involves the actual presence of an object; yet the pure perception of space involved by geometry—which, as pure, is the perception of empty space, and which, as the perception of empty space, is a priori in the sense of temporally prior to the perception of actual objects—presupposes that an object is not actually present. The solution is given in the next section. "Were our perception necessarily of such a kind as to represent things as they are in themselves, no perception would take place a priori, but would always be empirical. For I can only know what is contained in the object in itself, if it is present and given to me. No doubt it is even then unintelligible how the perception of a present thing should make me know it as it is in itself, since its qualities cannot migrate over into my faculty of representation; but, even granting this possibility, such a perception would not occur a priori, i. e. before the object was presented to me; for without this presentation, no basis of the relation between my representation and the object can be imagined; the relation would then have to rest upon inspiration. It is therefore possible only in one way for my perception to precede the actuality of the object and to take place as a priori knowledge, viz. if it contains nothing but the form of the sensibility, which precedes in me, the subject, all actual impressions through which I am affected by objects. For I can know a priori that objects of the senses can only be perceived in accordance with this form of the sensibility. Hence it follows that propositions which concern merely this form of sensuous perception will be possible and valid for objects of the senses, and in the same way, conversely, that perceptions which are possible a priori can never concern any things other than objects of our senses."

This section clearly constitutes the turning-point in Kant's argument, and primarily expresses, in an expanded form, the central doctrine of § 3 of the Aesthetic, that an external perception anterior to objects themselves, and in which our conceptions of objects can be determined a priori, is possible, if, and only if, it has its seat in the subject as its formal nature of being affected by objects, and consequently as the form of the external sense in general. It argues that, since this is true, and since geometrical judgements involve such a perception anterior to objects, space must be only the[40] form of sensibility.

Now why does Kant think that this conclusion follows? Before we can answer this question we must remove an initial difficulty. In this passage Kant unquestionably identifies a form of perception with an actual perception. It is at once an actual perception and a capacity of perceiving. This is evident from the words, "It is possible only in one way for my perception to precede the actuality of the object ... viz. if it contains nothing but the form of the sensibility."[41] The identification becomes more explicit a little later. "A pure perception (of space and time) can underlie the empirical perception of objects, because it is nothing but the mere form of the sensibility, which precedes the actual appearance of the objects, in that it in fact first makes them possible. Yet this faculty of perceiving a priori affects not the matter of the phenomenon, i. e. that in it which is sensation, for this constitutes that which is empirical, but only its form, viz. space and time."[42] His argument, however, can be successfully stated without this identification. It is only necessary to re-write his cardinal assertion in the form 'the perception of space must be nothing but the manifestation of the form of the sensibility'. Given this modification, the question becomes, 'Why does Kant think that the perception of empty space, involved by geometrical judgements, can be only a manifestation of our perceiving nature, and not in any way the apprehension of a real quality of objects?' The answer must be that it is because he thinks that, while in empirical perception a real object is present, in the perception of empty space a real object is not present. He regards this as proving that the latter perception is only of something subjective or mental. "Space and time, by being pure a priori perceptions, prove that they are mere forms of our sensibility which must precede all empirical perception, i. e. sense-perception of actual objects."[43] His main conclusion now follows easily enough. If in perceiving empty space we are only apprehending a manifestation of our perceiving nature, what we apprehend in a geometrical judgement is really a law of our perceiving nature, and therefore, while it must apply to our perceptions of objects or to objects as perceived, it cannot apply to objects apart from our perception, or, at least, there is no ground for holding that it does so.

If, however, this fairly represents Kant's thought, it must be allowed that the conclusion which he should have drawn is different, and even that the conclusion which he does draw is in reality incompatible with his starting-point.

His starting-point is the view that the truth of geometrical judgements presupposes a perception of empty space, in virtue of which we can discover rules of spatial relation which must apply to all spatial objects subsequently perceived. His problem is to discover the presupposition of this presupposition. The proper answer must be, not that space is a form of sensibility or a way in which objects appear to us, but that space is the form of all objects, i. e. that all objects are spatial.[44] For in that case they must be subject to the laws of space, and therefore if we can discover these laws by a study of empty space, the only condition to be satisfied, if the objects of subsequent perception are to conform to the laws which we discover, is that all objects should be spatial. Nothing is implied which enables us to decide whether the objects are objects as they are in themselves or objects as perceived; for in either case the required result follows. If in empirical perception we apprehend things only as they appear to us, and if space is the form of them as they appear to us, it will no doubt be true that the laws of spatial relation which we discover must apply to things as they appear to us. But on the other hand, if in empirical perception we apprehend things as they are, and if space is their form, i. e. if things are spatial, it will be equally true that the laws discovered by geometry must apply to things as they are.

