Page:Lectures on the Philosophy of Religion volume 3.djvu/257

characteristic to a second, or from a proposition already proved to another, should permit of being clearly exhibited; but we can see, too, that reasoned knowledge cannot go back in the same way from the second to the first, and cannot deduce the second from the first. Euclid first demonstrated the proposition of the known relation between the sides of a right-angled triangle by starting from this definite quality of the triangle, and deducing the relationship of the sides from it. Then the converse proposition was also demonstrated, and in this case he started from the fact of this relation, and deduced from it the right-angled character of the triangle, the sides of which had that relation to one another, and yet this was done in such a way that the demonstration of this second proposition presupposed and made use of the first. In another instance this demonstration of the converse proposition is given apagogically by presupposing the first. Thus the proposition, that if in a rectilineal figure the sum of the angles is equal to two right angles, the figure is a triangle, can be easily proved to follow apagogically from the proposition previously demonstrated that in a triangle the three angles together make two right angles. When it is shown that a predicate belongs to an object, we must go further if we are to show that such a predicate belongs to it exclusively, and that it is not merely one of the characteristics of the object which may belong to others as well, but that it is involved in the definition of the object. This proof might be stated in various ways, and is not compelled exactly to follow one single path, namely, that which starts from the conception of the second characteristic. Besides, in dealing with the connection between the so-called most real Essence and the absolutely necessary Essence, it is only one aspect of this latter that we have to take directly into account, and we have nothing at all to do with that aspect in reference to which Kant brings forward the difficulty discovered by him in the Ontological Proof.