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B. The Existence of an Infinite Being is Made Clear
74. Having shown the relative properties of the first being, I proceed further as follows to show the infinity of the first being and consequently the existence of an infinite being: first I show that the first efficient cause has intelligence and will such that its intelligence is of infinites distinctly and that its essence is representative of infinites (which essence indeed is its intelligence), and from this will be shown, secondly, its infinity. And thus, along with the triple primacy already shown, there will be a fourfold means for showing its infinity. But yet as to the fourth means, namely that the first efficient cause has intelligence and will, from which, as from a means added to the other three, its infinity is proved, I make a certain assumption with respect to it until distinction 35 [Ordinatio I d.35 q. un. n.2].
1. Conclusions preliminary to infinity are proposed and demonstrated
75. Now, that the first being has intelligence and will I argue thus: some agent is a per se first agent, because to every cause per accidens some cause per se is prior, Physics 2.6.198a8-9, where Aristotle intends this of nature, about which it is less evident; but every agent per se acts for an end.
76. And from this there is a twofold argument.
First thus: every natural agent, precisely considered, would act of necessity and just as much if it were not to act for any other end but was acting independently; 
therefore if it does not act save for an end, this is because it depends on an agent that loves the end; of such a sort is the first efficient cause, therefore etc 
.
77. Again, if the first agent acts for an end, then that end moves the first efficient cause either as loved by an act of will or as only naturally loved. If as loved by an act of will, the intended conclusion is gained. If only naturally loved, this is false, because it does not naturally love an end other than itself in the way the heavy loves the center and matter loves form; for then it would in some way be in relation to an end because inclined to an end. But if it only naturally loves the end which is itself, this is nothing save itself being itself, for this does not preserve the doubleness of idea in itself.87
78. Another argument, by as it were bringing together the reason already made, is as follows: the first efficient cause itself directs its effect to an end; therefore it directs either naturally or by knowing and loving the end. Not naturally, because a non-knower directs nothing save in virtue of a knower; for it belongs first to the wise to order things, Metaphysics 1.2.982a17-18; but the first efficient cause directs in virtue of nothing else, just as neither does it cause in virtue of anything else, - for then it would not be first; therefore etc .
79. Again, something is contingently caused; therefore the first cause causes contingently, therefore it causes willingly.
80. Proof of the first consequence: any second cause causes insofar as it is moved by the first cause; therefore if the first cause moves necessarily, any other cause is moved necessarily and anything else is caused necessarily; therefore if some second cause moves contingently, the first cause too will move contingently, because the second cause, to the extent it is moved by the first cause, does not cause save in virtue of the first cause.
81. Proof of the second consequence: there is no principle of contingent operation save the will or something concomitant to will, because any other thing acts from the necessity of nature, and so not contingently; therefore etc .
82. There is an instance against this reason, and first against the first consequence the argument is as follows, that our own willing could yet cause something contingently, and so there is no requirement that the first cause contingently cause it.
83. Again, the Philosopher conceded the antecedent, namely that something is contingently caused, and he denied the consequent in the sense of understanding it of will, namely that the first cause causes contingently, by positing contingency in inferior things, not because God wills contingently, but as a result of motion, which causes necessarily insofar as it is uniform but has deformity, and so contingency, following from its parts.
84. Against the second consequence, ‘if it causes contingently, therefore it causes willingly’: this does not seem to hold, because some of the things that are moved naturally can be impeded, and so the opposite can - contingently and violently - come about.
85. To the first [n.82] one must say that if God is the first moving or efficient cause with respect to our will, the same follows about it as about other things, because he necessarily either moves the will immediately or he moves another thing and this other thing, having been necessarily moved, would necessarily move the will, because this other thing only moves from the fact that it is moved. The ultimate result is that what is proximate to the will would necessarily move the will, even if what is proximate to the will is the will itself; and so it will necessarily will, and it will be necessarily willing. And further the impossibility follows that he necessarily causes whatever is caused.
