Questions on the Metaphysics of Aristotle

Question 6

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. 206 THE METAPHYSICS OF JOHN DUNS SCOTUS Can the infinite be known by us? “But there is no understanding, unless one comes to a halt,”13 namely, a line ends in a point.... About this we can ask further: Can the infinite be known by us? [Arguments Pro and Con] 11 [1] For the affirmative: God is infinite and we can known him, as we have said above;14 therefore, etc. 12 Also, knowledge is through all the causes; therefore, we know by means of the first cause, which is infinite. 13 We also define the infinite and assign attributes to it and give it a name, which signifies it; therefore, we understand it. 14 Also, all the species of any genus are known by us, because we can define them; but the species of numbers and figures are infinite, since we can always proceed to infinity beyond any given species; therefore, there are an infinity of things which are true species, even though they do not exist—just as the species of rose is a true species, even if no roses existed. Hence, these species can be known. 15 Also, in Physics IV, in the chapter “On the Void”:15 “If two bodies could be in the same place, any number could be together”; therefore, if we can think of two species at the same time, then, an infinity of species could be thought of, each one of which is a principle of knowing; therefore, etc.16 13 Aristotle, Metaphysics I, ch. 2, 994b 24-25. 14 Cf. supra, Bk. II, qq. 2-3, nn. 51-52. 15 Aristotle, Physics IV, ch. 8, 216b 10-12. 16 There is an interpolated text here found in one manuscript: [Objections] “Likewise, a specific nature in determined to no single individual, because ‘to be man’ is in Socrates as well as Plato, nor does such a nature pertain more to Socrates than to Plato. Given this, I argue as follows: a specific nature that is communicable and not determined to a single individual, is not restricted to a finite number of individuals. However, whatever such nature is not restricted to finitude, is not repugnant to be in an infinite number [of individuals] nor to contain an infinitude of individuals under it; therefore, etc. Likewise, that it would actually contain [an infinitude], I BOOK II QUESTIONS FOUR-SIX 207 16 For the negative: The Philosopher in Metaphysics II17 says that if the formal causes were...