The second form of the Cartesian argument is, that God cannot be thought of as a perfect Being unless He be also thought of as a necessarily existent Being; and that, therefore, the thought of God implies the existence of God. "Just as because," for example, "the equality of its three angles to two right angles is necessarily comprised in the idea of a triangle, the mind is firmly persuaded that the three angles of a triangle are equal to two right angles; so, from its perceiving necessary and eternal existence to be comprised in the idea which it has of an all-perfect Being, it ought manifestly to conclude that this all-perfect Being exists." Kant met this argument thus: "It is a contradiction that there should be a triangle the three angles of which are not equal to two right angles, or that there should be a God who is not necessarily existent. I cannot in either case retain the subject and do away with the predicate. If I assume a triangle, I must take it with its three angles. If I assume a God, I must grant Him to be necessarily existent. But why should I assume either that there is a triangle or that there is a God? I may annul the subject in both cases, and then there will be no contradiction in annulling the predicate in both cases. There may be no such thing as a triangle, why should there be such a Being as God?"
This reasoning of Kant has generally been accepted as conclusive. It does not appear to me to be so. He ought not merely to have asserted but to have shown that we can annul the subject in either of the cases mentioned. We obviously cannot. I can say "there is no triangle," but instead of annulling that implies the idea of a triangle, and from the idea of a triangle it follows that its three angles are equal to two right angles. In like manner I can say "there is no God," but that is not to annul but to imply the idea of God, and it is from the idea of God that, according to Descartes, the existence of God necessarily follows. Kant should have seen that the proposition "there is no God" could be no impediment to an argument the very purpose of which is to prove that that proposition is a self-contradiction. It is futile to meet this by saying that existence ought not to be included in any mere conception, for it is not existence but necessary existence which is included in the conception reasoned from, and that God can be thought of otherwise than as necessarily existent requires to be proved, not assumed. To affirm that existence cannot be given or reached through thought, but only through sense and sensuous experience, can prove nothing except the narrowness of the philosophy on which such a thesis is based.