86. To the second [n.83] I say that I do not here call contingent what is nonnecessary or non-eternal, but something whose opposite might happen when that something happens; therefore I said ‘something is contingently caused’ [n.79], and not ‘something is contingent’. Now I say that the Philosopher cannot deny the consequent by saving the antecedent through recourse to motion [n.83], because if that whole motion is from its cause necessarily, any part of it is necessarily caused when it is caused, that is, it is caused inevitably, so that the opposite cannot then be caused; and further, what is caused by any part of the motion is caused necessarily and unavoidably. Either therefore nothing happens contingently, that is avoidably, or the first thing causes immediately in such a way that it might also not cause.
87. To the third [n.84] I say that if some cause can impede it, this is only in virtue of a superior cause, and so on right up to the first cause, and if the first cause necessarily moves the cause immediate to itself, there will be necessity right up to the end; therefore it will impede necessarily, and consequently no other cause can naturally exercise its causality.88
88. Thus therefore it seems to have been shown in a triple way that the first agent has intelligence and will, the first of which ways is that nature acts for an end and only because it is dependent and directed to the end by a knower [n.76]; the second is that the first agent itself acts for an end [nn.77-78], and the third that some effect is, when caused, contingently caused [nn.79-87].
89. Further, as to the question preliminary to infinity, I prove second that the first agent’s understanding and will are the same as its essence, and first of the volition of itself as of an object such that the act of love of the first cause is essentially the same as the nature of that cause and as the nature of every act of its will.
Proof. The causality and causing of the final cause is simply first, according to Avicenna Metaphysics 6 ch.5 (95rb), who says that “if there is knowledge about any cause whatever, knowledge about the final cause would be noblest;” for this cause, as concerns its causality, precedes the efficient cause, because it moves the efficient cause to act, - and therefore the causality of the first cause and of its causing is, according to any causation in any genus of cause, through and through un-causable. But the causality of the first end is to move the efficient cause as a thing loved; but it is the same thing for the first end to move the first efficient cause as a thing loved by it and for the first efficient cause to love the first end, because for an object to be loved by the will is nothing other than for the will to love the object. Therefore that the first efficient cause loves the first end is through and through un-causable, and so is necessary of itself, and so it will be the same as the first nature. And there is as it were a reversal of the reasoning from the opposite of the conclusion, because if the first loving is other than the first nature, then it is causable, and consequently effectible; therefore it is from some per se efficient cause which loves the end. Therefore the first loving would be caused by some love of the end prior to that caused first loving, which is impossible.
90. Aristotle shows this fact about intelligence, Metaphysics 12.9.1074b17-21, because otherwise the first thing will not be the best substance, for it is through understanding that it is honorable.
91. Second, because otherwise the continuance of its activity will be laborious for it. Again, if it is not that [sc. the same as its essence], it will be in potency to its contradictory; on that potency labor follows, according to him.89
92. These reasons can be made clear by reason.
The first [n.90] thus: since the ultimate perfection of every being in first act exists in the second act whereby it is conjoined to what is best, especially if the best acts and does not merely make (for every intelligible is active, and the first nature is intelligible, from the previous conclusion [nn.75-88]), the consequence is that its ultimate perfection will be in second act; therefore if this act is not the substance of it, its substance will not be best, because its best is some other thing.
93. The second reason [n.91] can be made clear thus: a potency merely receptive is a potency for the contradictory; therefore since it is not of this sort [sc. in potency to the contradictory], therefore etc . - But because according to Aristotle this reason is not demonstrative but only probable, let the intended proposition be shown in another way, from the identity of the power and of the object in itself; therefore they will have the same act. But the consequence, plainly, is not valid; an instance is that an angel understands itself and loves itself and yet an angel’s act of loving and of understanding are not the same as its substance.90
94. This conclusion, namely that the divine essence is the same as its willing itself, is true from corollaries: for it follows first that that the will is the same as the first nature, because willing exists only in the will; therefore the will whose willing is un-causable is also un-causable;91 therefore etc . And likewise, willing is understood to be as it were posterior to the will; yet willing is the same as the first nature; therefore the will more so.
95. Again, second, it follows that understanding itself is the same as the first nature, because nothing is loved unless it is known; therefore if loving itself is necessarily existent from itself, the consequence is that understanding itself is necessarily existent from itself.
96. And if understanding is closer to the first nature than willing, then the consequence further is that the intellect is the same as the first nature, as was just argued about the will from willing [n.94].
