In the present chapter, we completed our proof of the apriority of the projective and equivalent metrical axioms, by showing the necessity, for experience, of some form of externality, given by sensation or intuition, and not merely inferred from other data. Without this, we said, a knowledge of diverse but interrelated things, the corner-stone of all experience, would be impossible. Finally, we discussed the contradictions arising out of the relativity and continuity of space, and endeavoured to overcome them by a reference to matter. This matter, we found, must consist of unextended atoms, localized by their spatial relations, and appearing, in Geometry, as points. But the non-spatial adjectives of matter, we contended, are irrelevant to Geometry, and its causal properties may be left out of account. To deal with the new contradictions, involved in such a notion of matter, would demand a fresh treatise, leading us, through Kinematics, into the domains of Dynamics and Physics. But to discuss the special difficulties of space is all that is possible in an essay on the Foundations of Geometry. FOOTNOTES: [178] Compare, with the following paragraphs, the admirable discussion in Mr Hobhouse's Theory of Knowledge (Methuen 1896), Part I. Chapter II. [179] I speak of sense-perception instead of sensation, so as not to prejudge the issue as to the sensational nature of space. [180] See Vaihinger's Commentar, II. pp. 86-7, 168-171. [181] See Caird, Critical Philosophy of Kant, Vol. I. p. 287. [182] Ursprung der Raumvorstellung, pp. 12-30. [183] See the references in Vaihinger's Commentar, II. p. 76 ff. [184] Commentar, II. p. 71 ff. [185] _E.g._ by Caird, _op. cit._ Vol. I. p. 286. [186] I have no wish to deny, however, that space is essential in the subsequent distinction of Self and not-Self. [187] See also Book I. Chap II. passim; especially p. 51 ff. and pp. 70-1. [188] Logic, p. 51 ff. [189] For the _This_, on such a hypothesis, has a purely temporal complexity, and is not resolvable into coexisting _Thises_. [190] Chapter III. Section A, (§ 131). [191] Cf. Hannequin, Essai critique sur l'hypothèse des atomes, Paris 1895, Chap. I. Section III.; especially p. 43. [192] See Chapter II. § 69 ff. [193] See third antinomy below, § 201 ff. [194] This atom, of course, must not be confounded with the atom of Chemistry. [195] Ursprung der Raumvorstellung, p. 15. [196] See Vaihinger's Commentar, II. pp. 189-190. [197] See ibid. p. 224 ff. for Kant's inconsistencies on this point. [198] The fourth and fifth in the first edition, the third and fourth in the second. [199] Cf. Vaihinger's Commentar, II. p. 218. [200] Cf. Vaihinger's Commentar, II. p. 207. [201] Cf. James, Psychology, Vol. II., p. 148 ff. Cambridge: PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. TRANSCRIBER'S NOTE Italic text is denoted by _underscores_. Bold text is denoted by =equal signs=.