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The Infinity of God

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The Infinity of God

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THE INFINITY OF GOD
Paul Gerard Horrigan, Ph.D., 2012.

God is Infinite
Against the erroneous views of a finite God,1 such as is asserted by the various forms of
finitism found in the writings of the utilitarianist John Stuart Mill,2 the pragmatist William
James,3 as well as in the writings of the process philosopher Alfred North Whitehead,4 and the
process theologian John Cobb,5 we affirm, instead, that God is not finite but is absolutely and
essentially Infinite.6
God is Pure Act of Being, without any potentiality (potency or potentiality understood in
the strict sense of passive potency). Since His Being is completely in act, He is completely
perfect. Absolutely nothing is lacking to His Being. Therefore, we affirm that God is also
infinite. There is no term or limit to His Being. Now, being perfect and being infinite are not the
same thing. Being perfect posits God in complete actuality of being and all the perfections of
being, while being infinite removes or denies any term or limit to God’s Being. But infinity
follows from perfection. As God’s Being is completely in act, there can be nothing potential or
limiting within it. God is infinite because His Act of Being (Esse) is identified with His Essence
(Essentia). His Esse is not received and limited by a distinct essence (essentia), He being the
Ipsum Esse Subsistens. St. Thomas states: “Now, the act of being (esse) is the most formal of all
things…Since, therefore, the divine esse (esse divinum) is not received in anything, but He is His
own subsistent esse…it is clear that God Himself is infinite and perfect.”7
De Veritate, q. 29, a. 3: “With regard to the formality of being (esse), then, only that can
be infinite which includes all the perfection of being (esse) – a perfection which is capable of
being diversified in an infinite number of different modes. In this respect only God is infinite
essentially, because His act of being (esse) is not limited to any determined perfection but
embraces every mode of perfection to which the formality of being can extend. For this reason
1

For brief descriptions and critiques of the finitist view of God: T. McTIGHE and L. H. KENDZIERSKY, The
Finite God in Contemporary Philosophy, “Proceedings of the American Catholic Philosophical Association,” 28
(1954), pp. 212-236 ; J. D. COLLINS, God Finite and in Process, in J. D. Collins, God in Modern Philosophy,
Regnery Gateway, Chicago, 1967, pp. 285-324.
2
J. STUART MILL, Three Essays on Religion, London, 1874, pp. 37-38.
3
W. JAMES, The Will to Believe, New York, 1897, p. 141 ; W. JAMES, A Pluralistic Universe, New York, 1909,
pp. 124ff.
4
A. N. WHITEHEAD, Religion in the Making, New York, 1926, p. 71; Cf. M. CORVEZ, De la science à Dieu,
Paris, 1986, pp. 86-87.
5
Cf. J. COBB, A Christian Natural Theology, Philadelphia, 1965.
6
Studies on infinity and Divine Infinity: G. F. J. LaMOUNTAIN, The Concept of the Infinite in the Philosophy of
St. Thomas Aquinas, “The Thomist,” 19 (1956), pp. 312-338 ; L. SWEENEY, Some Medieval Opponents of Divine
Infinity, “Mediaeval Studies,” 19 (1957) ; L. SWEENEY, Divine Infinity 1150-1250, “The Modern Schoolman,” 35
(1957-58) ; L. SWEENEY, Bonaventure and Aquinas on the Divine Being as Infinite, in R. J. Shahan and F. J.
Kovach (eds.), Bonaventure and Aquinas: Enduring Philosophers, University of Oklahoma Press, Norman, OK,
1976, pp. 133-153 ; L. SWEENEY, Divine Infinity in Greek and Medieval Thought, Peter Lang, New York, 1992.
7
Summa Theologiae, I, q. 7, a. 1, c.

