It will be seen at a glance that this is the central and vital question in the Theistic argument. If the order and arrangement of the universe is eternal, then that order is an inherent law of nature, and, as eternal, does not imply a cause ab extra: if it is not eternal, then the ultimate cause of that order must be a power above and beyond nature. In the former case the minor premise of the Theistic syllogism is utterly invalidated; in the latter case it is abundantly sustained.
Some Theistic writers--as Descartes, Pascal, Leibnitz, and Saisset--have made the fatal admission that the universe is, in some sense, infinite and eternal. In making this admission they have unwittingly surrendered the citadel of strength, and deprived the argument by which they would prove the being of a God of all its logical force. That argument is thus presented by Saisset: "The finite supposes the infinite. Extension supposes first space, then immensity: duration supposes first time, then eternity. A sudden and irresistible judgment refers this to the necessary, infinite, perfect being." [215] But if "the world is infinite and eternal," [216] may not nature, or the totality of all existence (τὺ πᾶν), be the necessary, infinite, and perfect Being? An infinite and eternal universe has the reason of its existence in itself, and the existence of such a universe can never prove to us the existence of an infinite and eternal God.
[Footnote 215: ][ (return) ] "Modern Pantheism," vol. ii. p. 205.
[Footnote 216: ][ (return) ] Ibid, p. 123.
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]
[Footnote 217: ][ (return) ] "The infinite is distinct from the finite, and consequently from the multiplication of the finite by itself; that is, from the indefinite. That which is not infinite, added as many times as you please to itself, will not become infinite."--Cousin, "Hist, of Philos.," vol. ii. p. 231.
[Footnote 218: ][ (return) ] Saisset, "Modern Pantheism," vol. ii. pp. 127, 128.
The introduction of the idea of "the mathematical infinite" into metaphysical speculation, especially by Kant and Hamilton, with the design, it would seem, of transforming the idea of infinity into a sensuous conception, has generated innumerable paralogisms which disfigure the pages of their philosophical writings. This procedure is grounded in the common fallacy of supposing that infinity and quantity are compatible attributes, and susceptible of mathematical synthesis. This insidious and plausible error is ably refuted by a writer in the "North American Review." [219] We can not do better than transfer his argument to our pages in an abridged form.
[Footnote 219: ][ (return) ] "The Conditioned and the Unconditioned," No. CCV. art. iii. (1864).
Mathematics is conversant with quantities and quantitative relations. The conception of quantity, therefore, if rigorously analyzed, will indicate à priori the natural and impassable boundaries of the science; while a subsequent examination of the quantities called infinite in the mathematical sense, and of the algebraic symbol of infinity, will be seen to verify the results of this á priori analysis.