Scholastica commentaria in Primam Partem Summae Theologicae

SUMMARY OF THE ARTICLE.

FIRST conclusion: It is impossible that there be an infinite in act according to multitude, neither through itself, nor through an accident.

Second conclusion: An infinite in potency, according to multitude, is given in things. The reason is: because the increase of multitude follows upon the division of the continuum, which proceeds to infinity.

COMMENTARY.

IT IS DOUBTED concerning these three articles, whether in natural things, or according to the supernatural power of God, there can be given an infinite in act, or an infinite simply, whether according to the substance of the thing, or according to continuous or discrete quantity, or even according to the multitude of spirits. And indeed the common opinion is negative. Which St. Thomas holds in the articles, and in Quodl. 9, art. 1; Durandus and St. Bonaventure in 1 Sent., d. 43, q. 2; Scotus, d. 2, q. 3, Marsilius q. 42. But the opposite opinion, as to multitude and magnitude, is held by Ockham in 2, q. 8, in the answer to the second reason; and Gregory in 1, at 43; Gabriel, however, in 2, dist. 1, q. 3, reckons each opinion to be probable. But that the teaching of St. Thomas may be explained, argument is made in many ways for the affirmative side.

First, God by a single act knows distinctly the infinite species of possible angels; therefore he can will them to be. The antecedent is granted by all. The consequence is proved: because the divine will can will at once all things which the divine intellect at once knows to be feasible through its power: but from the divine will proceeds the existence of things; therefore there could at once be infinite species of things, nay rather something infinite according to essence: namely, the highest created angel, who would exceed the rest to infinity.

Second, the grace of union of the Word to the humanity was made by God: but it is simply infinite in act; therefore an infinite in act is given. The major is proved, because the grace of union is not from eternity. The minor is proved, because the humanity is raised through the grace of union to the personal to-be of the Word of God, which is infinite in act. It is confirmed: the merit of Christ is asserted by all theologians to be infinite: but it is not infinite in potency only, therefore it is in act. The minor is proved: because in fact he merited condignly, to the equality of justice, the remission of all sins; therefore.

Third. God knows infinite distinct equal parts, existing in the continuum, and not sharing in one another; therefore he will be able to separate them really, and then there will be given an infinite in act, according to multitude. The antecedent is proved: because not all the equal parts are finite; for if they are finite, let it be designated how many there are, e.g. a thousand: then each part will be able to be divided into two equal parts, and then there will be twice a thousand; and so consequently never will so many equal parts be assigned, but that there are more existing in the continuum.

Fourth. Continuous quantity follows matter; but matter of itself is infinite; therefore there can be given an infinite quantity according to magnitude, at least in potency, which is against St. Thomas in art. 3, at the third.

Fifth. Between substance, as it is the most general genus, and man, as he is the atomic species, there are infinite degrees of perfection; but man is more perfect than all of them: therefore he is infinitely perfect. The antecedent is proved: for God can produce infinite species between man and corporeal substance.

Sixth. God could have created the world from eternity, and on each day, or each year, create one angel, or one soul: therefore now there would be infinite angels, and consequently there could be an infinite according to multitude. The consequence is plain: because angels and souls are immortal.

Seventh. If infinite combustibles were applied to the same fire, it would produce infinite heats, indeed it would be increased to infinity; therefore neither is it determined as to its mode of acting, nor as to power, but it has it infinite. The consequence is proved: because through the application, nothing of power accrues to the fire itself.

Eighth. If God acted from necessity of nature, he would produce an infinite effect, since he would act according to the utmost of his power, which is infinite: therefore, even though he acts freely, he will be able to produce an infinite effect. The consequence is proved: because God is not of lesser power from the fact that he is a free agent, than if he were an agent from necessity of nature. It is confirmed: whatever does not imply contradiction, God can do; but that there be an infinite multitude of things, or an infinite magnitude, does not imply contradiction; therefore. The minor is proved: because the reasons of St. Thomas are of all the best, and they are not demonstrative.

For the decision of this question note that God can be considered in two ways with respect to those things which he is said to be able, or not able, to do. In one way, insofar as he can operate through infinite power, abstracting from the order of the divine Wisdom and Goodness, which order is taken from the intended end. In another way he can be considered, insofar as he can operate not only powerfully, but wisely and perfectly. If he be considered in the first way, God can do many things which do not befit the order of the Wisdom and Goodness of God; e.g. he could have produced a world without any intellectual creature, which operation nevertheless would not seem to befit the divine Wisdom: since the divine Power and Goodness would be manifested to no one. Likewise he could have founded the souls of men without powers. In the second way, however, all things which God does, it is necessary that they be done according to the order of the divine Wisdom and Goodness, with respect to the manifestation of his glory. From this it follows that the impossible can also be taken in two ways. In one way, as it is opposed to the possible through the absolute power of God in the prior way: and so, that alone is said to be impossible which implies contradiction, and consequently is outside the nature of being, and outside the nature of the word, that is, of the spiritual conception, since the intellect cannot conceive two contradictories as true at once, as Aristotle says in 4 Metaph. And so is to be understood that Luke 1: "No word shall be impossible with God"; that is, everything which falls under the concept of the mind. In another way that is said to be impossible which, although it does not imply contradiction if considered according to itself, nevertheless does not befit the order of the divine Wisdom and Goodness, according to which order it is necessary that all things be done in measure and weight.