97. There is a fourth consequence too, that the idea of understanding itself is the same as itself, because the idea necessarily exists of itself if understanding necessarily exist of itself, and if the idea of understanding itself is as it were pre-understood in the intellect itself.
98. Having shown of self-understanding and self-willing that they are the same as the essence of the first being, I show from other things the proposition intended, namely about all its understanding and willing.
And let the third conclusion be this: no understanding can be an accident of the first nature. The proof is that it has been shown of the first nature that it is in itself the first effective thing [nn.43-56]; therefore it has from itself the resources whence, after everything else has been removed, it can cause anything causable, at least as first cause of the causable. But with its knowledge removed it does not have the resources whence it might cause the causable; therefore knowledge of anything else whatever is not other than its nature. - The proof of the assumption is that nothing can cause except from love of the end, by loving it, because it cannot otherwise be a per se agent, because neither can it act, for an end; as it is, however, there is pre-understood in its willing of anything for the end its understanding of it; therefore before the first moment in which it is understood to be causing or willing a, necessarily it is pre-understood to be understanding a; so without this it cannot per se bring a about, and so in the case of other things.
99. Again, the same thing is proved because all understandings of the same intellect have a like relation to the intellect, according to their essential identity or accidental identity with it (as is clear of every created intellect and its understandings), because they seem to be perfections of the same genus; therefore if some of them have a subject that receives them, then all of them do, and if one of them is an accident each of them is. But it cannot be that any of them is an accident in the first thing, from the preceding conclusion [n.89], because an accident would be a non-understanding of itself; therefore none of them will there be an accident.
100. Again, understanding, if it is what can be an accident, will be received in the intellect as in a subject; therefore received also in the understanding which is the same as the intellect, and thus a more perfect understanding will be in the receptive power in respect of a more imperfect understanding.
101. Again, the same understanding can be about setting several objects in order, therefore the more perfect it is the more the objects; therefore the most perfect understanding, with which a more perfect degree of being understood is incompossible, will be the same as the understanding of all objects. The understanding of the first thing is most perfect in this way; therefore it is the same as the understanding of all objects, and the understanding which is of itself is the same as itself, from what has just preceded [n.89]; therefore the understanding of all things is the same as itself. And I intend the same conclusion to be understood about willing.
102. Again, the intellect is nothing but a certain understanding; but this intellect is the same for all things, and so is something that cannot be for any other object; therefore neither can it understand any other thing. Therefore the intellect is the same as the understanding of all things. - It is the fallacy of the accident to conclude from the identity of certain things among themselves to their identity with respect to a third thing with respect to which they are extraneous;92 and it is plain from a similitude: to understand is the same as to will; ‘if therefore to understand itself belongs to something, then to will itself too belongs to the same thing’, does not follow, but it only follows that to will belongs to it; which willing indeed is something that belongs to the same thing, because one must so understand ‘same thing’ that the inference can be drawn in a divided, not a conjoined, manner, because of being an accident.93
103. Again, the intellect of the first thing has one act that is adequate to itself and coeternal, because understanding itself is the same as itself; therefore it cannot have any other understanding. - The consequence is not valid. An example about the blessed who at the same time see God and something else even if they see God according to the utmost of their capacity, as is posited about the soul of Christ, and still he can see something else.
104. Again an argument: this intellect has in itself through identity the greatest perfection of understanding; therefore it has every other understanding. - Response: this does not follow, because an understanding that is lesser can be causable and therefore can differ from the un-causable, but the greatest understanding cannot.
105. The fourth principal conclusion about the intellect and the will of God is this: the intellect of the first thing understands always and with a distinct and necessary act any intelligible thing naturally before that thing exists in itself.
106. The proof of the first part is that the first thing can know what is thus intelligible; for this belongs to perfection in the intellect, to be able distinctly and actually to know any intelligible thing, nay to posit this is necessary for the idea of intellect, because every intellect is of the whole of being taken in the most common way, as will be determined later [I d.3 p.1 q.3 nn.3, 8-12, 24]. But the intellect of the first thing can only have an understanding the same as itself, from what was just said [n.98]; therefore it has actual and distinct understanding of any intelligible whatever, and this the same as itself and so always and necessarily.
