Kant's Theory of Knowledge Part 3

2. "We can never represent to ourselves that there is no s.p.a.ce, 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]

[17] B. 38, M. 24.

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 s.p.a.ce than that there is no s.p.a.ce. If, on the other hand, 'represent' or 'think' means 'make a mental picture of', the a.s.sertion is equally false. Kant is thinking of empty s.p.a.ce as a kind of receptacle for objects, and the _a priori_ character of our apprehension of s.p.a.ce lies, as before, in the supposed fact that in order to apprehend objects in s.p.a.ce we must begin with the apprehension of empty s.p.a.ce.

The examination of Kant's arguments for the _perceptive_ character of our apprehension of s.p.a.ce is a more complicated matter. By way of preliminary it should be noticed that they presuppose the possibility in general of distinguis.h.i.+ng 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 s.p.a.ce in particular belongs to perception.

[18] B. 35, M. 22 (quoted p. 39). It is noteworthy (1) that the pa.s.sage contains no _argument_ to show that extension and shape are not, equally with divisibility, _thought_ to belong to an object, (2) that impenetrability, which is here said to belong to sensation, obviously cannot do so, and (3) that (as has been pointed out, p. 39) the last sentence of the paragraph in question presupposes that we have a perception of empty s.p.a.ce, and that this is a _form_ of perception.

There appears to be no way of distinguis.h.i.+ng 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.

[19] And _not_ as mutually involved in the apprehension of any individual reality.

[20] This distinction is of course different to that previously drawn _within_ perception in the full sense between perception in a narrow sense and conception (pp. 28-9).

Kant's arguments to show that our apprehension of s.p.a.ce belongs to perception are two in number, and both are directed to show not, as they should, that s.p.a.ce is a _form_ of perception, but that it is a _perception_.[21] The first runs thus: "s.p.a.ce 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 s.p.a.ce, and if we speak of many s.p.a.ces we mean thereby only parts of one and the same unique s.p.a.ce. Again, these parts cannot precede the one all-embracing s.p.a.ce as the component parts, as it were, out of which it can be composed, but can be thought only in it. s.p.a.ce is essentially one; the manifold in it, and consequently the general conception of s.p.a.ces in general, rests solely upon limitations."[22]

[21] Kant uses the phrase 'pure perception'; but 'pure' can only mean 'not containing sensation', and consequently adds nothing relevant.

[22] B. 39, M. 24. The concluding sentences of the paragraph need not be considered.

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 s.p.a.ce and then become aware of its parts by dividing it. Parts of s.p.a.ce are essentially limitations of the one s.p.a.ce; therefore to apprehend them we must first apprehend s.p.a.ce. And since s.p.a.ce is _one_, it must be object of perception; in other words, s.p.a.ce, in the sense of the one all-embracing s.p.a.ce, i. e. the totality of individual s.p.a.ces, is something perceived.

The argument appears open to two objections. In the _first_ place, we do _not_ perceive s.p.a.ce as a whole, and then, by dividing it, come to apprehend individual s.p.a.ces. We perceive individual s.p.a.ces, or, rather, individual bodies occupying individual s.p.a.ces.[23] We then apprehend that these s.p.a.ces, as s.p.a.ces, involve an infinity of other s.p.a.ces. In other words, it is reflection on the general nature of s.p.a.ce, the apprehension of which is involved in our apprehension of individual s.p.a.ces or rather of bodies in s.p.a.ce, which gives rise to the apprehension of the totality[24] of s.p.a.ces, the apprehension being an act, not of perception, but of thought or conception. It is necessary, then, to distinguish (_a_) individual s.p.a.ces, which we perceive; (_b_) the nature of s.p.a.ce in general, of which we become aware by reflecting upon the character of perceived individual s.p.a.ces, and which we conceive; (_c_) the totality of individual s.p.a.ces, the thought of which we reach by considering the nature of s.p.a.ce in general.

[23] This contention is not refuted by the objection that our distinct apprehension of an individual s.p.a.ce is always bound up with an indistinct apprehension of the s.p.a.ces immediately surrounding it. For our indistinct apprehension cannot be supposed to be of the whole of the surrounding s.p.a.ce.

[24] It is here a.s.sumed that a whole or a totality can be infinite. Cf. p. 102.

In the _second_ place, the distinctions just drawn afford no ground for distinguis.h.i.+ng s.p.a.ce 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]

[25] For a possible objection and the answer thereto, see note, p. 70.

Both in the case of colour and in that of s.p.a.ce 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 s.p.a.ce, whereas there are many individual colours. But the a.s.sertion that there is only one s.p.a.ce simply means that all individual bodies in s.p.a.ce are related spatially. This will be admitted, if the attempt be made to think of two bodies as in different s.p.a.ces 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 s.p.a.ce, the difference is due to the special nature of the universals conceived, and does not imply a difference between s.p.a.ce and colour in respect of perception and conception. In any case, s.p.a.ce as a whole is not object of perception, which it must be if Kant is to show that s.p.a.ce, as being one, is perceived; for s.p.a.ce in this context must mean the totality of individual s.p.a.ces.