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He is essentially infinite. This kind of infinity cannot apply to any creature, for the act of being
(esse) of every creature is limited to the perfection of its own species.”
All of God’s perfections are actually infinite. His Goodness is infinite. His Truth is
infinite. His Wisdom is infinite. His Will is infinite. His Power is infinite, etc. But the ultimate
root for infinity is the act of being (esse) itself, the source of every perfection and every actuality.
And God is Pure Act of Being, His Esse being identified with His Essence, unreceived by a
really distinct essence co-principle that would limit it. Therefore, God is Infinite. Now, infinity is
an attribute that pertains to God inasmuch as He is Ipsum Esse Subsistens, in Whom Esse and
Essentia are identified. Thus, we do not say that God is His own Esse because He is infinite;
rather, we say that He is infinite because He is identified with His own Esse. God is the Ipsum
Esse Subsistens, His Esse is not received by a really distinct essence co-principle that would limit
it (which the case with creatures, finite beings that only participate in esse). This is an answer to
the error of Duns Scotus, who places radical infinity as the root of all the divine perfections,8 an
erroneous position also subscribed to by Nicholas of Cusa.9
Summa Theologiae, I, q. 7, a. 1, c.: “A thing is called infinite because it is not finite
(limited). 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 the act of being (esse) is the
most formal of all things, as appears from what is shown above (q. 4, a. 1, ob. 3). Since therefore
the divine esse (esse divinum) is not an esse received in anything, but He is His own subsistent
esse as was shown above (q. 3, a. 4), it is clear that God Himself is infinite and perfect.”10
Commenting on the above text from the Summa Theologiae, Garrigou-Lagrange writes:
“That God is infinite is proved from reason from the following argument, which St. Thomas
considers a simple corollary of the assertion that God is self-subsisting Being.11 Whereas matter
is called infinite by an infinity of imperfection, the unreceived form is infinite by an infinity of
perfection, at least relatively so. Thus, if whiteness were not received in anything, it would have
the total perfection of whiteness without any limit. But being is the most formal of all things, as
it is the actuality of forms themselves. Therefore being that is not received in anything – and this
being is God – is infinite by an infinity of perfection, and not merely relatively as included in
some genus as would be the case with whiteness that is not received in anything, but is so
absolutely, transcending every genus.”12

8

Cf. DUNS SCOTUS, Opus Oxoniense, I, a. 3, pars I, q. 2.
Cf. NICHOLAS OF CUSA, De visione Dei, ch. 13; De veneratione sapientiae, ch. 29.
10
Summa Theologiae, I, q. 7, a. 1, c.
11
Summa Theologiae, I, q. 3, a. 4.
12
R. GARRIGOU-LAGRANGE, The One God, B. Herder, St. Louis, 1943, pp. 236-237.
9

2

Summa Contra Gentiles, I, chapter 43 (That God is Infinite): “[1] Since, as the
philosophers teach, “the infinite accompanies quantity,” infinity cannot be attributed to God on
the ground of multitude. For we have shown that there is only one God and that no composition
of parts or accidents is found in Him. Nor, again, according to continuous quantity can God be
called infinite, since we have shown that He is incorporeal. It remains, then, to investigate
whether according to spiritual magnitude it befits God to be infinite.
“[2] We speak of spiritual magnitude with reference to two points: namely, power and the
goodness or completeness of one’s own nature. For something is said to be more or less white
according to the mode in which its whiteness is completed. The magnitude of its power likewise
is measured from the magnitude of its action or its works. Of these magnitudes one follows the
other. For, from the fact that something is in act it is active, and hence the mode of the magnitude
of its power is according to the mode in which it is completed in its act. Thus, it remains that
spiritual beings are called great according to the mode of their completion. Augustine himself
says that ‘in beings that are great but not in bulk, to be greater is the same as to be better.’
“[3] We must therefore show that God is infinite according to the mode of this sort of
magnitude. The infinite here will not be taken in the sense of privation, as in the case of
dimensive or numerical quantity. For this quantity is of a nature to have a limit, so that such
things are called infinites according as there is removed from them the limits they have by
nature; which means that in their case the infinite designates an imperfection. But in God the
infinite is understood only in a negative way, because there is no terminus or limit to His
perfection: He is supremely perfect. It is thus that the infinite ought to be attributed to God.
“[4] For everything that according to its nature is finite is determined to the nature of
some genus. God, however, is not in any genus; His perfection, as was shown above, rather
contains the perfections of all the genera. God is, therefore, infinite.
“[5) Again, every act inhering in another is terminated by that in which it inheres, since
what is in another is in it according to the mode of the receiver. Hence, an act that exists in
nothing is terminated by nothing. Thus, if whiteness were self-existing, the perfection of
whiteness in it would not be terminated so as not to have whatever can be had of the perfection
of whiteness. But God is act in no way existing in another, for neither is He a form in matter, as
we have proved, nor does His being inhere in some form or nature, since He is His own being, as
was proved above. It remains, then, that God is infinite.
“[6] Furthermore, in reality we find something that is potency alone, namely, prime
matter, something that is act alone, namely, God, as was shown above, and something that is act
and potency, namely, the rest of things. But, since potency is said relatively to act, it cannot
exceed act either in a particular case or absolutely. Hence, since prime matter is infinite in its
potentiality, it remains that God, Who is pure act, is infinite in His actuality.
“[7] Moreover, an act is all the more perfect by as much as it has less of potency mixed
with it. Hence, every act with which potency is mixed is terminated in its perfection. But, as was
shown above, God is pure act without any potency. He is, therefore, infinite.

