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St. Thomas Aquinas
Summa Theologica

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  • FIRST PART (FP: QQ 1-119)
      • Aquin.: SMT FP Q[7] Out. Para. 1/2 - THE INFINITY OF GOD (FOUR ARTICLES)
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Aquin.: SMT FP Q[7] Out. Para. 1/2 - THE INFINITY OF GOD (FOUR ARTICLES)

After considering the divine perfection we must consider the divine
infinity, and God's existence in things: for God is everywhere, and in all things, inasmuch as He is boundless and infinite.

Aquin.: SMT FP Q[7] Out. Para. 2/2

Concerning the first, there are four points of inquiry:

(1) Whether God is infinite?

(2) Whether anything besides Him is infinite in essence?

(3) Whether anything can be infinitude in magnitude?

(4) Whether an infinite multitude can exist?


Aquin.: SMT FP Q[7] A[1] Thes. Para. 1/1

Whether God is infinite?

Aquin.: SMT FP Q[7] A[1] Obj. 1 Para. 1/1

OBJ 1: It seems that God is not infinite. For everything infinite is
imperfect, as the Philosopher says; because it has parts and matter, as
is said in Phys. iii. But God is most perfect; therefore He is not
infinite.

Aquin.: SMT FP Q[7] A[1] Obj. 2 Para. 1/1

OBJ 2: Further, according to the Philosopher (Phys. i), finite and
infinite belong to quantity. But there is no quantity in God, for He is
not a body, as was shown above (Q[3], A[1]). Therefore it does not belong
to Him to be infinite.

Aquin.: SMT FP Q[7] A[1] Obj. 3 Para. 1/1

OBJ 3: Further, what is here in such a way as not to be elsewhere, is
finite according to place. Therefore that which is a thing in such a way
as not to be another thing, is finite according to substance. But God is
this, and not another; for He is not a stone or wood. Therefore God is
not infinite in substance.

Aquin.: SMT FP Q[7] A[1] OTC Para. 1/1

On the contrary, Damascene says (De Fide Orth. i, 4) that "God is
infinite and eternal, and boundless."

Aquin.: SMT FP Q[7] A[1] Body Para. 1/3

I answer that, All the ancient philosophers attribute infinitude to the
first principle, as is said (Phys. iii), and with reason; for they
considered that things flow forth infinitely from the first principle.
But because some erred concerning the nature of the first principle, as a
consequence they erred also concerning its infinity; forasmuch as they
asserted that matter was the first principle; consequently they
attributed to the first principle a material infinity to the effect that
some infinite body was the first principle of things.

Aquin.: SMT FP Q[7] A[1] Body Para. 2/3

We must consider therefore that a thing is called infinite because it is
not finite. Now matter is in a way made finite by form, and the form by
matter. Matter indeed is made finite by form, inasmuch as matter, before
it receives its form, is in potentiality to many forms; but on receiving
a form, it is terminated by that one. Again, form is made finite by
matter, inasmuch as form, considered in itself, is common to many; but
when received in matter, the form is determined to this one particular
thing. Now matter is perfected by the form by which it is made finite;
therefore infinite as attributed to matter, has the nature of something
imperfect; for it is as it were formless matter. On the other hand, form
is not made perfect by matter, but rather is contracted by matter; and
hence the infinite, regarded on the part of the form not determined by
matter, has the nature of something perfect. Now being is the most formal
of all things, as appears from what is shown above (Q[4], A[1], OBJ[3]).
Since therefore the divine being is not a being received in anything, but
He is His own subsistent being as was shown above (Q[3], A[4]), it is
clear that God Himself is infinite and perfect.

Aquin.: SMT FP Q[7] A[1] Body Para. 3/3

From this appears the Reply to the First Objection.

Aquin.: SMT FP Q[7] A[1] R.O. 2 Para. 1/1

Reply OBJ 2: Quantity is terminated by its form, which can be seen in
the fact that a figure which consists in quantity terminated, is a kind
of quantitative form. Hence the infinite of quantity is the infinite of
matter; such a kind of infinite cannot be attributed to God; as was said
above, in this article.