Again, Kant's starting-point really commits him to the view that space is a characteristic of things as they are. For—paradoxical though it may be—his problem is to explain the possibility of perceiving a priori, i. e. of perceiving the characteristics of an object anterior to the actual presence of the object in perception.[45] This implies that empirical perception, which involves the actual presence of the object, involves no difficulty; in other words, it is implied that empirical perception is of objects as they are. And we find Kant admitting this to the extent of allowing for the sake of argument that the perception of a present thing can make us know the thing as it is in itself.[46] But if empirical perception gives us things as they are, and if, as is the case, and as Kant really presupposes, the objects of empirical perception are spatial, then, since space is their form, the judgements of geometry must relate to things as they are. It is true that on this view Kant's first presupposition of geometrical judgements has to be stated by saying that we are able to perceive a real characteristic of things in space, before we perceive the things; and, no doubt, Kant thinks this impossible. According to him, when we perceive empty space no object is present, and therefore what is before the mind must be merely mental. But no greater difficulty is involved than that involved in the corresponding supposition required by Kant's own view. It is really just as difficult to hold that we can perceive a characteristic of things as they appear to us before they appear, as to hold that we can perceive a characteristic of them as they are in themselves before we perceive them.

The fact is that the real difficulty with which Kant is grappling in the Prolegomena arises, not from the supposition that spatial bodies are things in themselves, but from the supposed presupposition of geometry that we must be able to perceive empty space before we perceive bodies in it. It is, of course, impossible to defend the perception of empty space, but if it be maintained, the space perceived must be conceded to be not, as Kant thinks, something mental or subjective, but a real characteristic of things. For, as has been pointed out, the paradox of pure perception is reached solely through the consideration that, while in empirical perception we perceive objects, in pure perception we do not, and since the objects of empirical perception are spatial, space must be a real characteristic of them.

The general result of the preceding criticism is that Kant's conclusion does not follow from the premises by which he supports it. It should therefore be asked whether it is not possible to take advantage of this hiatus by presenting the argument for the merely phenomenal character of space without any appeal to the possibility of perceiving empty space. For it is clear that what was primarily before Kant, in writing the Critique, was the a priori character of geometrical judgements themselves, and not the existence of a perception of empty space which they were held to presuppose.[47]

If, then, the conclusion that space is only the form of sensibility can be connected with the a priori character of geometrical judgements without presupposing the existence of a perception of empty space, his position will be rendered more plausible.

This can be done as follows. The essential characteristic of a geometrical judgement is not that it takes place prior to experience, but that it is not based upon experience. Thus a judgement, arrived at by an activity of the mind in which it remains within itself and does not appeal to actual experience of the objects to which the judgement relates, is implied to hold good of those objects. If the objects were things as they are in themselves, the validity of the judgement could not be justified, for it would involve the gratuitous assumption that a necessity of thought is binding on things which ex hypothesi are independent of the nature of the mind. If, however, the objects in question are things as perceived, they will be through and through conditioned by the mind's perceiving nature; and, consequently, if a geometrical rule, e. g. that a three-sided figure must have three angles, is really a law of the mind's perceiving nature, all individual perceptions, i. e. all objects as perceived by us, will necessarily conform to the law. Therefore, in the latter case, and in that only, will the universal validity of geometrical judgements be justified. Since, then, geometrical judgements are universally valid, space, which is that of which geometrical laws are the laws, must be merely a form of perception or a characteristic of objects as perceived by us.

This appears to be the best form in which the substance of Kant's argument, stripped of unessentials, can be stated. It will be necessary to consider both the argument and its conclusion.

The argument, so stated, is undeniably plausible. Nevertheless, examination of it reveals two fatal defects. In the first place, its starting-point is false. To Kant the paradox of geometrical judgements lies in the fact that they are not based upon an appeal to experience of the things to which they relate. It is implied, therefore, that judgements which are based on experience involve no paradox, and for the reason that in experience we apprehend things as they are.[48] In contrast with this, it is implied that in geometrical judgements the connexion which we apprehend is not real, i. e. does not relate to things as they are. Otherwise, there would be no difficulty; if in geometry we apprehended rules of connexion relating to things as they are, we could allow without difficulty that the things must conform to them. No such distinction, however, can be drawn between a priori and empirical judgements. For the necessity of connexion, e. g. between being a three-sided figure and being a three-angled figure, is as much a characteristic of things as the empirically-observed shape of an individual body, e. g. a table. Geometrical judgements, therefore, cannot be distinguished from empirical judgements on the ground that in the former the mind remains within itself, and does not immediately apprehend fact or a real characteristic of reality.[49] Moreover, since in a geometrical judgement we do in fact think that we are apprehending a real connexion, i. e. a connexion which applies to things and to things as they are in themselves, to question the reality of the connexion is to question the validity of thinking altogether, and to do this is implicitly to question the validity of our thought about the nature of our own mind, as well as the validity of our thought about things independent of the mind. Yet Kant's argument, in the form in which it has just been stated, presupposes that our thought is valid at any rate when it is concerned with our perceptions of things, even if it is not valid when concerned with the things as they are in themselves.

