83. We will make this solution clearer. The intelligence of God is infinite; and he cannot understand more than he now understands; all progress would suppose imperfection, because it would involve a change from a less to a greater intelligence. If, then, we say that God will never understand more than he does now, do we limit his intelligence? Certainly not. He cannot understand more, because he understands all that is real and all that is possible, and we cannot, without contradiction, conceive that he can understand more than he now does: this is not to limit his intelligence, but to affirm its infinity: it is not susceptible of perfection, because it is infinite. This will enable us to understand the expression cannot, as applied to God. What is denied is not a perfection, but an absurdity: wherefore St. Thomas very opportunely observes, that we should much better say that the thing cannot be done, than that God cannot do it.
[CHAPTER XII.]
SOLUTION OF VARIOUS OBJECTIONS AGAINST THE POSSIBILITY OF AN INFINITE EXTENSION.
84. The discussions on the possibility of an infinite extension are of a very ancient date. How could it be otherwise? Must not the glorious spectacle of the universe, and the space which we imagine beyond the boundaries of all worlds, naturally have given rise to questions as to the existence or possibility of a limit to this immensity?
Some philosophers think an infinite extension impossible. Let us see on what they found their opinion.
85. Extension is a property of a finite substance, and that which belongs to a finite thing cannot be infinite; therefore it is impossible to conceive infinity of any kind in a finite being. This argument is not conclusive. It is true that an extended substance is finite, in the sense that it does not possess absolute infinity such as is conceived in the Supreme Being; but it does not follow from this that it cannot be infinite under certain aspects. Neither is it correct to say that no finite substance can have an infinite property, because the properties flow from the substance, and the infinite cannot proceed from the finite. In order that this argument may be valid, it is necessary to prove that all the properties of a being emanate from its substance: figures are accidental properties of bodies, and yet many of them have no relation to the substance, and are mere accidents which appear or disappear, not by the internal force of the substance, but by the action of an external cause. We see extension in bodies; but as we know not the essence of corporeal substance, we cannot say how far this property is connected with the substance, whether it is an emanation from it, or only something which has been given to it and may be taken from it without any essential alteration.[39]
Moreover, when we say that the infinite cannot proceed from the finite, we do not deny that an infinite property may proceed from a substance finite in its essence.
When we admit the infinite property, we admit at the same time all that is necessary in the substance in order that this property may have its root in it, so long as we do not deny the character of finite which essentially belongs to every creature. When we deny that creatures are or can be infinite, we speak of essential infinity, of that infinity which implies necessity of being and absolute independence under every aspect; but we do not deny them a relative infinity, such as that of extension.
To undertake to prove that infinite extension is impossible, because every property of a finite substance must be finite, is equivalent to supposing the very thing in dispute; for the precise question is, whether one of these properties, namely, extension, can be infinite. In order to establish the negative proposition, "No property of a finite substance can be infinite," it is necessary to prove this of extension. Hence the argument which we are imposing implies, in some manner, a begging of the question, when they found it on a general proposition which can only be certain when the present question is solved.