107. The second part, about priority, is proved thus, that whatever is the same as itself is necessarily existent, as was plain above [n.106]; but the being of things other than itself is not necessarily existent. Necessary existence is of itself prior in nature to everything non-necessary.
108. It is proved in another way, that the existence of anything else depends on the first thing as on a cause and, as a cause is of something causable, knowledge of the causable on the part of the cause is necessarily included; therefore the knowledge will be naturally prior to the very existence of the known thing.
109. The first part of the conclusion is also proved in another way, that a perfect artisan distinctly knows everything to be done before it is done, otherwise he would not operate perfectly, because knowledge is the measure by which he operates; therefore God is in possession of distinct and actual knowledge, or at any rate habitual knowledge, of all things producible by him prior to those things.
110. Against this: there is an instance about art, that universal art suffices for producing universal things [Scotus, Metaphysics I q.5 nn.3-4, VII p.2 q.15 n.1] - Look there for a response [ibid. VII p.2 q.15 n.9]. response [ibid. VII p.2 q.15 n.9].
2. The infinity of God is proved directly
111. Having shown these preliminaries I argue for infinity in four ways.
[First way] - First by way of efficacy, where the intended proposition will be shown in a twofold way: first because it is the first efficient cause of all things, second because the efficient cause, plainly, knows distinctly all make-able things; third, infinity will be shown by way of the end, and fourth by way of eminence.
The first way, on the part of the cause, is touched on by the Philosopher, Physics 8.10.266a10-24, 266b6-20, 267b17-26 and Metaphysics 12.7.1073a3-13, because it moves with an infinite motion; therefore it has an infinite power.
112. This way is confirmed as to the antecedent as follows: the intended proposition is proved just as much whether it can move through an infinity as whether it does move through an infinity, because the existence of it must be actual just as much as the power of it is; the thing is clear of the first thing to the extent it exists of itself [n.58]. Although therefore it may not move with an infinite motion in the way Aristotle understands, yet if that antecedent is taken to be what, for its part, can move, the antecedent is held to be true and equally sufficient for inferring the intended proposition.
113. The consequence [n.111] is proved thus, that if it exists of itself, it does not move with an infinite motion by virtue of another; therefore it does not receive its thus moving from another, but it has in its own active virtue its whole effect all at once, because it has it independently. But what has in its virtue an infinite effect all at once is infinite; therefore etc .
114. The first consequence [n.111] is confirmed in another way thus: the first mover has all at once in its virtue all the effects that can be produced by motion; but those effects are infinite if the motion is infinite; therefore etc .
115. Against these clarifications of Aristotle, whatever may be true of the antecedent, yet the first consequence does not seem well proved.
Not in the first way [n.113], because a greater duration does not add any perfection, for a whiteness that persists for one year is not more perfect than if it persisted for only one day; therefore a motion of however long a duration is not a more perfect effect than the motion of one day. Therefore from the fact that the agent has all at once in its active virtue a moving with an infinite motion, the perfection is not proved to be greater in this case than in that, save that the agent moves for a longer time, and of itself; and so one would need to show that the eternity of the agent would prove its infinity, otherwise it could not be proved from the infinity of its motion. - Then as to the form of the argument: the final proposition of the confirmation [n.113] is denied, save of infinity of duration.94
116. The second confirmation [n.114] of the consequence is also refuted, because a greater intensive perfection is not proved by the fact that any agent of the same species can go on successively producing as much and as long as it lasts, because what has power for one such thing in one stretch of time has power by the same virtue for a thousand such things if it last a thousand stretches of time. And, among philosophers, an infinity is not possible except a numerical one of effects producible by motion (namely of effects that can come to be and pass away), because in species they posited a finitude. Therefore an intensive infinity in an agent no more follows from the fact that it has power for an infinite number of things in succession than if it has power for two things only; for only a numerical infinity is possible according to philosophers. - But if someone prove an infinity of species to be possible, by proving some of the heavenly motions to be incommensurable and so never able to return to the same form, even if they endure an infinite time and even if conjunctions infinite in species cause generable things infinite in species, whatever may in itself be true about this, yet it is nothing to the intention of the philosopher, who denied an infinity of species.