Aquin.: SMT FP Q[7] A[1] R.O. 3 Para. 1/1

Reply OBJ 3: The fact that the being of God is self-subsisting, not
received in any other, and is thus called infinite, shows Him to be
distinguished from all other beings, and all others to be apart from Him.
Even so, were there such a thing as a self-subsisting whiteness, the very
fact that it did not exist in anything else, would make it distinct from
every other whiteness existing in a subject.

Aquin.: SMT FP Q[7] A[2] Thes. Para. 1/1

Whether anything but God can be essentially infinite?

Aquin.: SMT FP Q[7] A[2] Obj. 1 Para. 1/1

OBJ 1: It seems that something else besides God can be essentially
infinite. For the power of anything is proportioned to its essence. Now
if the essence of God is infinite, His power must also be infinite.
Therefore He can produce an infinite effect, since the extent of a power
is known by its effect.

Aquin.: SMT FP Q[7] A[2] Obj. 2 Para. 1/1

OBJ 2: Further, whatever has infinite power, has an infinite essence.
Now the created intellect has an infinite power; for it apprehends the
universal, which can extend itself to an infinitude of singular things.
Therefore every created intellectual substance is infinite.
Aquin.: SMT FP Q[7] A[2] Obj. 3 Para. 1/1

OBJ 3: Further, primary matter is something other than God, as was shown
above (Q[3], A[8]). But primary matter is infinite. Therefore something
besides God can be infinite.

Aquin.: SMT FP Q[7] A[2] OTC Para. 1/1

On the contrary, The infinite cannot have a beginning, as said in Phys.
iii. But everything outside God is from God as from its first principle.
Therefore besides God nothing can be infinite.

Aquin.: SMT FP Q[7] A[2] Body Para. 1/1
I answer that, Things other than God can be relatively infinite, but not
absolutely infinite. For with regard to infinite as applied to matter, it
is manifest that everything actually existing possesses a form; and thus
its matter is determined by form. But because matter, considered as
existing under some substantial form, remains in potentiality to many
accidental forms, which is absolutely finite can be relatively infinite;
as, for example, wood is finite according to its own form, but still it
is relatively infinite, inasmuch as it is in potentiality to an infinite
number of shapes. But if we speak of the infinite in reference to form,
it is manifest that those things, the forms of which are in matter, are
absolutely finite, and in no way infinite. If, however, any created forms
are not received into matter, but are self-subsisting, as some think is
the case with angels, these will be relatively infinite, inasmuch as such
kinds of forms are not terminated, nor contracted by any matter. But
because a created form thus subsisting has being, and yet is not its own
being, it follows that its being is received and contracted to a
determinate nature. Hence it cannot be absolutely infinite.

Aquin.: SMT FP Q[7] A[2] R.O. 1 Para. 1/1

Reply OBJ 1: It is against the nature of a made thing for its essence to
be its existence; because subsisting being is not a created being; hence
it is against the nature of a made thing to be absolutely infinite.
Therefore, as God, although He has infinite power, cannot make a thing to
be not made (for this would imply that two contradictories are true at
the same time), so likewise He cannot make anything to be absolutely
infinite.

Aquin.: SMT FP Q[7] A[2] R.O. 2 Para. 1/1

Reply OBJ 2: The fact that the power of the intellect extends itself in
a way to infinite things, is because the intellect is a form not in
matter, but either wholly separated from matter, as is the angelic
substance, or at least an intellectual power, which is not the act of any
organ, in the intellectual soul joined to a body.

Aquin.: SMT FP Q[7] A[2] R.O. 3 Para. 1/1

Reply OBJ 3: Primary matter does not exist by itself in nature, since it
is not actually being, but potentially only; hence it is something
concreated rather than created. Nevertheless, primary matter even as a
potentiality is not absolutely infinite, but relatively, because its
potentiality extends only to natural forms.