This consideration leads to the second criticism. The supposition that space is only a form of perception, even if it be true, in no way assists the explanation of the universal validity of geometrical judgements. Kant's argument really confuses a necessity of relation with the consciousness of a necessity of relation. No doubt, if it be a law of our perceiving nature that, whenever we perceive an object as a three-sided figure, the object as perceived contains three angles, it follows that any object as perceived will conform to this law; just as if it be a law of things as they are in themselves that three-sided figures contain three angles, all three-sided figures will in themselves have three angles. But what has to be explained is the universal applicability, not of a law, but of a judgement about a law. For Kant's real problem is to explain why our judgement that a three-sided figure must contain three angles must apply to all three-sided figures. Of course, if it be granted that in the judgement we apprehend the true law, the problem may be regarded as solved. But how are we to know that what we judge is the true law? The answer is in no way facilitated by the supposition that the judgement relates to our perceiving nature. It can just as well be urged that what we think to be a necessity of our perceiving nature is not a necessity of it, as that what we think to be a necessity of things as they are in themselves is not a necessity of them. The best, or rather the only possible, answer is simply that that of which we apprehend the necessity must be true, or, in other words, that we must accept the validity of thought. Hence nothing is gained by the supposition that space is a form of sensibility. If what we judge to be necessary is, as such, valid, a judgement relating to things in themselves will be as valid as a judgement relating to our perceiving nature.[50]

This difficulty is concealed from Kant by his insistence on the perception of space involved in geometrical judgements. This leads him at times to identify the judgement and the perception, and, therefore, to speak of the judgement as a perception. Thus we find him saying that mathematical judgements are always perceptive,[51] and that "It is only possible for my perception to precede the actuality of the object and take place as a priori knowledge, if &c."[52] Hence, if, in addition, a geometrical judgement, as being a judgement about a necessity, be identified with a necessity of judging, the conformity of things to these universal judgements will become the conformity of things to rules or necessities of our judging, i. e. of our perceiving nature, and Kant's conclusion will at once follow.[53] Unfortunately for Kant, a geometrical judgement, however closely related to a perception, must itself, as the apprehension of what is necessary and universal, be an act of thought rather than of perception, and therefore the original problem of the conformity of things to our mind can be forced upon him again, even after he thinks that he has solved it, in the new form of that of the conformity within the mind of perceiving to thinking.

The fact is simply that the universal validity of geometrical judgements can in no way be 'explained'. It is not in the least explained or made easier to accept by the supposition that objects are 'phenomena'. These judgements must be accepted as being what we presuppose them to be in making them, viz. the direct apprehension of necessities of relation between real characteristics of real things. To explain them by reference to the phenomenal character of what is known is really—though contrary to Kant's intention—to throw doubt upon their validity; otherwise, they would not need explanation. As a matter of fact, it is impossible to question their validity. In the act of judging, doubt is impossible. Doubt can arise only when we subsequently reflect and temporarily lose our hold upon the consciousness of necessity in judging.[54] The doubt, however, since it is non-existent in our geometrical consciousness, is really groundless,[55] and, therefore, the problem to which it gives rise is unreal. Moreover if, per impossibile, doubt could be raised, it could not be set at rest. No vindication of a judgement in which we are conscious of a necessity could do more than take the problem a stage further back, by basing it upon some other consciousness of a necessity; and since this latter judgement could be questioned for precisely the same reason, we should only be embarking upon an infinite process.

We may now consider Kant's conclusion in abstraction from the arguments by which he reaches it. It raises three main difficulties.

