41. The difficulties in the application of the idea of infinity, seem on the one hand, to prove that either this idea does not exist in us, or is very confused; and on the other hand, that we possess it, and in a very perfect degree. Why do we discover that numbers are not infinite, although at first they seem to be? Why do we deny the infinity of certain dimensions, notwithstanding their infinite prolongation in one sense? Because, on examining these objects, we find that they do not correspond to the type of infinity. If this type did not exist in our mind, how could it be possible for us to make use of it? How could we compare beings with it, if we did not know it? Is it possible to know when any thing arrives at a turn, if we have no idea of that turn? It is comparing without a point of comparison; that is, it is exercising a contradictory act. 42. Although these arguments in favor of the existence of the idea of the infinite, if we examine our own mind, we cannot deny that we find there a certain vagueness and confusion which inspire strong doubts as to the reality of this idea. What is presented to our mind, when we think of the infinite? The imagination abandoned to itself, extends space, expands dimensions, multiplies numbers indefinitely, but it offers nothing to the intellect which has the marks of infinity. If we leave the imagination, and regard the understanding only, it gives a type by which to judge of the infinity or not-infinity of the objects presented to it, but if we reflect on the type itself, it loses the clearness it possessed before, and we even ask if the type really exists. 43. Do we, therefore, deny the existence of this idea? are we going to renounce our intention of explaining it? We do neither. I believe that it is necessary to admit the idea, that it is not impossible to explain it, and that we may even point out the reason of its obscurity. 44. Before passing further, I wish to observe, that one of the causes of the difficulties in the explanation of the idea of the infinite, arises from our not distinguishing the intuitive from the abstract cognition.[36] Many difficulties would be avoided by attending to this distinction. When we say that the idea of the infinite is not intuitive, but abstract, we give the key to the solution of the principal objections brought against it. [36] See Book V., Ch. XI. 45. We have no intuitive idea of infinity; that is to say, this idea does not present to our mind an infinite object; we can have this intuition only when we see the essence of God, which will happen in a future life.