118. If perfection is being, it seems that the perfection of the infinite being must consist in certain properties which are found formally in it, and therefore exclude all imperfection. An absolutely indeterminate being, that is, a being without any property, is impossible. What conception can we form of _a thing_ without intelligence, without will, and without liberty? The propositions in which these properties are affirmed of God, are true; therefore these properties really exist in the subject of which they are affirmed. 119. An infinitely perfect being must have all perfection; but in what sense are we to understand _all_? Does it mean all possible perfections? But what perfections are possible? Those which are not repugnant. To what is the repugnance to be referred? It must be either a mutual repugnance, or a repugnance to a third: if the first, it is necessary to presuppose one of the two extremes, in order that the other may be repugnant to it; in that case, which is to be preferred? If the second, what is the third to which they are repugnant? On what is it founded? If by all perfection is meant all that we can conceive, the same difficulty remains. For if we speak of the conception of a finite being, the conception is not infinite; if of the conception of an infinite being, it is a begging of the question, because in explaining the perfections of the infinite being we appeal to its conception. These difficulties can only be solved by determining more precisely the meaning of these ideas. 120. A thing may be denied of another in two manners: by referring the negation to a property, or to an individual. When I say a surface is not a triangle, I may refer the predicate either to the species of triangle in general, or to an individual triangle. In the first instance, I deny that the figure is triangular; in the second, I deny that the figure is another given triangle. When I say God is not extended, I deny a property; when I say God is not the world, I deny an individual. It is evident that in order to attribute absolute infinity to any being, it is necessary that no being should be denied of it, either with respect to properties or to individuals, and that the predicate should be affirmed without destroying the principle of contradiction. This exception is absolutely indispensable, unless we wish to make the infinite being the greatest of all absurdities, a jumble of contradictions. I believe that this will explain to a great extent the idea of absolute infinity, not considered in the abstract, but applied to a really existent being. CHAPTER XVI. ALL THE REALITY CONTAINED IN INDETERMINATE CONCEPTIONS IS AFFIRMED OF GOD. 121. We have seen that our cognitions are of two classes: some are general and indeterminate, others intuitive. All the objects which we know, whether indeterminately or intuitively, may be affirmed of God, provided they involve no contradiction.