=Third Paragraph.=--The third and fourth paragraphs of this section ought to have had a separate heading. They summarise the total argument of the _Aesthetic_ in regard to space as well as time, distinguish its tenets from those of Newton and of Leibniz, and draw a general conclusion. The summary follows the strict synthetic method. The opening sentences illustrate Kant’s failure to distinguish between the problems of pure and of applied mathematics, and also show how completely he tends to conceive mathematics as typified by geometry. The criticism of alternative views traverses the ground of the famous controversy between Leibniz and Clarke. Their _Streitschriften_ were, as we have good circumstantial grounds for believing,[554] a chief influence in the development of Kant’s own views. Kant, who originally held the Leibnizian position, was by 1768[555] more or less converted to the Newtonian teaching, and in the _Dissertation_ of 1770 developed his subjectivist standpoint with the conscious intention of retaining the advantages while remedying the defects of both alternatives.[556] For convenience we may limit the discussion to space. (_a_) The view propounded by Newton, and defended by Clarke, is that space has an existence in and by itself, independent alike of the mind which apprehends it and of the objects with which it is filled. (_b_) The view held by Leibniz is that space is an empirical concept abstracted from our confused sense-experience of the relations of real things.[557] The criticism of (_a_) is twofold. First, it involves belief in an eternal and infinite _Unding_. Secondly, it leads to metaphysical difficulties, especially in regard to the existence of God. If space is absolutely real, how is it to be reconciled with the omnipresence of God? Newton’s view of space as the =sensorium Dei= can hardly be regarded as satisfactory. The objection to (_b_) is that it cannot account for the apodictic certainty of geometry, nor guarantee its application to experience. The concept of space, when regarded as of sensuous origin, is something that may distort (and according to the Leibnizian teaching does actually distort) what it professes to represent, and is something from which restrictions that hold in the natural world have been omitted.[558] As empirical, it cannot serve as basis for the universal and necessary judgments of mathematical science.[559] The first view has, however, the advantage of keeping the sphere of appearances open for mathematical science. As space is infinite and all-comprehensive, its laws hold universally. The second view has the advantage of not subjecting reality to space conditions. These advantages are retained, while the objections are removed, by the teaching of the _Aesthetic_.