117. The ultimate probability that occurs for making clear the consequence of the Philosopher is as follows: whatever has power for many things at once, each of which requires some perfection proper to itself, is shown by the plurality of such things to be more perfect. Thus it seems one should conclude about the first agent that if it can cause infinite things all at once then its virtue must be infinite, and consequently that if the first agent has all at once the virtue to cause infinite things, then, as far depends on itself, it can produce them all at once; even if the nature of the effect does not permit of this, yet the infinity of the thing’s virtue follows. The proof of this ultimate consequence is that what cannot cause a white and a black thing is not thereby less perfect, because these things are not simultaneously causable; for this non-simultaneity comes from a repugnance in them and not from a defect in the agent.
118. And from this I prove infinity as follows:95 if the first thing had all causality formally at the same time, although the causable things might not be able to be put into being all at once, it would be infinite, because, as far as depends on itself, it could produce infinite things all at once; and having power for several things at once proves a greater power intensively; therefore if it has this power more perfectly than if it had all causality formally, its intensive infinity would follow all the more. But all the causality for anything whatever as to the whole of what exists in reality itself is had by it more eminently than if it was had by it formally.
119. Although, therefore, I believe that omnipotence properly speaking, according to the intention of theologians, is a matter of belief only and cannot be proved by natural reason, as will be said later [I d.42 q. un. nn.2-3; below n.178], nevertheless an infinite potency can be naturally proved that, as far as depends on itself, has all at once of itself all the causality able to produce infinite things, provided these infinite things are capable of being made to be all at once.
120. If you object that the first thing does not of itself have power for infinite things all at once, because it has not been proved to be the total cause of infinite things,96 this objection poses no obstacle, because if it had all at once the source whence it was the total cause, it would be in nothing more perfect than it is now when it has the source whence it is first cause. - Also because the second causes are not required for its perfection in causing, because then a thing more removed from the first cause would be more perfect because it would require a more perfect cause. But if second causes are, according to the philosophers, required together with the first cause, this is because of the imperfection of the effect, so that the first thing along with some imperfect cause might cause an imperfect thing, because according to them it could not cause it immediately. -Also because, according to Aristotle [Metaphysics 5.16.1021b31-32, 12.7.1072b28-34], the totality of perfections is more eminent in the first thing than if their formalities themselves were present in it, supposing they could be present in it; the proof of which is that a second cause proximate to the first cause has the whole of its causative perfection from the first cause alone; therefore the first cause has that whole perfection more eminently than the second cause, which has it formally. The consequence is plain, because the first cause is the total and equivocal cause with respect to the second cause [n.69]. One may ask a similar question of the third cause with respect to the second cause or with respect to the first; if the answer is with respect to the first [sc. that the third has its whole causative perfection from the first cause], the proposition intended is gained; if with respect to the second, it follows that the second contains eminently the total perfection which is formally in the third. But the second has from the first that it thus contains the perfection of the third, from what has just been shown above [n.120]; therefore the first has to contain more eminently the perfection of the third than the second does, and so on in all other cases right up to the last cause. Wherefore that the first cause possesses eminently the whole causative perfection of all the causes, and possesses it more perfectly than if it had the causality of all of them formally, were that possible, seems in my judgment capable of being proved by the argument of Aristotle posited above [n.111] about the infinite substance, which is taken from the Physics and Metaphysics.97
121. According to this way of efficacy there is an argument98 that it has infinite power because it creates, for99 between the extremes in the case of creation [sc. the extremes of creator and created] there is an infinite distance.100 But this antecedent is set down only as something believed [n.119], and it is true that101 not-being would in duration as it were precede being,102 not however in nature as it were, after the way of Avicenna.103 - The antecedent is shown104 by the fact that at least the first nature after God is from him and not from itself, nor does it receive being on the presupposition of anything else; therefore it is created.105 But if one takes being and not-being as in this way prior in nature, then they are in that case not extremes of a change which that virtue would cause, nor does the causing of the effect require a changing.
But whatever may be true of the antecedent, the consequence is not proved, because when there is no distance intermediate between the extremes106 but the extremes are said to be distant precisely by reason of being extremes between each other, then there is as much distance as there is an extreme that is greater. An example: God is infinitely distant from the creature, even than the highest possible creature, not because of any distance between the extremes but because of the infinity of one extreme.