THESE things supposed, let the first conclusion be: It most manifestly implies contradiction that something be made or created, and be infinite according to essence. This St. Thomas demonstrates here, art. 2, at the first.

Second conclusion: It is impossible, at least according to the order of the divine Wisdom, that an infinite according to magnitude or multitude be made. It is proved: because the order of the divine Wisdom demands that created things have among themselves some order and proportion: but such an infinite would have in itself no order, for it would be as it were a Chaos and a certain confusion of infinite things and of infinite magnitude; therefore. It is confirmed: because every order of things is reduced to unity and proportion, but in the infinite there would be no proportion, nor a unity to which the infinite would be reduced. For neither would it be double to its half, nor would it have any other proportion.

Third conclusion: The reasons of St. Thomas in art. 3 and 4 prove absolutely that it is impossible that there be given an infinite according to magnitude, or multitude, in act. And besides it is proved: because the opposite is simply unintelligible. Concerning which matter see Soto, q. ult., 3 Physic., where he recounts very many unfitting consequences which would follow from the positing of the infinite. The whole difficulty, therefore, is in the solution of the arguments to the opposite.

TO the first, I deny the consequence; and to the proof it is said that the act of the divine will cannot be borne to the whole collection of possible things, so as to will it to be. The reason of which is, because although the intellect understands them by naturally understanding the divine Essence, yet that understanding communicates nothing to the possible things understood and existing only in the power of the infinite cause. But the act of the divine will is the free cause of the existence of things unto the outside. Whence it is never directed to the whole collection of things understood in the divine Essence, otherwise the omnipotence of God would be exhausted, nor could he further create one angel.

To the second it is answered from St. Thomas in 3 p., q. 7, artic. 11, that the grace of union is infinite according as the person of the Word is infinite. And note that the divine Word itself was the greatest good granted to the human nature, that it be to it the person terminating the dependence of the humanity as to its being supposited. Moreover that the grace of union is said to be made, posits no change in the gift itself which is the divine Word, but in the humanity which was assumed that it be united; for in this mode of speaking we say, God is made a refuge to us, and a column becomes my right hand, without change of himself through my change. Whence to the argument in form it is said that that consequence is worth nothing: God makes in time the grace of union, therefore he made an infinite: but it only follows that what before was infinite, he made the grace of union, that is, the gift to which the human nature would be united. But concerning the habitual grace of Christ, in what way it is infinite, this is not the place for disputing, but above. Now, however, the opinion pleases us which asserts that the habitual grace of Christ is infinite in act, but in a qualified sense, namely in the to-be of habitual grace, not in the account of being. Just as the angelic likeness is said to be infinite in act, but in a qualified sense, because it has every possible perfection of its species. So the habitual grace of Christ has every perfection which can pertain to the account of habitual grace according to the order of the divine Wisdom, according to that John 3: For God doth not give the Spirit by measure (that is, the gifts of the Holy Spirit); where Augustine says, namely, to the man Christ, since to Christ the Lord, as head, all habitual graces were given, whence they are derived to the members. In another way it can be said to be infinite, since it is a principle concurring to the infinite merit such as was the merit of Christ. And in this way also the habit of charity in Christ can be said to be infinite charity, insofar as it is the principle of infinite merit. But the merit of Christ is said to be infinite, not only insofar as it is an act which proceeds from the habit of charity and from habitual grace, but insofar as both charity and habitual grace are founded and rooted in the grace of union, since these habits are perfected in such to-be of grace and of meritorious charity by the subject itself, namely by the soul which exists through the existence of the Word of God; otherwise the habit of grace and of charity would not be a proportionate principle with the effect as to the infinity, although there would be proportion as to the substance of the meritorious act. From which it follows that with respect to the infinity of the merit of Christ, habitual grace and charity concur instrumentally, and not as the formal principle by which the agent is in act for so great an infinite merit. And through this the answer to the confirmation is plain: for the merit of Christ is not something simply infinite in act, but in the account of merit, insofar as it is accepted for satisfaction condignly for sins.

To the third, I grant the antecedent, and I deny the consequence. The reason is, because the divine knowledge does not make those parts be beings in act; but by division they become beings in act, and therefore they cannot at once be divided. Moreover, although this proposition be granted — infinite equal parts are in the continuum — yet to no designated part are there given infinite equals; otherwise the magnitude would be infinite in act.