Kant's second argument is stated as follows: "s.p.a.ce 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, s.p.a.ce is so conceived, for all parts of s.p.a.ce _ad infinitum_ exist simultaneously.

Consequently the original representation of s.p.a.ce 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 const.i.tute the conception itself (e. g. that of triangularity or redness) are not infinite; but the elements which go to const.i.tute s.p.a.ce are infinite, and therefore s.p.a.ce is not a conception but a perception.

Though, however, s.p.a.ce in the sense of the infinity of s.p.a.ces may be said to contain an infinite number of s.p.a.ces if it be meant that it _is_ these infinite s.p.a.ces, it does not follow, nor is it true, that s.p.a.ce 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 s.p.a.ce,[26] from which it is to follow that s.p.a.ce 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 pa.s.sage 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 s.p.a.ce, 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 pa.s.sage 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 pa.s.sage in the _Prolegomena_.

[26] viz. that it is _a priori_ and a pure perception.

[27] ---- 6-11.

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 s.p.a.ce. 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 s.p.a.ce.

The argument of -- 3 runs as follows: "Geometry is a science which determines the properties of s.p.a.ce synthetically and yet _a priori_.

What, then, must be the representation of s.p.a.ce, 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. s.p.a.ce 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]

[28] 'External perception' can only mean perception of what is spatial.

[29] _Vorhergeht._

[30] 'Formal nature _to be affected by objects_' is not relevant to the context.

Here three steps are taken. From the _synthetic_ character of geometrical judgements it is concluded that s.p.a.ce 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 s.p.a.ce 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 s.p.a.ce before we perceive objects in it, and thereby are able to antic.i.p.ate the spatial relations which condition these objects, it is concluded that s.p.a.ce is only a characteristic of our perceiving nature, and consequently that s.p.a.ce is a property not of things in themselves, but only of things as perceived by us.[32]

[31] Cf. B. 42, M. 26 (a) fin., (b) second sentence.

[32] Cf. B. 43, M. 26-7.

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 s.p.a.ce, 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 s.p.a.ce _is the manifestation of_ the mind's perceiving nature, but that it _is_ the mind's perceiving nature. For the conclusion is that s.p.a.ce[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 pa.s.sage in the _Prolegomena_.[34]

[33] Kant draws no distinction between s.p.a.ce and the perception of s.p.a.ce, or, rather, habitually speaks of s.p.a.ce as a perception. No doubt he considers that his view that s.p.a.ce is only a characteristic of phenomena justifies the identification of s.p.a.ce and the perception of it.

Occasionally, however, he distinguishes them. Thus he sometimes speaks of the representation of s.p.a.ce (e. g.

B. 38-40, M. 23-4); in _Prol._, -- 11, he speaks of a pure perception of s.p.a.ce and time; and in B. 40, M. 25, he says that our representation of s.p.a.ce must be perception. But this language is due to the pressure of the facts, and not to his general theory; cf. pp. 135-6.

[34] ---- 6-11.

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 pa.s.sage 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.

[35] B. 740 ff., M. 434 ff. Compare especially the following: "_Philosophical_ knowledge is _knowledge of reason_ by means of _conceptions_; mathematical knowledge is knowledge by means of the _construction_ of conceptions. But the _construction_ of a conception means the _a priori_ presentation of a perception corresponding to it. The construction of a conception therefore demands a _non-empirical_ perception, which, therefore, as a perception, is an _individual_ object, but which none the less, as the construction of a conception (a universal representation), must express in the representation universal validity for all possible perceptions which come under that conception. Thus I construct a triangle by presenting the object corresponding to the conception, either by mere imagination in pure perception, or also, in accordance with pure perception, on paper in empirical perception, but in both cases completely _a priori_, without having borrowed the pattern of it from any experience. The individual drawn figure is empirical, but nevertheless serves to indicate the conception without prejudice to its universality, because in this empirical perception we always attend only to the act of construction of the conception, to which many determinations, e. g. the magnitude of the sides and of the angles, are wholly indifferent, and accordingly abstract from these differences, which do not change the conception of the triangle."

The account in the _Prolegomena_, however, differs from that of the _Doctrine of Method_ in one important respect. It a.s.serts 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]

[36] This becomes more explicit in -- 8 and ff.

[37] This is also, and more obviously, implied in ---- 8-11.

The thought of the pa.s.sage 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 s.p.a.ce. s.p.a.ce is that _in which_ it must be constructed and perceived. A perception[38] of empty s.p.a.ce 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.'

[38] _Pure_ perception only means that the s.p.a.ce perceived is empty.

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 s.p.a.ce involved by geometry--which, as pure, is the perception of empty s.p.a.ce, and which, as the perception of empty s.p.a.ce, is _a priori_ in the sense of temporally prior to the perception of actual objects--presupposes that an object is not actually present.

[39] _Prol._ -- 8.

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.