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64 I turn now from these things to the thesis to be proved and declare that this most eminent being, which is both the ultimate
and as well as the first efficient cause, is infinite.
65 The first proof of this makes use of the notion of efficiency as employed by the Philosopher in Bk. VIII of the Physics
where he argues that, inasmuch as the first mover moves for an infinite time, it follows that he has infinite power.
66 Of course you may object to this argument on two grounds: first, the antecedent as a matter of fact is not true, since
motion will not continue forever.
67 Furthermore, the inference itself seems to be invalid, since, according to the mind of the Philosopher, a body like the sun,
though its power is finite, will continue to move things for an infinite time -- and as a matter of fact, it could move things for
an infinite period.
68 For these reasons, some reword the argument in this fashion. Where a cause produces its effects in virtue of itself alone,
it has in its power at once all the effects which are produced in succession, for such an agent cannot receive power to act
from anything other than itself, and hence it holds within its power at one and the same time all the effects it will eventually
produce. The first efficient cause acts in virtue of itself and hence holds in its power at one and the same time all the effects
which are successively produced, and these are potentially infinite. But this is to have infinite power. Now this is not, they
say, the case with the sun, since it acts in virtue of something other than itself, and consequently it does hold in its power at
one and the same time all of the effects it will eventually produce.
69 Also, were the first mover to move for an infinite period of time, it could produce eventually an infinity of things, because
with each movement it could produce something and this by reason of itself alone. But to possess in itself an ability to
produce an infinity of things is to possess infinite power.
70 These reasons, however, are not conclusive because an effect does not become more perfect because it continues to exist
for more than a moment. Whiteness which lasts for a hundred years, for instance, is not more perfect than whiteness which
lasts for a day. In like manner, a cause does not become more perfect because it produces its effect repeatedly instead of
once. The same strength that enables something to move once a day, will enable it to move for an infinite period of time. All
that is established, consequently, is the eternity of the cause, but from this one cannot infer its infinity.
71 Furthermore, to produce several individuals of the same species successively is not a matter of any greater perfection than
to produce one individual at one time. Something hot [like the sun], for example, does not become more perfect by making
several things hot over a period of time than it was when making one thing hot. But this infinity of things which are produced
by means of motion concerns things which are only individually, and not specifically, distinct. Consequently, its production
implies no greater perfection [in the cause] than does the production of a single individual.
72 Still one must say that the argument of the Philosopher is valid, for even though the antecedent is false if it is understood
of what is actually the case, the antecedent is true if you take it of what could be the case, without averting to whether it is or
not. For if the first mover could move for an infinite period of time and it does not derive this power from anything other than
itself, then it possesses such power of itself. And from this follows the further conclusion that it is of infinite power, so that
the inference is valid. The proof lies in this. Whenever numerical plurality in one extreme requires a greater perfection in the
other extreme, where the plurality of the one is infinite, the perfection of the other is infinite. For example, if to carry ten
objects requires more strength than to carry one, then to carry an infinite number requires infinite strength. To produce
several things at one time, however, requires more power than to produce but one; therefore, to produce an infinity requires
infinite power. But the first mover, so far as it itself is concerned, could produce an infinity at one time, as I shall prove.
Therefore, in itself it will be of infinite power. -- Proof of the assumption: It is clear that the first efficient cause has power
as a remote cause to cause an infinity at once, if such an infinity were able to be produced. But if the proximate causes by
which things are produced successively all existed at the same time as the remote first cause, they could produce an infinity
at once. Since the power of the first efficient cause, however, includes all the formal powers of the intermediary causes
which are potentially infinite, and it possesses all of the causalities of all intermediary causes in an even more perfect way
than if they were actualized, as will be proved, it follows that the first efficient cause, so far as it itself is concerned, has
power to produce an actual infinity. Proof of the assumption: It is clear that the first cause possesses the causality of the
proximate cause more perfectly than the latter, because this latter has its causality only in virtue of the first cause. Similarly,
the second cause possesses the causality of the third cause more perfectly than the latter, since the third cause receives its
causality from the second, and so on down to the lowest cause. Consequently, the first cause possesses more perfectly the
causalities of the intermediary causes, from first to last, than they do themselves.
