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Aquinas considered this argument to be the strongest argument against the eternity of the
world 92 and responded to it in several of his treatises. In Writings on the Sentences, Aquinas uses
an argument from Algazel’s Metaphysics. Souls separated from their bodies form an accidental
infinity because they “have no dependence upon one another.” 93 While this distinction might
seem forced, it arises from a detailed analysis of Aristotle’s argument for the impossibility of an
actual infinity. The prohibition of an actual infinity was only established by Aristotle for material
things that are essentially depended upon one another. 94 Hence, the prohibition does not exclude
the possibility of an actual infinity of spiritual beings.
In Summa Contra Gentiles, Aquinas calls this argument difficult but not very useful
because it “supposes many things.” 95 He answers it by first giving opinions that are not
consistent with Christian revelation: mortality of human souls, existence of only one separated
intellect, and reincarnation. At the end however, Aquinas states that “there are those who do not
consider incongruous that, in the realm of things devoid of order, actual infinities should be
found.” 96 Aquinas’ response here shows that his prohibition of actual infinities is not absolute
but depends on order.
In Summa Theologica, Aquinas mentions Algazel’s argument again but immediately
notes that his argument has been disproved in an earlier question. 97 Ultimately, Aquinas judges
the argument as irrelevant because it is specific to man and the question of the eternity of the
world does not require eternal existence of men but only of some creature. 98 Aquinas takes up
92
Baldner and Carroll, Aquinas on Creation, 104.
Ibid, 105.
94
Ibid.
95
Aquinas, SCG, II, 38.
96
Ibid.
97
Aquinas, ST, I, q. 7, a. 4.
98
Ibid.
93
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