Page:Mind (New Series) Volume 8.djvu/520

V. KANT'S PROOF OF THE PROPOSITION, "MATHEMATICAL JUDGMENTS ARE ONE AND ALL SYNTHETICAL". BY BRUCE McEwEN. IT needs no very profound analysis of the Critique of Pure Beason to demonstrate that the ^Esthetic, as it stands in the forefront of Kant's system, fulfils a distinctly double purpose. Leaving aside the doctrine of Time and regarding only the doctrine of Space, we find that it presents itself to us under two quite different aspects, according as we look at it from one or the other of two points of view towards which the author himself repeatedly directs our attention. Considered alone and by itself, the ^Esthetic has a purely dogmatical, asser- toric or didactical value : it is a theory as to the nature of Space and of Spatial existences. But when we pass beyond this first crude conception of the Esthetic, and begin to trace out the various lines of connexion, which lead to every part of Kant's speculations, when we examine the internal arrangement of the matter of the Critique and the relations of interdependence and mutual defence, which Kant strives to establish between all portions of his system, there is gradually unfolded before our eyes the higher purpose of the Esthetic, as a first apology for the whole. However much we may prize the content of the doctrine of Space for its own sake, still to the true Kantian it will always seem rela- tively more important to regard the Esthetic as giving us, in Kant's own words, " one part of the answer necessary for the solution of the great general problem of the Transcen- dental Philosophy, namely the problem: How are synthetical propositions a priori possible ? " The vindication of those forms of knowledge, which are at once synthetic and a priori^ is the object of the new Criticism from beginning to end, and with his doctrine of Space and the corresponding real science, Pure Mathematics, Kant introduces the thin end of the wedge destined to cleave asunder the sceptical denial of the reality of all knowledge of this type. " When Hume felt the truly philosophic impulse to cast his glance over the