73 Another proof of the implication is this. It is not that the causality of the production is more perfect that the second cause
is needed to work with the first cause. (Proof: if it were for the sake of a more perfect causality that several causes are
needed to produce a given effect, then the effect produced by the lot would be more perfect than the effect produced by one
cause; now it is the effect furthest removed [from the first cause] that needs all the causes, whereas the nearest effect needs
only the first cause. But since the more remote effect is less perfect than the proximate effect, it follows that it is not
because of any weakness in its causality that the first cause requires the cooperation of a second cause.) Hence, if the first
cause could produce an actual infinity of effects provided only that all of the infinitely numerous intermediary causes were
actualized, then it follows that so far as the first cause itself is concerned, it could produce an infinity, and consequently, it
will be infinitely powerful.
74 That is why the philosophers wished to say that the reason a second cause was needed to cooperate with the first cause was
not because of any deficiency as regards causality, but it was to explain how an imperfect effect could be produced. For they
thought that it was only through the intervention of some intermediary cause that an imperfect effect could be produced by a
perfect first cause.
75 Using this way of efficiency, some add as a further proof of our thesis that inasmuch as the first being is able to create, it
must have infinite power. They show that this follows because there is an infinite distance between contradictories which
nothing short of an infinite power can bridge. Hence, since to create is to make something from nothing, it follows that if the
first efficient cause can create, its power is infinite.
76 This argument, however, has no force.
First, it assumes that there is a creation -- which is something we take on faith -- and consequently, it is not a
demonstration.
Secondly, between contradictories there is the least of all "distance," for no matter how little something departs from the one
extreme, it immediately comes under the other. Hence there is the least latitude or distance here, although virtually speaking
the distance between contradictories is greatest because this minimal distance between them establishes the "distance" and
opposition between all other extremes.
77 What is more, the argument has another defect inasmuch as distance can be understood to be infinite in two ways. Either
the distance in itself is infinite in the sense that it lacks limits as would be the case if one has an endless line, or the distance
is infinite by reason of one of the extremes. We speak of a creature being infinitely distant from God, for instance. This is
only because the one extreme is infinite. And even if we assumed the existence of the most perfect creature possible,
between such a creature and God there would still be an infinite distance in the second sense. And it is in just this sense that
"distance" between something and nothing or between affirmation and negation is to be understood. Consequently, negation is
no more distant from affirmation than is the affirmation itself, and therefore whatever is able to make the affirmation is able
to bridge the distance. Consequently, the argument is not conclusive.
78 The second main argument for infinity stems from divine knowledge. As was said above, whenever numerical plurality
implies the presence of greater perfection, then an infinite number implies the presence of infinite perfection. Knowledge
whereby several things are known distinctly is more perfect than knowledge whereby only one such is known, as I shall prove.
Hence, knowledge of an actual infinity requires infinite perfection. Now the first intelligent and efficient cause with a single
intellection knows an infinity of things actually and distinctly, as I shall show. Therefore, it is actually of infinite perfection.
79 Proof of the first assumption: To know each object distinctly requires some perfection, hence to know several objects in
this way is something more perfect. If then there is a single intellection which actually contains the knowledge of them all, it
will be of greater perfection than would be the knowledge of only one.
Proof of the second assumption, that God's knowledge has to do with an actual infinity, like an infinity of figures and
numbers: Wherever you have a potential infinity, if all its members were to exist at the same time, you would have an actual
infinity. This is clear if you consider the consequences of any alternate hypothesis. Consider the intelligibles which we know
by thinking of one after another. They are potentially infinite and they are all actually known by God, because he knows
whatever can be. Hence, he knows an actual infinity.
