Ordinatio

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 it, to wit the efficient cause, knows distinctly all make-able things. Third, infinity will be shown by way of 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.

This reason is strengthened as to the antecedent as follows: the intended proposition is proved just as much if it can move through the infinite as if it were to move through the infinite, because it must be as equally in act as its power is; the thing is clear of the first thing to the extent it exists of itself [n.58]. Although therefore it not move with an infinite motion in the way Aristotle understands, yet if this antecedent be taken that, as far as it is of itself, it can move, a true antecedent is had and one equally sufficient for inferring the intended proposition.

The consequence [n.111] is proved thus, because if it is of itself, it moves with an infinite motion not by virtue of another; therefore it does not receive its moving thus 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.

The first consequence [n.111] is strengthened in another way as follows: 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.

Against these declarations 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 adds nothing of 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, a greater perfection is not proved here than in there, 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.¹

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 producing successively as many times as long as it lasts, because what has power for one such thing in one time has power by the same virtue for a thousand such things if it last a thousand times. And, among philosophers, an infinity is not possible save a numerical one of effects producible by motion (namely of things 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 a infinity of species possible, by proving some of the heavenly motions to be incommensurable and so never able to return to uniformity, even if they were to endure an infinite time and even if conjunctions infinite in species were to cause generable things infinite in species, whatever may be about this in itself, yet it is nothing to the intention of the philosopher, who denied an infinity of species.

The last probability that occurs for making clear the consequence of the Philosopher is this: whatever has power for some many things at once, any one 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 could cause infinite things all at once, that its virtue would 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 could produce them all at once; although the nature of the effect does not permit it, yet the infinity of the thing’s virtue follows. The proof of this ultimate consequence is because what cannot cause a white and a black thing is not less perfect, because they are not simultaneously causable; for this non-simultaneity comes from a repugnance in them and not from a defect in the agent.

And from this I prove infinity as follows:² if the first thing had all causality formally at the same time, although the causable things could not 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 follows all the more. But it does have all the causality of anything whatever as to the whole of what exists in reality itself more eminently than if it existed formally.

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 in I d.42 [q. un. nn.2-3; below n.178], nevertheless an infinite potency can be naturally proved that at once, as far as depends on itself, has all the causality that would be at once capable of infinite things, if they were makeable at once.

If you object, 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,³ this puts nothing in the way, because if it had all at once that whereby it was the total cause, it would be nothing more perfect than it is now when it has that whereby it is first cause. – Also because the second causes are not required because of perfection in causing, because then what is 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 coulc cause an imperfect thing, which according to them it could not cause 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, if they could be present in it; the proof of which is because 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 that 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 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.⁴

According to this way of efficacy there is an argument⁵ that it has infinite power because it creates, for⁶ between the extremes in the case of creation [sc. the extremes of creator and created] there is an infinite distance.⁷ But this antecedent is set down only as something believed [n.119], and it is true that⁸ not-being would in duration as it were precede being,⁹ not however in nature as it were, after the way of Avicenna.¹⁰ – The antecedent is shown¹¹ 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.¹² 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 its being effected require its being changed. But whatever be true of the antecedent, the consequence is not proved, because when there is no distance intermediate between the extremes¹³ 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 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.

It is in this way, then, that contradictories are not separate by any intermediates, because contradictories are immediate [Aristotle, Posterior Analytics 1.2.72a12-13] – such that however little something recedes from one extreme it is at once under the other extreme – but they are distant because of the extremes in themselves. Therefore this distance is as great as the extreme which is more perfect; it is finite;¹⁴ therefore etc.

There is a confirmation, because 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 this transition infinity does not follow unless it follow from total power over its positive term. That term is finite.¹⁵

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 extend itself to the contradictories. Their distance then is infinite, that is, indeterminate as to any distance, 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.¹⁶

[The second way] – Having shown the intended proposition by way of the first efficient cause because the first efficient cause implies infinity, the second way follows, from the fact that it distinctly understands all make-able things. Here I argue as follows: intelligibles are infinite, and this actually, in an intellect that understands everything; therefore the intellect that understands them actually all at once is infinite. Of this sort is the intellect of the first thing.

Of this sort of 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 those 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.

The consequence of the first enthymeme [n.125] I prove thus, because where plurality requires or implies a greater perfection than fewness does, there a numerical infinite implies infinite perfection. An example: being able to carry ten things requires a greater perfection of moving virtue than being able to carry five; therefore being able to carry an infinite number of things implies an infinite moving virtue. Therefore, in the matter at hand, since to understand a is a perfection and to understand b is similarly a perfection, never is there the same understanding of the a and b and equally distinctly as two understandings would be, unless the perfections of the two understandings are included eminently in the one, and so on about three understandings, and further about an infinite number.¹⁷ It might also be argued in a like way about the idea itself of understanding as has been argued about the intellect and act, because a greater perfection in an act of understanding is inferred from the plurality of the things of which there is an idea of understanding them distinctly, because it is necessary that it include eminently the perfections of all the proper operations of understanding, each of which, according to its proper idea, posits some perfection; therefore infinite operations imply infinite perfection.

