The prize essay On the Principles of Natural Theology and Morals brings forward the same fundamental opposition. Here, for the first time, appears definitely the distinction between synthesis and analysis, and in the distinction is found the reason for the superior certainty and clearness of mathematics as op posed to philosophy. Mathematics proceeds synthetically, for in it the notions are constructed. Metaphysics is analytical in method in it the notions are given, and by analysis they are cleared up. Kant does not, in this place, raise the question as to the reason for assuming that the arbitrary synthesis of mathe matical construction has any reference to reality. The deeper significance of synthesis has not yet become apparent.
In the Only Possible Ground of Proof for the Existence of God, the argument, though largely Leibnizian, advances one step farther towards the ultimate inquiry. For there Kant states precisely his fundamental doctrine that real existence is not a predicate to be added in thought to the conception of a possible subject. So far as thought is concerned, possibility, not real existence, is con tained in judgment.
The year 1765 was marked by the publication of Leibniz's post humous Nouveaux Essais, in which his theory of knowledge is more fully stated than in any of his previous tracts. Kant gave some attention to this work, though no reference to it occurs in his writings, and it may have assisted to give additional precision to his doctrine. In the essay, Dreams of a Clairvoyant, published 1766, he emphasizes his previous conclusion that connections of real fact are mediated in our thought by ultimate notions, but adds that the warrant for such notions can be furnished only by experience. He is inclined, therefore, to regard as the function of metaphysics the complete statement of these ultimate, indemon strable notions, and theref ore the determination of the limits to knowledge by their means. Even at this point, the difficulty raised by Hume does not occur to him. He still appears to think that experience does warrant the employment of such notions, and when there is taken into account his correspondence with Lambert during the next few years, one would be inclined to say that the Architektonik of the latter represents most completely Kant's idea of philosophy.
On another side Kant had been shaking himself free from the principles of the Leibnizian philosophy. According to Leibniz, space resulted from the relations of monads to one another. But Kant began to see that such a conception did not accord with the manner in which we determine directions or positions in space.
In the essay, On the Ground of distinguishing Particular Divisions in Space, he pointed out that the idea of space as a whole is not deducible from the experience of particular spaces, or particular relations of objects in space, that we only cognize relations in space by reference to space as a whole, and finally that definite positions involve reference to space as a given whole.