80 The third argument for infinity is drawn from the fact that the divine essence itself serves as the [principle or] reason why
God knows. For just as knowledge wherein several things are grasped distinctly is more perfect than that wherein but one is
known, so also is the principle for knowing several things more perfect than is a principle for knowing only one of them. And
an essence which represents several things distinctly will be more perfect than one which represents but one. But the divine
essence represents an infinity of things distinctly, and consequently, its power of representation is infinite. Therefore the
[essence itself] is infinite.
81 What is more, the reason this is so lies not merely in the ability of [the essence] to make all things known distinctly but
because it produces a clear vision of a thing like a stone. If something is the precise effect of some cause, and nevertheless
something else can produce the same effect in even more perfect fashion, the proper cause cannot add anything to the
perfection of the latter. If something be the precise cause of a for instance, and if b causes the same effect even more
perfectly, then it is impossible that a should add anything to b. For were there any perfection to be added, it would be because
b lacked some perfection needed to produce the effect in question, since it is precisely this effect that a's power is adequate
to achieve. Any object, however, by its very nature is fitted to be the precise and proper cause of an [intuition or] vision of
itself. It is impossible, then, that such a vision be achieved in an even more perfect manner unless it be by reason of
something to which nothing in the way of perfection could be added. But such a vision is had even more perfectly by reason
of the divine essence, so that neither a stone, nor any other essence, could add anything to the perfection of the divine
essence. But anything of this kind is infinite. Therefore, etc.
82 The fourth argument for infinity is derived from the fact that God is an end. Our will can love a good that exceeds that of
any finite good. This we know, first, because our intellect can know such a good, and also because our will is inclined to seek
an infinite good, for it delights in evoking such an act of love, which would not be the case if it were not inclined to do so. If
the ultimate end were not an infinite good, however, the will would not be inclined towards, nor seek, an infinite good. Proof:
It is incompatible with the very notion of an ultimate end that there be any good greater than it, as we have shown [Cf. par. 60].
For then it could either exist of itself, or in virtue of another, neither of which can be assumed to be the case. If the ultimate
end, then, were finite and not infinite, it would be impossible for any good to be infinite. And if this were so, the will could
neither love the infinite nor be inclined towards it, because it has no inclination towards the opposite of its object.
83 The fifth argument for infinity is based on the eminence [of God]. Anything to which infinity is not repugnant, is not
simply perfect unless it is infinite. For instance, if the tenth degree of some perfection is not repugnant to a certain thing,
then it is not simply perfect unless it possesses the tenth degree. But to being qua being infinity is not repugnant, as will be
proved. Therefore, the most eminent and most perfect being will be infinite.
84 Proof of the assumption: If "infinite" were repugnant to "being," then the repugnance would either be formal, like "man" and
"not-man," or virtual, like "man" and "not-risible." The first is not the case, for formal repugnance stems from the meaning of
the terms. But as Avicenna teaches in Bk. I of the Metaphysics, the meaning and notion of "being" cannot be made any clearer.
The concept of "infinite" is also clear, because the infinite is that which cannot be surpassed. But there is no contradiction
between these notions, for there is no contradiction that something be a being and that it cannot be surpassed. Neither is there
any virtual repugnance, for the primary attributes of "being" such as "true," and "good" and such like, are most evidently
characteristic of being. But this is not the case with "infinite," for "being" does not of itself include "infinite" as a coextensive
attribute. Consequently, "being is infinite" is not a primary truth unless you add in disjunction its opposite [viz. "being is either
infinite or finite"].
85 Also since an amount of power is of greater perfection than an amount of mass, and since infinity is not repugnant to the
latter, then neither is it opposed to the former.
86 Another proof of the same point is this. Any faculty naturally perceives any lack of harmony in its object, and it will not
naturally put up with it or be content with it. If then "infinite" were something that contradicted "being," our mind would be
naturally repelled by "infinite being" as something which includes a contradiction. But this is false, for our mind rather than
finding any contradiction discovers its rest therein.
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