122. It is in this way, then, that contradictories are not distant by anything intermediate, because contradictories are immediate [Aristotle, Posterior Analytics 1.2.72a12-13] - such that however little anything recedes from one extreme it is at once under the other extreme - but they are distant because of the extremes in themselves. Therefore the distance is as great as the extreme which is more perfect; that extreme is infinite; therefore etc .
123. There is a confirmation, that the total power over the positive term of a distance of this sort is power over the distance or the transition from extreme to extreme; therefore, from power over that transition infinity does not follow unless it follows from total power over its positive term. That term is finite.107
124. Now as for what is commonly said, that contradictories are infinitely distant, it can be understood thus, that is, indeterminately, because just as there is no distance so small that it does not suffice for contradictories, so there is no distance so great that, even if it were greater than the greatest possible, it would not stretch itself to the contradictories. Their distance then is infinite, that is, indeterminate to any magnitude, great or small; and therefore from such an infinity of distance the consequent about an infinite power intensively does not follow, just as neither does it follow on the smallest distance in which an infinite distance is thus preserved; and what does not follow on the antecedent does not follow on the consequent either.108
125. [The second way] - Having shown the intended proposition by way of the first efficient power, because the first efficient power involves infinity, the second way follows, from the fact that it distinctly understands all make-able things. Here I argue as follows: the intelligibles are infinite, and that actually, in an intellect that understands everything; therefore the intellect that understands them actually all at once is infinite. Of this sort is the first intellect.
126. Of such an enthymeme I prove the antecedent and the consequent.
As to all things that are infinite in potency, such that in taking one after another no end can be reached, if all these things are actual at once, they are actually infinite; intelligibles are of this sort with respect to a created intellect, as is plain, and in the divine intellect all things are at once understood actually that are understood successively by a created intellect; therefore an infinity of things is in the divine intellect actually understood. Of this sort of syllogism I prove the major (although it seems sufficiently evident), because all such things that can be taken one after another are, when they are simultaneously existent, either actually finite or actually infinite; if they are actually finite, then by taking one after another one can in the end actually take them all; therefore if they cannot all be actually taken, then if such things are actually simultaneous, they are actually infinite.
127. The consequence of the first enthymeme [n.125] I prove thus, that where a plurality requires or involves a greater perfection than a fewness does, there numerical infinity involves infinite perfection. An example: being able to carry ten things requires a greater perfection of virtue than being able to carry five; therefore being able to carry an infinite number of things involves an infinite moving virtue. Therefore, in the proposed case, since to understand a is a perfection and to understand b is similarly a perfection, there is never one and the same understanding of a and b, and with as much distinctness as two understandings would have, unless the perfections of the two understandings are included eminently in that one understanding; and thus about three understandings, and so on about an infinite number.109 Likewise one might also argue about the very idea of understanding what has been argued about intellect and about act, that a greater perfection in an act of understanding is implied from a plurality of things where there is the idea of distinctly understanding them, because this act must include the perfections eminently of all understanding’s proper operations, each of which, according to its proper idea, posits some perfection; therefore infinite operations involve infinite perfection.
128. Second, following on this way about the understanding of the first thing I show the intended proposition thus: a first cause to which, in accord with the utmost of its causality, a second cause adds some perfection in causing, does not seem able on its own to cause as perfect an effect as it can cause along with the second, because the causality of the first cause alone is diminished in respect of the causality of both; therefore if that which is naturally from the second cause and from the first simultaneously is much more perfectly from the first alone, the second cause adds no perfection to the first; but every finite thing adds some perfection to a finite thing; therefore such a first cause is infinite.
129. To the proposed case: the knowledge of a thing is naturally generated by that thing as from the proximate cause, and especially the knowledge which is vision or intuitive understanding; therefore if that knowledge is, without all action of such an object, in any intellect merely by virtue of another prior object which is naturally a superior cause with respect to such knowledge, the result is that that superior object is infinite in knowability, because the inferior object adds nothing in knowability to it; such a superior object is the first nature, because from the mere presence of it in the intellect of the first thing, without any other objection accompanying it, there is in the intellect of the first thing knowledge of any object whatever. Therefore no other intelligible adds anything to it in knowability; therefore it is infinite in knowability. Therefore it is such in its reality, because each thing is related to existence as it is to knowability, from Metaphysics 2.1.993b30-31.
