Commentaria in Primam Partem Summae Theologiae

In the title, according to any multitude whatsoever, whether of the genus of quantity or outside the genus. And from this it is clear that this question is higher and more universal than the inquiry made in III Physics¹: for there the discussion concerns only material multitude, following upon the division of the continuum; here, however, the discussion concerns multitude universally, whether material or immaterial.

II. In the body there are two parts: first, he reports the opinion of Avicenna and Algazel; second, by refuting it, he answers the question².

III. As to the first point, he sets out two propositions and explains them. The one is: it is impossible for an actually infinite multitude to exist per se. The other: it is possible for an actually infinite multitude to exist per accidens. Both are explained once their terms are made clear, namely an infinite multitude per se and an infinite multitude per accidens. They are proved as follows: because the work would never be completed if it depended on infinites per se; but not so per accidens, as is clear from the example of the letter.

IV. As to the second point, there are two conclusions answering the question, according to the diversity of act in relation to potency. The first is: It is impossible for there to be an actually infinite multitude, whether per se or per accidens. The second is: It is possible for there to be an infinite multitude in potency³.

The first conclusion is proved in two ways⁴. Every multitude actually existing is in some species of multitude: therefore it exists according to some species of number: therefore it is finite. – The antecedent is evident. The first consequence is proved: because the species of multitude are according to the species of numbers. The second: because number is a multitude measured by one.

V. Concerning the first consequence and its proof, a doubt is raised. For multitude is something more common than number, and consequently it ought to have more species than number: otherwise it would not retain the character of the more common. Therefore the species of multitude are not according to the species of number. – And this is confirmed as follows: for it can be said that the species of finite multitude are according to the species of number; but not the species of multitude absolutely. – And Aristotle attests to this in Book V Metaphysics, in the chapter on Quantity⁵, saying that finite plurality is number: as though he were excepting infinity.

VI. To this it is briefly answered that, since we naturally come to know what is unknown through what is better known, and since we experience that all the species of multitude that we know are proportional to the species of number, it is sufficiently in accord with the art that a universal proposition can be formed, namely, that every species of multitude is according to some species of number.

To the objection, however, it is said that it is one thing that all the species of multitude are species of number, which is false; and another, that all the species of multitude are according to the species of number, that is, proportional to them, which is what was assumed, and is true. Hence multitude, because it is something more universal, has far more species than number: for it has all the species of number, and all the species of immaterial multitude, which is not properly number, etc. – And by this the answer to the confirmation is clear, namely that this would be said willingly, not rationally. – The text of Aristotle, moreover, is no obstacle. Since nothing from it can be drawn for the purpose at hand except that an infinite plurality would not be a number: but this does not stand in the way of this argument, but rather confirms the second consequence, as is evident.

VII. Secondly, the same conclusion is proved⁶. Every multitude actually existing in the nature of things is created; therefore it is comprehended under some definite intention of the Creator; therefore under a definite number. Therefore it is impossible that it be infinite. – The antecedent is evident. The first consequence, however, is proved: because an agent acting not in vain accomplishes something. The remaining consequences are left as evident.

VIII. Concerning this argument a doubt is raised: for it either assumes something false, or it does not infer what is intended. For when it is assumed that every creature is comprehended under some definite intention of the Creator, this is understood either of a definite intention with respect to the certainty of the end; or with respect to the certainty of the means by which the end is attained.

If with certainty of an end, then it can be expounded in two ways: either so that the created thing itself is a certain end; or so that it has a certain end. If therefore the sense is that every created thing is comprehended under some intention of the creator as a certain end, the proposition seems manifestly false: since something created is neither the end of the creator, nor of any other creature, for instance the lowest creature. – If however the sense is that every created thing is comprehended under some intention of the creator as ordered to a certain end, the proposition is most true: because God himself, and the participation in his goodness, is the certain end of every created thing intended by the creator. But then nothing follows for the purpose: for from this it does not follow, therefore under a certain number.

But if the sense is that every created thing is comprehended under some intention of the creator, as a certain means through which the end is acquired, the proposition seems false and unproven. False indeed: because it can be comprehended under the intention of the creator in another way than this. For it can be intended not as a certain means for acquiring the end, but as accompanying or proceeding from a certain means through which the end is acquired: as is clear from Averroes, XII Metaphysics, commentary 37, where he holds that the intelligences move the spheres so as to be assimilated to God by emanating beings; and from this it follows that infinite circulations are caused by them and infinite effects, and infinite souls created, according to Avicenna. – Unproven, however: because from that means, no agent acts anything in vain, nothing else can be inferred except, therefore it acts on account of an end; which granted, it would be said that an infinite multitude is on account of an extrinsic end, namely God and the perpetual preservation of the assimilation causing it to God, as the philosophers say.

