FOOTNOTES
[1] B. 58, M. 35.
[2] Cf. B. 43 init., M. 26 med.
[3] e. g. B. 34, 35, M. 22; B. 41, M. 25; Prol. §§ 9-11. The commonest expression of the confusion is to be found in the repeated assertion that space is a pure perception.
[4] 'Corresponds to' must mean 'is'.
[5] B. 34, M. 21.
[6] Cf. pp. 30-2.
[7] It is impossible, of course, to see how such a process can give us knowledge of the spatial world, for, whatever bodies in space are, they are not arrangements of sensations. Nevertheless, Kant's theory of perception really precludes him from holding that bodies are anything else than arrangements of sensations, and he seems at times to accept this view explicitly, e. g. B. 38, M. 23 (quoted p. 41), where he speaks of our representing sensations as external to and next to each other, and, therefore, as in different places.
[8] It may be noted that it would have been more natural to describe the particular shape of the phenomenon (i. e. the particular spatial arrangement of the sensations) rather than space as the form of the phenomenon; for the matter to which the form is opposed is said to be sensation, and that of which it is the matter is said to be the phenomenon, i. e. a body in space.
[9] Cf. note 4, p. 38.
[10] Cf. Prol. § 11 and p. 137.
[11] Cf. p. 41, note 1.
[12] Cf. p. 51, note 1.
[13] The same confusion (and due to the same cause) is implied Prol. § 11, and B. 42 (b), M. 26 (b) first paragraph. Cf. B. 49 (b), M. 30 (b).
[14] Begriff (conception) here is to be understood loosely not as something opposed to Anschauung (perception), but as equivalent to the genus of which Anschauung and Begriff are species, i. e. Vorstellung, which maybe rendered by 'representation' or 'idea', in the general sense in which these words are sometimes used to include 'thought' and 'perception'.
[15] The next sentence shows that 'external' means, not 'produced by something external to the mind', but simply 'spatial'.
[16] B. 38, M. 23-4.
[17] B. 38, M. 24.
[18] B. 35, M. 22 (quoted p. 39). It is noteworthy (1) that the passage 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 space, and that this is a form of perception.
[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).
[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.
[23] This contention is not refuted by the objection that our distinct apprehension of an individual space is always bound up with an indistinct apprehension of the spaces immediately surrounding it. For our indistinct apprehension cannot be supposed to be of the whole of the surrounding space.
[24] It is here assumed that a whole or a totality can be infinite. Cf. p. 102.
[25] For a possible objection and the answer thereto, see note, p. 70.
[26] viz. that it is a priori and a pure perception.
[27] §§ 6-11.
[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.
[31] Cf. B. 42, M. 26 (a) fin., (b) second sentence.
[32] Cf. B. 43, M. 26-7.
[33] Kant draws no distinction between space and the perception of space, or, rather, habitually speaks of space as a perception. No doubt he considers that his view that space is only a characteristic of phenomena justifies the identification of space and the perception of it. Occasionally, however, he distinguishes them. Thus he sometimes speaks of the representation of space (e. g. B. 38-40, M. 23-4); in Prol., § 11, he speaks of a pure perception of space and time; and in B. 40, M. 25, he says that our representation of space 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.
[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."
[36] This becomes more explicit in § 8 and ff.
[37] This is also, and more obviously, implied in §§ 8-11.
[38] Pure perception only means that the space perceived is empty.
[39] Prol. § 8.
[40] The and not a, because, for the moment, time is ignored.
[41] Prol., § 9.
[42] Prol., § 11.
[43] Prol., § 10.
[44] Kant expresses the assertion that space is the form of all objects by saying that space is the form of phenomena. This of course renders easy an unconscious transition from the thesis that space is the form of objects to the quite different thesis that space is the form of sensibility; cf. p. 39.
[45] Cf. Prol., Section 8.
[46] Prol., § 9 (cf. p. 55).
[47] The difficulty with which Kant is struggling in the Prolegomena, §§ 6-11, can be stated from a rather different point of view by saying that the thought that geometrical judgements imply a perception of empty space led him to apply the term 'a priori' to perception as well as to judgement. The term, a priori, applied to judgements has a valid meaning; it means, not that the judgement is made prior to all experience, but that it is not based upon experience, being originated by the mind in virtue of its own powers of thinking. Applied to perception, however, 'a priori' must mean prior to all experience, and, since the object of perception is essentially individual (cf. B. 741, M. 435), this use of the term gives rise to the impossible task of explaining how a perception can take place prior to the actual experience of an individual in perception (cf. Prol., § 8).
[48] Cf. p. 17.
[49] For the reasons which led Kant to draw this distinction between empirical and a priori judgements, cf. pp. 21-2.
[50] The same criticism can be urged against Kant's appeal to the necessity of constructing geometrical figures. The conclusion drawn from the necessity of construction is stated thus: "If the object (the triangle) were something in itself without relation to you the subject, how could you say that that which lies necessarily in your subjective conditions of constructing a triangle must also necessarily belong to the triangle in itself?" (B. 65, M. 39). Kant's thought is that the laws of the mind's constructing nature must apply to objects, if, and only if, the objects are the mind's own construction. Hence it is open to the above criticism if, in the criticism, 'construct' be substituted for 'perceive'.
[51] Prol., § 7.
[52] Prol., § 9.
[53] Cf. (Introduction, B. xvii, M. xxix): "But if the object (as object of the senses) conforms to the nature of our faculty of perception, I can quite well represent to myself the possibility of a priori knowledge of it [i. e. mathematical knowledge]."
[54] Cf. Descartes, Princ. Phil. i. § 13, and Medit. v sub fin.
[55] The view that kinds of space other than that with which we are acquainted are possible, though usually held and discussed by mathematicians, belongs to them qua metaphysicians, and not qua mathematicians.
[56] The first sentence shows that 'relative determinations' means, not 'determinations of objects in relation to us', but 'determinations of objects in relation to one another.' Cf. B. 37, M. 23; and B. 66 fin., 67 init., M. 40 (where these meanings are confused).
[57] B. 42, M. 26.
[58] This conclusion is also to be expected because, inconsistently with his real view, Kant is here (B. 41-2, M. 25-6) under the influence of the presupposition of our ordinary consciousness that in perception we are confronted by things in themselves, known to be spatial, and not by appearances produced by unknown things in themselves. Cf. (B. 41, M. 25) "and thereby of obtaining immediate representation of them [i. e. objects];" and (B. 42, M. 26) "the receptivity of the subject to be affected by objects necessarily precedes all perceptions of these objects." These sentences identify things in themselves and bodies in space, and thereby imply that in empirical perception we perceive things in themselves and as they are.
[59] A. reads 'only under'
[60] B. 43, M. 27.