In the first place, it is not the conclusion to be expected from Kant's own standpoint. The phenomenal character of space is inferred, not from the fact that we make judgements at all, but from the fact that we make judgements of a particular kind, viz. a priori judgements. From this point of view empirical judgements present no difficulty. It should, therefore, be expected that the qualities which we attribute to things in empirical judgements are not phenomenal, but belong to things as they are. Kant himself implies this in drawing his conclusion concerning the nature of space. "Space does not represent any quality of things in themselves or things in relation to one another; that is, it does not represent any determination of things which would attach to the objects themselves and would remain, even though we abstracted from all subjective conditions of perception. For neither absolute nor relative[56] determinations of objects can be perceived prior to the existence of the things to which they belong, and therefore not a priori."[57] It is, of course, implied that in experience, where we do not discover determinations of objects prior to the existence of the objects, we do apprehend determinations of things as they are in themselves, and not as they are in relation to us. Thus we should expect the conclusion to be, not that all that we know is phenomenal—which is Kant's real position—but that spatial (and temporal) relations alone are phenomenal, i. e. that they alone are the result of a transmutation due to the nature of our perceiving faculties.[58] This conclusion would, of course, be absurd, for what Kant considers to be the empirically known qualities of objects disappear, if the spatial character of objects is removed. Moreover, Kant is prevented by his theory of perception from seeing that this is the real solution of his problem, absurd though it may be. Since perception is held to arise through the origination of sensations by things in themselves, empirical knowledge is naturally thought of as knowledge about sensations, and since sensations are palpably within the mind, and are held to be due to things in themselves, knowledge about sensations can be regarded as phenomenal.

On the other hand, if we consider Kant's conclusion from the point of view, not of the problem which originates it, but of the distinction in terms of which he states it, viz. that between things as they are in themselves and things as perceived by us, we are led to expect the contrary result. Since perception is the being affected by things, and since the nature of the affection depends upon the nature of our capacity of being affected, in all perception the object will become distorted or transformed, as it were, by our capacity of being affected. The conclusion, therefore, should be that in all judgements, empirical as well as a priori, we apprehend things only as perceived. The reason why Kant does not draw this conclusion is probably that given above, viz. that by the time Kant reaches the solution of his problem empirical knowledge has come to relate to sensation only; consequently, it has ceased to occur to him that empirical judgements could possibly give us knowledge of things as they are. Nevertheless, Kant should not have retained in his formulation of the problem a distinction irreconcilable with his solution of it; and if he had realized that he was doing so he might have been compelled to modify his whole view.

The second difficulty is more serious. If the truth of geometrical judgements presupposes that space is only a property of objects as perceived by us, it is a paradox that geometricians should be convinced, as they are, of the truth of their judgements. They undoubtedly think that their judgements apply to things as they are in themselves, and not merely as they appear to us. They certainly do not think that the relations which they discover apply to objects only as perceived. Not only, therefore, do they not think that bodies in space are phenomena, but they do not even leave it an open question whether bodies are phenomena or not. Hence, if Kant be right, they are really in a state of illusion, for on his view the true geometrical judgement should include in itself the phenomenal character of spatial relations; it should be illustrated by expressing Euclid I. 5 in the form that the equality of the angles at the base of an isosceles triangle belongs to objects as perceived. Kant himself lays this down. "The proposition 'all objects are beside one another in space' is valid under[59] the limitation that these things are taken as objects of our sensuous perception. If I join the condition to the perception, and say 'all things, as external phenomena, are beside one another in space', the rule is valid universally, and without limitation."[60] Kant, then, is in effect allowing that it is possible for geometricians to make judgements, of the necessity of which they are convinced, and yet to be wrong; and that, therefore, the apprehension of the necessity of a judgement is no ground of its truth. It follows that the truth of geometrical judgements can no longer be accepted as a starting-point of discussion, and, therefore, as a ground for inferring the phenomenal character of space.

There seems, indeed, one way of avoiding this consequence, viz. to suppose that for Kant it was an absolute starting-point, which nothing would have caused him to abandon, that only those judgements of which we apprehend the necessity are true. It would, of course, follow that geometricians would be unable to apprehend the necessity of geometrical judgements, and therefore to make such judgements, until they had discovered that things as spatial were only phenomena. It would not be enough that they should think that the phenomenal or non-phenomenal character of things as spatial must be left an open question for the theory of knowledge to decide. In this way the necessity of admitting the illusory character of geometry would be avoided. The remedy, however, is at least as bad as the disease. For it would imply that geometry must be preceded by a theory of knowledge, which is palpably contrary to fact. Nor could Kant accept it; for he avowedly bases his theory of knowledge, i. e. his view that objects as spatial are phenomena, upon the truth of geometry; this procedure would be circular if the making of true geometrical judgements was allowed to require the prior adoption of his theory of knowledge.

The third difficulty is the most fundamental. Kant's conclusion (and also, of course, his argument) presupposes the validity of the distinction between phenomena and things in themselves. If, then, this distinction should prove untenable in principle, Kant's conclusion with regard to space must fail on general grounds, and it will even have been unnecessary to consider his arguments for it. The importance of the issue, however, requires that it should be considered in a separate chapter.