IX. Concerning the same point again, a doubt arises: because in it there seems to be committed the fallacy of the divided sense taken as composite, proceeding from any created thing to many, indeed to infinitely many, things collectively. For although any created thing whatsoever is the terminus of some definite intention and operation of the creator himself, nevertheless it does not follow that many created things must be the terminus of one intention and operation, but rather of many intentions and creations. And consequently infinitely many created things will be the termini of infinitely many intentions, just as of creations.

X. Concerning the same point, a doubt still remains: because the root of it—namely, that every created thing is comprehended under some definite intention of the creator—although true of creatures per se, would nevertheless be denied by Avicenna with respect to creatures per accidens. For an accidental infinity is intended only accidentally, as the text says; and consequently it is created only accidentally. Now a thing is called created per accidens when it must be created for the preparation of another thing, as happens with the intellectual soul, which, once nature has prepared a suitably disposed body, is always created. And since infinitely many bodies have already been prepared, infinitely many souls have been created; and these souls, as such, have happened to remain in act, because they are incorruptible. Thus their infinity is not posited as intended per se, but follows upon the eternity of human generation.

XI. For the clarification of this process⁷, note first that created can be taken properly, as distinguished against caused: and it can be taken commonly, so that it makes no difference to say caused or created. That it is taken commonly, the universal proof of the text indicates, when for its proof it assumed that an agent does not act in vain. But that it is taken properly, the very formal signification of the word shows. - Now it matters little or nothing in which way it is taken. For if it is taken properly, the words of the proof must be weighed when he says something acts, that is, attains the proper term of its operation. And by this are excluded all things consequent upon the proper and intended work of the agent: and of every created being it is verified that it is the proper term of creation. But if it is taken commonly, what is caused must be restricted to what is properly caused, as distinguished against what is consequent upon causation.

Truth, in either way, is restricted to caused things or to created things actually existing, so that collapsed things are excluded. And this is hinted at in the text, where it says of the creator's. For what has been created and perseveres is, in a certain way, continuously being created, because it is preserved: for it depends both in its coming-to-be and in its being (esse) on the creator. - But what falls under the creator's intention includes not only what is actually comprehended, but also what is comprehensible, even if it were not actually comprehended.

XII. But from the fact that the proposition assumed concerns only things existing in act, which are the proper terms of action, the solution of all objections is had.⁸ For all things existing in act the Creator can order both as a means toward the acquisition of some end, and intend as an end to be attained through something else. Since, indeed, it is posited to exist in act, its production is already posited as terminated; and consequently it can be directed as a means toward acquiring something; and likewise it could have been an end intended and acquired through some means; nor does the ratio of end, or the ratio of means to an end, conflict with that which exists in act. And therefore, since intention properly belongs only to an end and to the means through which the end is to be acquired, everything existing in act is comprehensible under a certain intention of the creator, both as end and as means. As end, indeed: both because there is no creature so lowly that it is not, or cannot be, the end of something else; and because at least it is a certain end of its own production; and because this is understood insofar as it is from itself: for nothing repugnant to the ratio of end belongs, insofar as it is from itself, to any created thing existing in act, although perhaps something may be the end of nothing. As means, however: because after it there remain many productions and noble perfections of many things, to one of which it can be ordered as a means, being already ens in actu.

Nor does the first objection against this member stand in the way. For, as is already clear from what has been said⁹, speaking formally of the created, it cannot be a proper consequent of the term of creation; rather, the created must terminate the creation. Now such a created thing must be intended either as an end or as a means to an end. — Nor is it true that this has not been proven. For from that assumed proposition, an agent does nothing in vain, the term of the interior intention is most fittingly concluded from the end of the exterior operation. For since the operation of no agent is in vain, but directed to a certain proper end, the intention of the one operating must also be with respect to a certain end: for the intention of the agent establishes the end of the operation. — And thus the response to the first objections is clear.