To the fourth it is answered from Cajetan in this place, that continuous quantity can be considered in two ways: in one way according to that which is in it of act, and so it follows the form; in another way according to that which is in it of potency, and so it follows matter. And since there is very much in it of potency by which it regards matter (for quantity is defined by Aristotle in 5 Metaph. as divisible into those things which are in it, etc.), therefore, speaking simply, quantity is an accident which follows the composite by reason of matter. For no accident immediately follows matter: for it must first be informed by the substantial form. But because St. Thomas was speaking in art. 3 of the infinite in act, denying it to be possible in a natural body, therefore he took quantity according to that by which it is in act, and so it follows the limitation of the form.

To the fifth it is answered in two ways. First, I deny the major; indeed between corporeal substance and man there cannot be given infinite knowable species of substance, because man is the most perfect possible species of that genus of corporeal substance. Since, therefore, there is given the most perfect and the lowest, or the first and the last, under that possible genus, there will not be infinite intermediate species. Second it is answered, I deny the consequence: because such degrees of perfection possible to be made by God are not commensurable among themselves according to a determinate proportion, so that e.g. the horse be in double more perfect than the ass; but they will be commensurable among themselves according to geometrical proportion, in which there is not given a least degree; and so we grant that short of man, by the power of God, infinite degrees even of animals can be multiplied to infinity, just as continuous quantity is divided to infinity. Let there be an example in mathematics: the circular figure is the most perfect of all possibles, and nevertheless the species of figures short of it can be multiplied to infinity even by us. Likewise also the angle of contingence, which results from the contact of a circle upon a straight line, can grow to infinity, and become greater and greater, the smaller and smaller the circle be; yet it will never reach the quantity of the least rectilinear angle.

To the sixth, see St. Thomas below, q. 46, art. 1 and 2, at the eighth. Now, however, it is answered first, that time could not have been from eternity, since it follows the local motion of some substance; but substance has its whole to-be at once, while motion is successive; it is necessary, therefore, that substance flow forth from God wholly at once, while motion be posterior to substance: but where there is prior and posterior, it is necessary that there be a beginning of being. And it is confirmed: because the substance of the sun could not have been created except in one place, e.g. let the sun have been created from eternity in Aries; then it is necessary that before it was not in another sign: consequently it is also necessary that from Aries it have passed even to Libra, and again from Libra even to Aries, and so there will be given a first circulation, and there is given a last: therefore time could not have been from eternity, since infinite circulations have not passed. Second it is answered that although time had been from eternity, and on each day God could have created one angel, nevertheless not in all collectively, because it implies contradiction that there be given an infinite multitude in act. Third it is answered from Soto, 3 Physic., q. 4, at the 5th, that God could indeed have collectively created one angel, so that there had been no day on which he had not created; yet he could not have conserved them all, but he must successively annihilate infinite angels. But against this there seems to be: first, that the annihilation of an angel is a miracle, and beyond the nature of the angel; then it seems absurd that God could not have conserved the substance which he had once created, if he were to create another. And finally it is proved that he would have annihilated none, lest there be given an infinite. Because when he would annihilate this singular angel on this determinate day, either there are infinite angels, or not: if the first, therefore then the infinite in act does not cease to be through the annihilation of this angel; but if there were not yet infinite, why would this angel be annihilated by God? Whence the 1st and 2nd solution satisfies the argument more.

To the seventh it is answered that the infinite power of some agent is not shown from the fact that it would produce infinite effects of the same species, if infinite possibles were applied, since that multitude of effects proceeds not from the power of the agent, but from the infinite application of matter. Moreover, that fire naturally cannot grow to infinity syncategorematically comes from the order of the Universe, since the orb of the moon is finite. To which order of the Universe even the single parts of the Universe have a natural inclination. Just as water naturally ascends upward lest there be a vacuum, although such motion does not befit water according to the particular inclination of its species, but insofar as it is a part of the Universe. Cajetan, however, on art. 3, says that fire through itself one cannot grow to infinity, but fire through an accident one has no term of increase from within, but from the order of the Universe, which is from without. But he calls fire through itself one, which cannot be divided into two fires: because a determinate quantity is required as to smallness that fire be conserved. Whence there can be so small a fire that it cannot be divided into two fires. But when fire has so great a quantity that it can be divided into several fires, it is called by Cajetan through an accident one fire.

To the eighth it is answered: granted that God were to act unto the outside from necessity of nature. Whence it is no wonder if, one impossible being admitted, another follow. Nevertheless the consequence can be denied. And the reason of the difference is, because an agent from free choice must necessarily determine its intention to a certain and determinate effect. To the confirmation it is said that the reasons of St. Thomas which proceed concerning multitude and magnitude, seem to us demonstrations: for it implies contradiction that something be in a genus, and in no species; therefore if some whole quantum exists, it must be in some species of quantity, therefore in some species of measure. Likewise if some multitude of things is, it must be in a species of multitude measurable by unity.