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“[8] Again, considered absolutely, being is infinite, since there are infinite and infinite
modes in which it can be participated. If, then, the being of some thing is finite, that being must
be limited by something other that is somehow its cause. But there can be no cause of the divine
being, for God is a necessary being through Himself. Therefore, His being is infinite, and so is
He.
“[9] Then, too, what has a certain perfection is the more perfect as it participates in that
perfection more fully. But there cannot be a mode of perfection, nor is one thinkable, by which a
given perfection is possessed more fully than it is possessed by the being that is perfect through
its essence and whose being is its goodness. In no way, therefore, is it possible to think of
anything better or more perfect than God. Hence, God is infinite in goodness.
“[10] Our intellect, furthermore, extends to the infinite in understanding; and a sign of
this is that, given any finite quantity, our intellect can think of a greater one. But this ordination
of the intellect would be in vain unless an infinite intelligible reality existed. There must,
therefore, be some infinite intelligible reality, which must be the greatest of beings. This we call
God. God is, therefore, infinite.
“[11] Again, an effect cannot transcend its cause. But our intellect can be only from God,
Who is the first cause of all things. Our intellect, therefore, cannot think of anything greater than
God. If, then, it can think of something greater than every finite thing, it remains that God is not
finite.
“[12] There is also the argument that an infinite power cannot reside in a finite essence.
For each thing acts through its form, which is either its essence or a part of the essence, whereas
power is the name of a principle of action. But God does not have a finite active power. For He
moves in an infinite time, which can be done only by an infinite power, as we have proved
above. It remains, then, that God’s essence is infinite.
“[13] This argument, however, is according to those who posit the eternity of the world.
If we do not posit it, there is all the greater confirmation for the view that the power of God is
infinite. For each agent is the more powerful in acting according as it reduces to act a potency
more removed from act; just as a greater power is needed to heat water than air. But that which
in no way exists is infinitely distant from act, nor is it in any way in potency. If, then, the world
was made after previously not being at all, the power of its maker must be infinite.
“[14] This argument holds in proving the infinity of the divine power even according to
those who posit the eternity of the world. For they acknowledge that God is the cause of the
substance of the world, though they consider this substance to be everlasting. They say that God
is the cause of an everlasting world in the same way as a foot would have been the cause of an
imprint if it had been pressed on sand from all eternity. If we adopt this position, according to
our previous argumentation it still follows that the power of God is infinite. For, whether God
produced things in time, as we hold, or from all eternity, according to them, nothing can be in
reality that God did not produce; for God is the universal source of being. Thus, God produced
the world without the supposition of any pre-existent matter or potency. Now, we must gather
the proportion of an active power according to the proportion of a passive potency, for the
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greater the potency that preexists or is presupposed, by so much the greater active power will it
be brought to actual fulfillment. It remains, therefore, that, since a finite power produces a given
effect by presupposing the potency of matter, the power of God, which presupposes no potency,
is infinite, not finite. Thus, so is His essence infinite.
“[15] Each thing, moreover, is more enduring according as its cause is more efficacious.
Hence, that being whose duration is infinite must have been from a cause of infinite
efficaciousness. But the duration of God is infinite, for we have shown above that He is eternal.
Since, then, He has no other cause of His being than Himself, He must be infinite.
“[16] The authority of Sacred Scripture is witness to this truth. For the psalmist says:
‘Great is the Lord, and greatly to be praised: and of His greatness there is no end’ (Ps. 144:3).
“[17] The sayings of the most ancient philosophers are likewise a witness to this truth.
They all posited an infinite first principle of things, as though compelled by truth itself. Yet they
did not recognize their own voice. They judged the infinity of the first principle in terms of
discrete quantity, following Democritus, who posited infinite atoms as the principles of things,
and also Anaxagoras, who posited infinite similar parts as the principles of things. Or they
judged infinity in terms of continuous quantity, following those who posited that the first
principle of all things was some element or a confused infinite body. But, since it was shown by
the effort of later philosophers that there is no infinite body, given that there must be a first
principle that is in some way infinite, we conclude that the infinite which is the first principle is
neither a body nor a power in a body.”
Only God is Absolutely Infinite
Summa Theologiae, I, q. 7, a. 2, c.: “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, what 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 the angels, these will be relatively infinite, inasmuch as such kinds of forms are not
terminated, not contracted by any matter. But because a created form thus subsisting has being,
any 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.”13
Commenting on the above text from the second article of the seventh question of the
Prima Pars, Garrigou-Lagrange states: “Things other than God can be relatively infinite, but not
absolutely infinite. …The reason is that absolute infinity is the infinity of the being that is not
received in any other, and there can be only one such infinity, just as, if whiteness were not
received in any other, there would be but one whiteness.
13

