Digital Continent Digital Continent_Template amended | Page 36

In the Writings on the Sentences, Aquinas includes this objection as the fourth argument
for the necessity of a temporal beginning. 63 Aquinas agrees that “an addition cannot be made to
an entire infinite succession, even if ‘infinite’ is taken as a potential infinite.” 64 However, he
notes that infinite past time has a finite part. It is like a ray that has no beginning but has a
definite end, for the present moment is the end of the past time. Therefore, even though one
cannot add to the “infinite side” of the past time one can add to its “finite side.” 65 Secondly,
Aquinas notes that mathematical notions of “being greater than” and “addition” apply only to
what is actual. To justify this position Aquinas considers numbers greater than ten and numbers
greater than one hundred. Clearly both sets are infinite and because numbers between ten and
one hundred exist, the set of numbers greater than ten seems bigger than the set of numbers
bigger than one hundred. In fact our intuition suggests that there are exactly ninety numbers
more in the first set. According to Aquinas, the solution here is not to claim that the addition of
numbers does not make sense in general but to restrict mathematical notions to what is actual,
i.e., only to finite numbers. By actual, Aquinas does not mean only that which exists in reality
but also admits of the actual in the mind or in the imagination. 66 For Aquinas, an actual infinity
can exist neither in reality, nor in the mind, nor in the imagination. 67 Infinity is indeterminate
and as such is not a quantity, and hence it cannot be measured by a number. It is a multitude but
not a number for “number is multitude measured by one.” 68 By dealing only with the finite end
of the past time, Aquinas is able to show that the flow of time does not add to the infinity of past
events.
63
Baldner and Carroll, Aquinas on Creation, 94.
Ibid, 103.
65
Ibid.
66
Ibid.
67
Ibid, 104.
68
Bonansea, "The Question,” 16.
64
Page 26 of 62