XIII. To the second doubt, however¹⁰, it is said that, since the whole multitude of beings in act can be taken as one created thing—because it does not exceed the universe, which has the character of a single first created object of thought—it follows that not only individual created things, but all things together, insofar as they coexist in act, are comprehensible under some one definite intention of the Creator. And therefore no sophism is committed in the matter at hand, where from the opponent's proposition that an infinite multitude exists in act there is inferred: therefore it is comprehensible under a definite intention of the Creator, therefore it is not infinite; for the infinity of a multitude is repugnant both by reason of the means for attaining the end and by reason of the end itself.

XIV. To the third doubt¹¹, it is said that what is created per accidens can be understood in two ways. In one way, as per accidens is distinguished from per se. And in this way, it is denied that anything is created per accidens: since every created thing is intended by the Creator in itself, just as it is also in itself the terminus of creation; otherwise it would not come to be from nothing. In another way, as per accidens is distinguished from per se primo, and signifies the same as through another. And in this way something is said to be created per accidens, that is, through another, at least occasionally. And in this way intellectual souls are created per accidens, both according to our opponent and according to us: though more per accidens with us than with him. But this does not prevent them from being individually intended in themselves, just as they are created in themselves. For although they have an order among themselves that is per accidens, yet when related to the Creator, they are both intended and produced in themselves: indeed, more per se than any corruptible thing whatsoever; for incorruptible things are more perfect and worthier parts of the universe, and on this account are more intended. A sign of this is that in the sphere of active things, only the species are intended per se, because they alone are perpetual. And since not only individual things, but infinitely many are posited together in act, it follows, as was said¹², that all are intended and produced per se, inasmuch as they are comprehensible under some one definite intention; indeed, even producible together in act, as far as lies in themselves.

XV. Note here that from this passage it follows that St. Thomas has removed for himself every path of reconciliation with the doctrine of Aristotle, according to his exposition. For he holds that Aristotle believed the intellective souls to be immortal, and numbered according to the number of bodies: and it is established that Aristotle held the world to be eternally generated. From these things, however, it manifestly follows that human souls are actually infinite: which is here judged impossible, and in II Cont. Gent., chap. LXXXI, it is said not to conflict with the doctrine of Aristotle in III Physic.¹³ and I Caeli¹⁴, because in both places the discussion was of the material infinite.

XVI. Concerning this conclusion¹⁵, many arguments are brought forward by Capreolus¹⁶ from Gregory and Adam: but all are reducible to three. First, then, he argues as follows. There are given infinitely many proportional parts in act in a continuum: therefore they can be given as separated. Ergo. — The inference is proved: because every absolute being (ens) that exists can be conserved by the divine power without that which is not of its essence; but the continuation of one with another is not of the essence of the parts; ergo.

Second, God, at any beginning of any proportional part of one hour, can create an angel; therefore in one hour he can create infinitely many angels in act. — And this is confirmed: because whatever God can do successively he can do simultaneously, in the case of permanent things.

Third, God is of no lesser power than infinitely many souls, if they existed, and than the fire of hell. But those souls could suffer infinite torments all at once, and the fire could inflict infinite torments, if there were infinitely many souls there. Therefore.

XVII. To the first two arguments the reply is brief: there is a fallacy of moving from the divided sense to the composite. For although continuity with another part does not belong to the essence of each single part, it nevertheless belongs to the essence of all of them together: because it belongs to their essence, taken together, that they be in potency, which is repugnant to the separation of each from the others. — And likewise it involves numbering the beginnings of all the proportional parts of an hour: for by that successive enumeration they are posited as completed at the end of the hour, and yet infinite. For if they are infinite, they will never be numbered; and if they are completed, they will not be infinite. God can therefore act in each of the beginnings, but not in all of them. — And by this the confirmation is answered: for neither simultaneously nor successively can He produce infinitely many things actually existing.

To the third, however: even granting the whole, nothing is obtained against the intended point. For it is not from a defect of divine power, but from the impossibility of the thing to be made, that there arises the fact that things cannot be infinite in act. Yet with this it stands that those conditionals are true: just as, if man is a lion, he is capable of roaring; nevertheless it does not follow, therefore God can make a man capable of roaring.

XVIII. The second conclusion¹⁷ is responsive: The infinite according to multitude is found in potency. — It is proved. The infinite is found in potency according to the division of the continuum; therefore also according to multitude. — The inference is proved: because an increase in multitude follows upon the division of magnitude. The antecedent is evident, and it is proved, because one proceeds to matter.