Summa Theologiae, I, q. 7, a. 2, c.

5

“However, immaterial forms, such as Michaelness, are relatively infinite with an infinity
of perfection. Thus Michael has all the perfection that belongs to his species.14 Infinity that is
said to be secundum quid is also relative, or as referring to some genus of infinity, whereas
infinity that said to be so simpliciter, is absolute infinity. But matter is relatively infinite, with an
infinity of imperfection, since it has a real capacity for receiving all natural forms.15
“It must be noted that the end of the argumentative part of this article again affirms
clearly the real distinction between created essence and act of being in the following words:
‘Because a created subsisting form (as Michaelness) has being, 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.’”16
The nature of a pure form such as an angel (finite pure spirit) is not received in matter
and, therefore is not limited. An angel is infinite in the order of essence and since it realizes the
fullness of its specific perfection, it is actually, not potentially, infinite. Nevertheless, the actual
infinity which is attributable to angelic forms is not predicated of them in an absolute way or
unqualifiedly (simpliciter), but only qualifiedly (secundum quid). The reason for this is that
angels are not their own act of being. Though angels are infinite as regards their essence,
nevertheless, this is not an existential infinity. St. Thomas states in Summa Theologiae, I, q. 50,
a. 2, ad 4: “Every creature is finite, simply speaking, inasmuch as its act of being (esse) is not
absolutely subsistent but is terminated in some nature to which it is communicated. Nothing,
however, prevents some creature from being infinite relatively. Material creatures have an
infinity on the side of the matter, but they are finite on the part of the form, which is limited by
the matter in which it is received. But created immaterial substances are finite according to their
act of being (esse), but infinite in that their forms are not received in anything. Thus, we might
speak of whiteness, existing separately, as infinite precisely as white, because it would not be
contracted to any subject; its act of being (esse), however, would be finite, because it would be
determined to a certain specific nature.”17
There is a real distinction of essence (essentia) and act of being (esse) in an angel (finite
pure spirit), the former metaphysical co-principle limiting the latter. In contrast to this, God
alone is His own Act of Being (Esse), Whose Esse is unreceived by a really distinct essence that
would limit it. God is Ipsum Esse Subsistens. Therefore, He is infinite unqualifiedly, infinite
simpliciter.
Critiques of Pantheist Objections to the Infinity of God
Garrigou-Lagrange’s Critique: “To the infinite, pantheism says, nothing can be added; if
therefore the universe is added to the being of God, as a new reality, the being of God is not
infinite.

