Descartes maintained that the extension of the world is indefinite; but this is a term which, although it has a very rational meaning when it refers to the compass of our understanding, has no meaning when applied to things. There is no objection to saying that the extension of the world is indefinite, if it only means that we cannot assign its limits; but in the reality, the limits exist or do not exist, indifferently of our power of assigning them; there is no medium between yes and no; therefore there is no medium between the existence and the non-existence of these limits. If they exist, the extension of the world is finite; if they do not exist, it is infinite;--in either case, the word indefinite expresses nothing. The argument of Descartes proves nothing, or it proves the true infinity of the world. For, if we must remove its limits indefinitely because we always conceive indefinitely an extension beyond every other extension, as, on the other hand, we know that this series of conceptions has no limit, we may at once transfer the unlimitedness to the object which corresponds to those conceptions, and affirm that the extension of the world is absolutely infinite. Unfortunately, the argument of Descartes is without any basis; for it consists in a transition from the ideal, or, rather, imaginary order, to the real order, which is contrary to good logic.[41] [41] See Book III., Chapter VIII. 89. Leibnitz maintained, that although God could have made the material universe finite in its extension, it is more in conformity with his wisdom not to have done so. "Thus I do not say," he writes,[42] "as is here imputed to me, that God cannot give limits to the extension of matter; but the appearance is that he does not wish it, but preferred to give it more." The opinion of Leibnitz is founded on his system of optimism, which is open to a multitude of objections, but it is not the place here to examine them. [42] _Lettres entre Leibnitz et Clarke_, Vième Écrit. de Leibnitz, § 73. 90. To speak frankly my own opinion, I say that this is a question which cannot be solved on purely philosophic principles; for, as the ideas contain no intrinsic necessity, either for or against the existence of an infinite extension, we must look for its solution to what experience teaches us. All the time occupied in attempting to solve this question is lost. What we can assert is, that the extension of the world exceeds all appreciation; and as the science of astronomy advances, greater depths are discovered in the ocean of space. Where is the shore? or is there any? Reason cannot answer such questions. What do we, poor insects, know, whose life is but a momentary dwelling on this little ball of dust, which we call the globe of the earth? CHAPTER XIV. POSSIBILITY OF AN ACTUAL INFINITE NUMBER.