Second, following on this way about the understanding of the first thing I show the thing proposed thus: a first cause to which, in accord with the utmost of its causality, a second cause adds something of 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 lessened in respect of the causality of both; therefore if that which is naturally from the second cause and from the first together be much more perfectly from the first alone, the second cause adds nothing of perfection to the first; but every finite thing adds some perfection to a finite thing; therefore such first cause is infinite.

To the matter at hand: 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 in any intellect, without any action of such an object, merely by virtue of another prior object which is of a nature to be a superior cause with respect to such knowledge, the result is that that superior object is infinite in knowability, because an 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. Thus therefore is it in entity, because as each thing is related to existence so is it to knowability, from Metaphysics 2.1.993b30-31.

[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 thence is argued a natural inclination in the will to something, because free will of itself, without a habit, promptly and with delight wants it; thus does it seem that we experience an infinite good in an act of loving, nay it does not seem that the will perfectly rests in anything else. And how would it not naturally hate that thing if it were the opposite of its object, just as it naturally 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 it, just as neither to what is repugnant to its object. This reason will be confirmed in the next way [n.136], about the intellect.

[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 is plain before [n.67]; but it is not incompossible to a finite thing that there be something more perfect; wherefore etc.

The proof of the minor is because an infinite thing is not repugnant to 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 being infinity is not repugnant; therefore the most perfect being is infinite. The minor here, which is accepted 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. Being is not explained by anything more known, the infinite we understand through the finite (I explain this in vulgar manner thus: the infinite is that which no given finite thing exceeds precisely by any finite relation, but it exceeds still any such assignable relation).

In this way, however, is the intended proposition proved: just as anything whose impossibility is not apparent must be posited as possible, so also must that whose incompossibility is not apparent be set down as compossible; here no incompossibility is apparent, because finitude is not of the idea of being, nor does it appear from the idea of being that finitude is a property convertible with being. One or other of these is required for the aforesaid repugnance; for the properties that belong to the first being, and are convertible with it, seem sufficiently known to be present in it.

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 being, that is, by existing in perfection all at once.

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].

Again, because the intellect, whose object is being, finds no repugnance in understanding something infinite, rather the infinite seems to be the most perfect intelligible. Now it is remarkable if to no intellect is a contradiction of this sort about its first object made plain although discord in sound so easily offends hearing; for if the disagreeable offends as soon as it is perceived, why does no intellect naturally flee from an intelligible infinite as from something not agreeable that thus destroys its first object?

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:¹⁸ 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.¹⁹

The aforesaid highest thinkable without contradiction can exist in reality. This is proved first about quidditative being, because in such a thinkable supremely the intellect rests; therefore in that thinkable is the idea of the first object of the intellect, namely the idea of being, and this in the highest degree. – And then the further argument is made that it exists, speaking of the being of existence: the supremely thinkable is not in the thinking intellect only, because then it could exist (because it is a possible thinkable) and could not exist (because existing by some cause is repugnant to its idea),²⁰ 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 exist, but rather that anything which exists is greater than everything which is in the intellect only.

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].

Finally the intended proposition is shown from negation of an extrinsic cause, because²¹ form is limited [or: made finite] through matter;²² therefore what is not of a nature to be in matter is infinite.^{23 24}

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.

I respond briefly to the argument, for any being has intrinsic to it a grade of its own perfection, in which grade it is finite if it is finite and in which it is infinite if it can be infinite, and not by any accident to it.

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,²⁵ 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,²⁶ 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 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.

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.

[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 being is simply first with a triple primacy, namely of efficacy, of end, and of eminence [nn.42-58, 60-61, 64-66], and so simply that it is incompossible that there is something prior [nn.59, 63, 67]. And herein is existence proved of God as to the properties of God in respect of creatures, or insofar as he determines the dependence of the relation of creatures to himself [n.39].

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] contains²⁷ 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]. According to the first way there is excluded a certain useless way about creation [nn.121-124], according to the second another way is touched on about the perfection and intelligibility of the first object [nn.128-129], according to 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].

From the premised conclusions, proved and shown, the argument to the question²⁸ goes as follows: some being triply first among beings exists in act [nn.41-73, 145]; and that triply first thing is infinite [nn.111-141, 146]; therefore some infinite real being exists in act [n.1]. And it is the most perfect conceivable, and the most perfect, absolute concept that we can naturally have about God, that he is infinite, as will be said in I d.3 [p.1 qq.1-2 n.17]. And thus it has been proved that God exists as to the concept or existence of him, the most perfect conceivable or possible to be had by us of God.