Questions on the Metaphysics of Aristotle

Question Five

204 THE METAPHYSICS OF JOHN DUNS SCOTUS 3 For the opposite: What the Philosopher says in the text4 of every type of cause proves that there is a status. QUESTION FIVE Can one proceed to infinity in effects so that there exists an actual infinity? [Arguments Pro and Con] 4 [For the affirmative] It seems that one can: Any difference among any sort of thing has another opposite difference that codivides that class of things. But the finite in act represents a difference in quantity. Therefore, it has the infinite as its opposite difference; and this is the infinite in act, not the infinite in potency, because opposed differences are not mutually compatible. But the same thing can be actually finite and potentially infinite. Therefore, the finite in act has as its opposite the infinite in act. 5 Also, according to Bk. VI of the Topics,5 Aristotle rejects the definition of a straight line as that “to which a middle is added to its ends, because those things that are infinite have neither a middle nor an end. But a straight line is infinite.” Therefore, infinity is not opposed to a straight line. 6 Also, according to Physics III:6 “Any magnitude that can exist potentially can exist actually.” But magnitude can be infinite potentially, because according to II On the Soul:7 “Fire goes on without limit so long as there is a supply of fuel.” 7 Also, “the continuum is divisible into divisibles that are always divisible,” according to Bk. VI of the Physics.8 But number 4 Aristotle, Metaphysics II, ch. 2, 994a 1-994b 31. 5 Aristotle, Topics Bk. VI, ch. 19, 148b 26-32. 6 Aristotle, Physics III, ch. 7, 207b 17-18. 7 Aristotle, De anima II, ch. 4, 416a 15-16. 8 Aristotle, Physics VI, ch. 1, 231b 15-16; De caelo et mundo I, ch. 1, 268a 6-7. BOOK II QUESTIONS FOUR-SIX 205 follows the divisions of the continuum, according to Bk. III of the Physics.9 Therefore, number is infinite. 8 It is objected here that number like division is only infinite in potency.—To the contrary: I De caelo et mundo:10 “If it could not have been made, it could not have come into being.” Therefore, if a continuum cannot be infinitely divided, then it is impossible that i t be potentially divided infinitely. 9 Also, what is said of number,11 that what is infinite in potency, is actually the case, I prove: It is conceded that number is infinite in potency. But given any species of number, a unit can be added to produce a new species. Therefore the species of number are infinite in potency. But each species adds a unit to the other; therefore, there is a certain species—which while being in potency—has in itself an infinity of units. The ideas of all possible species are in God actually. Therefore, he actually has an idea of a number having infinite units. But every species, whose idea God has in actuality, can be made by God in its singular. Therefore, some species having an infinity of units, is producible by God externally. 10 For the negative: The Philosopher says of numbers in Bk. III of the Physics12 that “every number is numerable.” But one can go through everything that is numerable, and every such thing is finite; therefore, etc. QUESTION SIX Text of Aristotle: “But there is no understanding, unless one comes to a halt...But if the kinds of causes had been infinite in number, then knowledge would have been impossible.” (Metaphysics II, ch. 2, 994b 20-28) 9 Aristotle, Physics III, ch. 7, 207a 32-207b 2. 10 Aristotle, De caelo et mundo I, ch. 1, 279b 12-31. 11 Cf. supra, n. 7. 12 Aristotle, Physics II, ch. 5, 204b 9-11. ...