130. [Third way] - Again in the third way, namely on the part of the end [n.111], the argument is as follows: our will can desire and love, as the intellect can understand, some other thing greater than any finite thing; and it seems that the inclination to loving an infinite good supremely is more natural, for a natural inclination in the will to something is argued from this, that free will of itself, without a habit, promptly and with delight wants it; thus it seems that we experience an infinite good in an act of loving it, nay it seems that the will does not perfectly rest in some other thing. And how would it not naturally hate that other thing if it were the opposite of its object, just as it hates not-being (according to Augustine On Free Choice of the Will 3 ch.6 n.18, ch.8 n.23)? It also seems that, if the infinite were repugnant to good, the will would, under the idea of the infinite, in no way rest in good, nor would it easily tend to good, just as neither to what is repugnant to its object. This reason will be confirmed in the next way [n.136], about the intellect.
131. [The fourth way] - Again, fourth, the intended proposition is shown by way of eminence [n.111], and I argue thus: it is incompossible with the most eminent thing that something else be more perfect, as was plain before [n.67]; but with a finite thing it is not incompossible that there be something more perfect; wherefore etc .
132. The proof of the minor is that an infinite thing is not repugnant to real being; but the infinite is greater than everything finite. There is another way of arguing for this and it is the same: that to which it is not repugnant to be intensively infinite is not supremely perfect unless it is infinite, because if it is finite it can be exceeded or excelled, because to be infinite is not repugnant to it; to real being infinity is not repugnant; therefore the most perfect real being is infinite. The minor here, which is taken up in the preceding argument, does not seem capable of being shown a priori, because as contradictories contradict by their proper ideas and as this fact cannot be proved by anything more manifest, so non-repugnant things are non-repugnant by their proper ideas and it does not seem possible for this to be shown save by explaining their ideas. Real being is not explained by anything more known, the infinite we understand through the finite (I explain this vulgarly thus: the infinite is that which no given finite thing exceeds precisely by any finite relation, but beyond any such assignable relation there is still excess).
133. Thus, however, may the intended proposition be proved: just as anything whose impossibility is not apparent is to be set down as possible, so also is that whose incompossibility is not apparent to be set down as compossible; here no incompossibility is apparent, because finitude is not in the idea of real being, nor does it appear from the idea of real being that finitude is a property convertible with real being. One or other of these is required for the aforesaid repugnance; for the properties that belong to the first real being, and are convertible with it, seem to be sufficiently known to be present in it.
134. Again there is proof thus: the infinite is not in its mode repugnant to quantity, that is, by taking part after part; therefore neither is the infinite in its mode repugnant to real being, that is, by being in perfection all at once.
135. Again, if quantity of virtue is simply more perfect than quantity of bulk, why will an infinite be possible in bulk and not in virtue? But if it is possible it is actual, as is plain from the third conclusion above, about effective primacy [n.58], and it will also be proved below [n.138].
136. Again, because the intellect, whose object is real being, finds no repugnance in understanding something infinite, nay rather the infinite seems to be the most perfect intelligible. Now it is remarkable if to no intellect a contradiction of this sort about its first object is made plain although discord in sound so easily offends the hearing; for if the discordant offends as soon as it is perceived, why does no intellect naturally flee from an intelligible infinite as from something not concordant that thus destroys its first object?
137. Hereby can be colored the reasoning of Anselm about the highest thinkable good in the Proslogion, [nn.11, 35] and his description must be understood in this way:110
God is that than which, when known without contradiction, a greater cannot be thought without contradiction. And the fact that ‘without contradiction’ must be added is plain, for a thing in the knowing or thinking of which contradiction is included is said not to be thinkable, because in that case there are two opposed thinkables with no way of producing a single thinkable thing, because neither determines the other.111
138. The aforesaid highest thinkable without contradiction can exist in reality. This is proved first about quidditative being, because in such a thinkable the intellect supremely rests; therefore in that thinkable is the idea of the first object of the intellect, namely the idea of real being, and this in the highest degree. - And then the argument further is made that it exists, speaking of the being of existence: the supremely thinkable is not in the thinking intellect only, because then it would both be able to exist, because it is a possible thinkable, and not be able to exist, because existing by some cause is repugnant to its idea,112 as was clear before in the second conclusion [n.57] about the way of efficacy; therefore what exists in reality is a greater thinkable than what exists in the intellect only. But this is not to be so understood that the same thing, if it is thought on, is thereby a greater thinkable if it exists, but rather that something which exists is greater than anything which is in the intellect only.
