57. The same reasoning destroys the opinion of indefinite or infinite extension. Descartes, explaining his doctrine on the idea of extension, says: "We shall also know that this world, or the extended matter which composes the universe, is without limits; for, no matter how far off we place these limits, we can imagine spaces indefinitely extended beyond them; and we not only imagine these spaces, but we conceive them as really existing such as we imagine them, and containing an indefinitely extended body, as the idea of extension which we conceive in every space is the true idea which we ought to form of a body."[42] [42] Descartes, Ibid., § II, p. 21. In this passage, besides the error in relation to the essence of bodies, there is a gratuitous transition from a purely ideal or rather, imaginary order, to the real order. It is certain that wherever I may imagine the limits of the universe, if I consider them as an immense arch surrounding it, I still imagine new immensities of space beyond this arch; but to conclude that the reality is as I imagine it, does not seem conformed to the rules of good logic. If it is as clear as Descartes supposes, if it is not only an imagination, but a conception founded on clear and distinct ideas, how happens it that so many philosophers see in all this only a play of the imagination? 58. Leibnitz thinks that space is "a relation, an order, not only between things existing, but also between possible things as if they existed."[43] He also believes vacuum impossible, but not for the reason which Descartes gives. These are his words: [43] Leibnitz, _Nouveaux Essais_. L. II., C. XIII., § 17. "_Philalethes._--Those who take matter and extension for the same thing, pretend that the sides of a hollow empty body would touch each other. But the space which is between the two bodies is enough to prevent their mutual contact. "_Theophilus._--I am of your opinion; for, although I do not admit a vacuum, I distinguish matter from extension, and concede that although there were a vacuum in a sphere, the opposite poles would not on that account unite. But I do not believe this is a case which the divine perfection would permit."[44] [44] Leibnitz, Ibid., § 21. 59. Leibnitz seems to me to commit what logicians call _petitio principii_, or, "begging the question." He says that in the case supposed, the sides would not touch each other, because the space between them would prevent it; but this is what he had to prove,--the real existence of this space. This reality is what Descartes denies.