ctual whole; therefore the infinite in quantity
refers to matter, and does not agree with the totality of magnitude;
yet it agrees with the totality of time and movement: for it is proper
to matter to be in potentiality.
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FOURTH ARTICLE [I, Q. 7, Art. 4]

Whether an Infinite Multitude Can Exist?

Objection 1: It seems that an actually infinite multitude is possible.
For it is not impossible for a potentiality to be made actual. But
number can be multiplied to infinity. Therefore it is possible for an
infinite multitude actually to exist.

Obj. 2: Further, it is possible for any individual of any species
to be made actual. But the species of figures are infinite. Therefore
an infinite number of actual figures is possible.

Obj. 3: Further, things not opposed to each other do not obstruct
each other. But supposing a multitude of things to exist, there can
still be many others not opposed to them. Therefore it is not
impossible for others also to coexist with them, and so on to
infinitude; therefore an actual infinite number of things is possible.

_On the contrary,_ It is written, "Thou hast ordered all things in
measure, and number, and weight" (Wis. 11:21).

_I answer that,_ A twofold opinion exists on this subject. Some, as
Avicenna and Algazel, said that it was impossible for an actually
infinite multitude to exist absolutely; but that an accidentally
infinite multitude was not impossible. A multitude is said to be
infinite absolutely, when an infinite multitude is necessary that
something may exist. Now this is impossible; because it would entail
something dependent on an infinity for its existence; and hence its
generation could never come to be, because it is impossible to pass
through an infinite medium.

A multitude is said to be accidentally infinite when its existence as
such is not necessary, but accidental. This can be shown, for example,
in the work of a carpenter requiring a certain absolute multitude;
namely, art in the soul, the movement of the hand, and a hammer; and
supposing that such things were infinitely multiplied, the
carpentering work would never be finished, forasmuch as it would
depend on an infinite number of causes. But the multitude of hammers,
inasmuch as one may be broken and another used, is an accidental
multitude; for it happens by accident that many hammers are used, and
it matters little whether one or two, or many are used, or an infinite
number, if