Note (return) — Chapter V

A closer examination of the statements and reasonings of Descartes, Pascal, and Leibnitz, as furnished by Saisset, will show that these distinguished mathematicans were misled by the false notion of "mathematical infinitude." Their infinite universe, after all, is not an "absolute," but a "relative" infinite; that is, the indefinite. "The universe must extend indefinitely in time and space, in the infinite greatness, and in the infinite littleness of its parts--in the infinite variety of its species, of its forms, and of its degrees of existence. The finite can not express the infinite but by being multiplied infinitely. The finite, so far as it is finite, is not in any reasonable relation, or in any intelligible proportion to the infinite. But the finite, as multiplied infinitely, 217 ages upon ages, spaces upon spaces, stars beyond stars, worlds beyond worlds, is a true expression of the Infinite Being. Does it follow, because the universe has no limits,--that it must therefore be eternal, immense, infinite as God himself? No; that is but a vain scruple, which springs from the imagination, and not from the reason. The imagination is always confounding what reason should ever distinguish, eternity and time, immensity and space, relative infinity and absolute infinity. The Creator alone is eternal, immense, absolutely infinite." 218