139. Or it [Anselm’s reasoning] is colored in another way thus: what exists is a greater thinkable; that is, it is more perfectly thinkable because visible or intelligible to intuitive intellection; when it does not exist, whether in itself or in something nobler to which it adds nothing, it is not visible. But what is visible is more perfectly thinkable than what is not visible but intelligible only in the abstract; therefore the most perfect thinkable exists. - The difference between intuitive and abstract intellection, and how the intuitive is more perfect, will be touched on later [I d.3 p.1 q.1-2 nn.29, 11, 18-19; q.3 nn.24, 10, 28], and elsewhere when there will be place for it [e.g. n.394 below, d.1 n.35 above].
140. Finally the intended proposition is shown from negation of an extrinsic cause, because113 form is limited, or made finite, through matter;114 therefore what is not of a nature to be in matter is infinite.115,116
141. This reasoning is not valid, because according to them an angel is immaterial; therefore it is in nature infinite. - Nor can they say that the existence of an angel limits its essence, because according to them existence is an accident of essence and naturally posterior; and thus in the first moment of nature the essence in itself, as prior to existence, seems to be intensively infinite, and consequently it will, in the second moment of nature, not be limitable by existence.
142. I respond briefly to the argument, for any real being has intrinsic to it its own grade of perfection, in which grade it is finite if it is finite and infinite if it can be infinite, and not by anything accidental to it.
143. There is also an argument ‘if form is limited in relation to matter, then if it is not in relation to matter it is not limited’; it is the fallacy of the consequent,117 just like ‘body is limited in relation to body, therefore if it is not in relation to body it will be infinite’; ‘therefore the furthest heaven will be actually infinite’. The sophism is the one in Physics 3.4.203b20-22, that just as body is limited first in itself,118 so a finite form is finite first in itself before it is limited in relation to matter, because of such a sort is nature in real beings, that it is limited, that is, before it is united to matter, for a second finitude presupposes a first and does not cause it. Therefore in some moment of nature it will be finite in essence, therefore not made finite by existence; therefore it is not, in a second moment, made finite by existence.
144. I assert briefly one proposition, that any absolute essence finite in itself is finite as pre-understood to every comparison of itself to another essence.
145. [Epilogue] - From what has been said the solution to the question is plain. For from the first article [nn.41-73] one gets that some existent real being is simply first with a triple primacy, namely of efficacy, of end, and of eminence [nn.42-58, 60-61, 6466], and so it is simply that which is incompossible with something else being first [nn.59, 63, 67]. And in this article existence is proved of God as to the properties of God in respect of creatures, or insofar as he determines the dependence of respect of creatures on himself [n.39].
146. From the second article [nn.74-144] one gets in a fourfold way that the first thing is infinite: namely first because it is the first efficient thing [nn.111-120], second because it is the first knower of all make-able things (the second way [nn.125-127] contains119 four conclusions about the intelligibility of the first thing [nn.75-110]), third because it is the ultimate end [n.130], fourth because it is eminent [n.131-136]. By occasion of the first way there is excluded a certain useless way about creation [nn.121-
124], by occasion of the second another way is touched on about the perfection and intelligibility of the first object [nn.128-129], by occasion of the fourth exposition is given of the argument of Anselm in Proslogion, ‘God is that than which a greater cannot be thought’ [nn.137-139, 11, 35]; lastly there is excluded a useless way inferring infinity from immateriality [nn.140-144].
147. From the premised conclusions, proved and shown, the argument to the question120 goes as follows: some real being triply first among beings actually exists [nn.41-73, 145]; and that triply first thing is infinite [nn.111-141, 146]; therefore some infinite real being actually exists [n.1]. And it is the most perfect conceivable, and the most perfect, absolute conceived, that we can naturally have about God, that he is infinite, as will be said later [I d.3 p.1 qq.1-2 n.17].
And thus it has been proved that God exists as to his concept or existence, the most perfect conceivable or possible to be had by us of God.