Aquin.: SMT FP Q[7] A[3] Thes. Para. 1/1

Whether an actually infinite magnitude can exist?

Aquin.: SMT FP Q[7] A[3] Obj. 1 Para. 1/1

OBJ 1: It seems that there can be something actually infinite in
magnitude. For in mathematics there is no error, since "there is no lie
in things abstract," as the Philosopher says (Phys. ii). But mathematics
uses the infinite in magnitude; thus, the geometrician in his
demonstrations says, "Let this line be infinite." Therefore it is not
impossible for a thing to be infinite in magnitude.

Aquin.: SMT FP Q[7] A[3] Obj. 2 Para. 1/1

OBJ 2: Further, what is not against the nature of anything, can agree
with it. Now to be infinite is not against the nature of magnitude; but
rather both the finite and the infinite seem to be properties of
quantity. Therefore it is not impossible for some magnitude to be
infinite.

Aquin.: SMT FP Q[7] A[3] Obj. 3 Para. 1/1

OBJ 3: Further, magnitude is infinitely divisible, for the continuous is
defined that which is infinitely divisible, as is clear from Phys. iii.
But contraries are concerned about one and the same thing. Since
therefore addition is opposed to division, and increase opposed to
diminution, it appears that magnitude can be increased to infinity.
Therefore it is possible for magnitude to be infinite.

Aquin.: SMT FP Q[7] A[3] Obj. 4 Para. 1/1

OBJ 4: Further, movement and time have quantity and continuity derived
from the magnitude over which movement passes, as is said in Phys. iv.
But it is not against the nature of time and movement to be infinite,
since every determinate indivisible in time and circular movement is both
a beginning and an end. Therefore neither is it against the nature of
magnitude to be infinite.

Aquin.: SMT FP Q[7] A[3] OTC Para. 1/1

On the contrary, Every body has a surface. But every body which has a
surface is finite; because surface is the term of a finite body.
Therefore all bodies are finite. The same applies both to surface and to
a line. Therefore nothing is infinite in magnitude.

Aquin.: SMT FP Q[7] A[3] Body Para. 1/4

I answer that, It is one thing to be infinite in essence, and another
to be infinite in magnitude. For granted that a body exists infinite in
magnitude, as fire or air, yet this could not be infinite in essence,
because its essence would be terminated in a species by its form, and
confined to individuality by matter. And so assuming from these premises
that no creature is infinite in essence, it still remains to inquire
whether any creature can be infinite in magnitude.

Aquin.: SMT FP Q[7] A[3] Body Para. 2/4

We must therefore observe that a body, which is a complete magnitude,
can be considered in two ways; mathematically, in respect to its quantity
only; and naturally, as regards its matter and form.

Aquin.: SMT FP Q[7] A[3] Body Para. 3/4

Now it is manifest that a natural body cannot be actually infinite. For
every natural body has some determined substantial form. Since therefore
the accidents follow upon the substantial form, it is necessary that
determinate accidents should follow upon a determinate form; and among
these accidents is quantity. So every natural body has a greater or
smaller determinate quantity. Hence it is impossible for a natural body
to be infinite. The same appears from movement; because every natural
body has some natural movement; whereas an infinite body could not have
any natural movement; neither direct, because nothing moves naturally by
a direct movement unless it is out of its place; and this could not
happen to an infinite body, for it would occupy every place, and thus
every place would be indifferently its own place. Neither could it move
circularly; forasmuch as circular motion requires that one part of the
body is necessarily transferred to a place occupied by another part, and
this could not happen as regards an infinite circular body: for if two
lines be drawn from the centre, the farther they extend from the centre,
the farther they are from each other; therefore, if a body were infinite,
the lines would be infinitely distant from each other; and thus one could
never occupy the place belonging to any other.

Aquin.: SMT FP Q[7] A[3] Body Para. 4/4

The same applies to a mathematical body. For if we imagine a
mathematical body actually existing, we must imagine it under some form,
because nothing is actual except by its form; hence, since the form of
quantity as such is figure, such a body must have some figure, and so
would be finite; for figure is confined by a term or boundary.