14

Summa Theologiae, I, q. 50, a. 4.
Summa Theologiae, I, q. 50, a. 4, ad 3.
16
R. GARRIGOU-LAGRANGE, op. cit., p. 240.
17
Summa Theologiae, I, q. 50, a. 2, ad 4.
15

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“It is easy to answer this. There can be no addition made to the infinite in the same order:
that is, no addition can be made to its being, its wisdom, its goodness, its power. But there is no
repugnance whatever in something being added in a lower order, as an effect is added to the
transcendent cause producing it. To deny this would be to refuse to the infinite Being the power
of producing an effect distinct from Himself; He would then no longer be infinite.
“But if this is so, the pantheist insists, more being and perfection will exist after the
production of created things than before, which is equivalent to saying that the greater comes
from the less.
“The traditional answer given in theology is, that after creation many beings exist, but
there is not more being or more perfection than before. Similarly, when a great teacher like St.
Thomas has trained several pupils, there are many that are learned, but there is no more learning
than before unless the pupils excel their master in knowledge. This being so, we can with even
greater truth say that after creation the world has many beings but not more being, many living
beings but not more life, many intellects but not more wisdom. He who is infinite being, infinite
life, infinite wisdom, already existed before creation, containing in Himself in an eminent degree
the limited perfections of created beings.
“Such is the infinity of God, an infinity of perfection which is the plenitude not of
quantity or extension, but of being, life, wisdom, holiness, and love.”18
Bittle’s Critique: “An objection has been raised against the ‘infinite perfection’ of God. It
runs somewhat as follows: Besides the essence of God there exist many other essences and
beings, namely, the physical world and everything in it. These essences and beings, and therefore
also their perfections, are not present in God. Consequently, their perfections are missing in the
essence and being of God, and He is not infinitely perfect.
“The answer to this objection is not difficult. The infinite being must certainly possess all
the perfections found in the beings present in the universe. However, it is not necessary for Him
to possess them according to their individual existence; it suffices, if He possesses these
perfections according to their worth or value virtually and eminently. These things do not and
cannot possess any perfection greater than His nor independent of Him; whatever they possess in
the line of reality and perfection, they have received from Him. So long as God does not lose any
perfection of His own thereby, one cannot say that these things possess perfections which He
does not possess. Their existence merely multiplies the number of beings possessing perfection,
but the perfection itself does not thereby become greater. A teacher imparting knowledge to his
pupils does not lose his own knowledge, nor do the pupils have a more perfect knowledge than
the teacher, nor does the addition of the knowledge of all the pupils to that of the teacher make
the knowledge as a whole greater or more perfect. The knowledge has the same amount of
perfection, whether communicated or not; the number of knowing individuals has been
increased, but not the perfection of the knowledge itself. The objection is thus seen to be invalid.
“A somewhat similar objection, though different in form, is also made against God’s
infinity. The beings in this world possess a certain amount of real perfection. Let us suppose that
18

R. GARRIGOU-LAGRANGE, Providence, Tan Books, Rockford, IL, 1998, pp. 95-96.

7

God’s perfection is infinite. Then the addition of the perfections of the creatures to the perfection
of God gives an amount of perfection which is greater than infinite. But that is impossible. Now,
one cannot deny the existence of creatural perfections. One must, therefore, deny the infinity of
God’s perfection.
“The answer to this objection is about the same as that to the foregoing objection. By
adding the perfections of creatures to the perfection of God one does not increase ‘perfection as
such,’ since perfections are predicated of God and creatures only in an analogical sense; one
merely increases the number of those possessing perfection. The number of creatures is only
finite, though it is potentially infinite; adding God as another number to the number of creatures
does not increase this number to such an extent that its magnitude would be ‘actually infinite.’”19
Holloway’s Critique: “It was objected that since the Being of God does not include the
being of the creature, God is not infinite but finite. Indeed the fact that God is subsistent Being
whose act of being is not received in anything, distinguishes God from all other beings and
removes all these beings from God. God is by His very essence, creatures are by participation.
But to answer the objection, we say that whatever of being is possessed by the creature God also
possesses in an infinitely more perfect way. Thus the fact that there are beings other than God
does not mean that God is not infinite in His being. Moreover, if the Being of God included the
participated being of the creatures, God would be finite, material, and so on, which is absurd.
“Finally, while the fact that infinite Being co-exists with finite beings gives us more
beings than the infinite Being alone, it does not give us more being (plura entia sed non plus
entis). For example, after a teacher communicates his knowledge to many students we have
many more who know (plures scientes), but we do not have any more knowledge (plus
scientiae). So, too, after the creative act of God, by which he communicates being to creatures,
there are more beings, but not more being.”20

19
20

C. BITTLE, God and His Creatures: Theodicy, Bruce, Milwaukee, 1953, pp. 230-231.
M. HOLLOWAY, Natural Theology, Appleton-Century-Crofts, New York, 1959, pp. 244-245.

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