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Objection 1: It is impossible for an infinite to be added to.
The flowing of time requires that the present day becomes part of the past. Hence, the
past time is continuously increasing, and hence “the past time can be greater than it is.” 61
However, if the world is eternal then there must exist right now an infinite number of past days
and hence any further “addition to it would make the infinite greater, and that is against the very
nature of infinity.” 62 In the mediaeval understanding, the infinite is indefinite and unending. It
cannot be added onto because it has no end, and it cannot be increased because it is already
infinite and nothing greater than it exists. Our naïve notion of addition arises from operating on
finite natural numbers. In adding two numbers, say 2 + 3, one simply tucks on the second
quantity to the first one and obtains a new quantity which in this case is five: ∘∘ + ∘∘∘=∘∘∘∘∘.
Moreover, adding numbers always results in an increase of both numbers. Both of these
properties of addition seem to fail if one allows for addition of actual infinities. Considering the
past time as actually infinite leads to a contradiction that the past time both increases and cannot
increase.
61
Steven E. Baldner and William E. Carroll, Aquinas on Creation, (Toronto: Pontifical Institute of Medieval Studies,
1997), 94.
62
Bonansea, "The Question,” 12.
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