Aquin.: SMT FP Q[7] A[3] R.O. 1 Para. 1/1

Reply OBJ 1: A geometrician does not need to assume a line actually
infinite, but takes some actually finite line, from which he subtracts
whatever he finds necessary; which line he calls infinite.

Aquin.: SMT FP Q[7] A[3] R.O. 2 Para. 1/1

Reply OBJ 2: Although the infinite is not against the nature of
magnitude in general, still it is against the nature of any species of
it; thus, for instance, it is against the nature of a bicubical or
tricubical magnitude, whether circular or triangular, and so on. Now what
is not possible in any species cannot exist in the genus; hence there
cannot be any infinite magnitude, since no species of magnitude is
infinite.

Aquin.: SMT FP Q[7] A[3] R.O. 3 Para. 1/1

Reply OBJ 3: The infinite in quantity, as was shown above, belongs to
matter. Now by division of the whole we approach to matter, forasmuch as
parts have the aspect of matter; but by addition we approach to the whole
which has the aspect of a form. Therefore the infinite is not in the
addition of magnitude, but only in division.

Aquin.: SMT FP Q[7] A[3] R.O. 4 Para. 1/1

Reply OBJ 4: Movement and time are whole, not actually but successively;
hence they have potentiality mixed with actuality. But magnitude is an
actual 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.


Aquin.: SMT FP Q[7] A[4] Thes. Para. 1/1

Whether an infinite multitude can exist?

Aquin.: SMT FP Q[7] A[4] Obj. 1 Para. 1/1

OBJ 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.

Aquin.: SMT FP Q[7] A[4] Obj. 2 Para. 1/1

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.

Aquin.: SMT FP Q[7] A[4] Obj. 3 Para. 1/1

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.

Aquin.: SMT FP Q[7] A[4] OTC Para. 1/1

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

Aquin.: SMT FP Q[7] A[4] Body Para. 1/3

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.

Aquin.: SMT FP Q[7] A[4] Body Para. 2/3

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 the work is carried on for an
infinite time. In this way they said that there can be an accidentally
infinite multitude.

Aquin.: SMT FP Q[7] A[4] Body Para. 3/3

This, however, is impossible; since every kind of multitude must belong
to a species of multitude. Now the species of multitude are to be
reckoned by the species of numbers. But no species of number is infinite;
for every number is multitude measured by one. Hence it is impossible for
there to be an actually infinite multitude, either absolute or
accidental. Likewise multitude in nature is created; and everything
created is comprehended under some clear intention of the Creator; for no
agent acts aimlessly. Hence everything created must be comprehended in a
certain number. Therefore it is impossible for an actually infinite
multitude to exist, even accidentally. But a potentially infinite
multitude is possible; because the increase of multitude follows upon the
division of magnitude; since the more a thing is divided, the greater
number of things result. Hence, as the infinite is to be found
potentially in the division of the continuous, because we thus approach
matter, as was shown in the preceding article, by the same rule, the
infinite can be also found potentially in the addition of multitude.

Aquin.: SMT FP Q[7] A[4] R.O. 1 Para. 1/1

Reply OBJ 1: Every potentiality is made actual according to its mode of
being; for instance, a day is reduced to act successively, and not all at
once. Likewise the infinite in multitude is reduced to act successively,
and not all at once; because every multitude can be succeeded by another
multitude to infinity.

Aquin.: SMT FP Q[7] A[4] R.O. 2 Para. 1/1

Reply OBJ 2: Species of figures are infinite by infinitude of number.
Now there are various species of figures, such as trilateral,
quadrilateral and so on; and as an infinitely numerable multitude is not
all at once reduced to act, so neither is the multitude of figures.
Aquin.: SMT FP Q[7] A[4] R.O. 3 Para. 1/1

Reply OBJ 3: Although the supposition of some things does not preclude
the supposition of others, still the supposition of an infinite number is
opposed to any single species of multitude. Hence it is not possible for
an actually infinite multitude to exist.





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