Commentaria in Primam Partem Summae Theologiae

In the title, it can be taken simply, according to logical possibility. – In the body, three things: first, he assigns the cause of the question, namely that it is not vain but necessary; second, he divides the body¹; third, he answers the question raised².

II. As to the first point, the necessity of the question at issue is shown from the extraneousness of infinity in respect of magnitude to infinity of essence: namely, that it is one thing to be infinite in essence and another to be infinite in quantity. And this is proved in the case of natural things. – Here note that between these infinities there is a twofold difference. One is a difference of separation, whereby one is not the other. And this is evident, since in God there is found infinity of essence without quantity, while among these things there can perhaps be found infinity of quantity without infinity of essence, as is clear from the conditional laid down in the text. – The other is a difference of consequence, because one does not entail the other: namely, neither does what is infinite in essence entail infinity of quantity, nor—and this was more open to doubt—does infinite magnitude entail infinite essence, as is shown in the text, if fire were infinite. And with regard to this difference the text is to be interpreted: quoniam est admodum ad propositum.

III. Concerning this part, a doubt immediately arises that troubles the minds of beginners: because, as is said in VIII Physics³, in an infinite magnitude there must be infinite power. Therefore an infinite essence: for power does not exceed essence. Hence, if there were an infinite fire, it would be of infinite power; and consequently of infinite essence. It is therefore false what is said in the text, that if there were an infinite magnitude, it would not have an infinite essence.

To this it is briefly said that the objection equivocates. For infinite essence can be understood in two ways. First, of the infinity proper to the essence as essence: which, as is clear from what was said⁴, is nothing other than indetermination, that is, a lack of essential terms, namely genus and difference. Second, of the infinity taken commonly, or quantitative, etc. In the case at hand, the objection proceeds from infinity in the second way: but the text speaks of infinity in the first way. And therefore significantly the text says infinite according to essence, and does not say infinite essence: for essential infinity is better explicated by the phrase "according to essence", as is clear.

IV. As to the second⁵, the distinction is this. "Body" can be taken in two ways: physically, for the subject of three-dimensional extension; and mathematically, for that very three-dimensional extension considered absolutely. The text is clear enough.

Note here that that famous distinction of body, posited by Albert the Great in Book I of the Physics⁶, concerning threefold body—namely, mathematical, physical, and metaphysical—although it is not found explicitly in St. Thomas, is nevertheless not only not opposed to his doctrine but accords with it. For in him as well, a being composed of matter and substantial form, insofar as it precedes the aptitude of itself for quantity and motion, is a body belonging to metaphysical consideration. But since with respect to infinity according to magnitude, the physical and metaphysical body are not placed in different classes; therefore here the substratum of three dimensions—namely, that composed of matter and form—constitutes only one single member; and it is called physical body because by its natural form it receives its species, as is evident inductively.

V. As to the third point⁷, the question is answered, in accordance with the two members of the distinction laid down, by two conclusions⁸, in the negative. The first is: No natural body can be infinite in magnitude.

It is proved in two ways⁹. First a priori. Accidents follow upon the substantial form; therefore determinate accidents follow upon a determinate form; therefore a determinate quantity, both in greater and in lesser. Therefore every natural body has a determinate quantity both in greater and in lesser. Therefore it cannot be actually infinite. — The second inference is proved: because quantity is one of the accidents that follow upon the substantial form. The third, however, is proved: because every natural body has a determinate substantial form.

VI. Concerning the first consequence, a doubt arises as to what sense it has. For either ly determinate accidents imports a generic or specific determination: and then the sense is that such accidents follow a form of such a species, say fire, according to species, say heat, light, such a figure, levity, etc. In this sense the consequence is excellent, but it does not infer the proposed conclusion: for from such a sense the second consequence does not follow, therefore a determinate quantity, both in greater and in lesser; for a greater and a lesser quantity are not of different species, as is evident. — Or it also signifies a gradual determination, with respect to qualities, and a determination of extension, with respect to quantity. And then the sense is that a determinate form is followed not only by these accidents according to species, such that not those; but by accidents in such a degree or extension, such that not in another. And according to this sense it is without doubt here intended.

But it can still be understood in two ways. First, that determinate accidents follow a certain form, not only in the whole, but in all and each of its parts: for instance, that a certain quantity follows the form of water, not only in some whole body of water, but in whatever integral parts. And this sense is foreign to truth and to our purpose: since there is no smallest part of water or of whiteness, as is said in the book On Sense and What Is Sensed¹⁰; but, given any part whatsoever, there is given a smaller one existing in it, in homogeneous things. — Secondly, that determinate accidents follow a certain form in the whole and in parts capable of existing separately. And this sense is directly intended: since in merely indwelling parts there is not the proper form itself, but a part of the form, both in act and in potency; whereas the text says that determinate accidents and a determinate quantity follow a determinate form. But whence this consequence holds in this sense, or what is its foundation, is hidden. And therefore it turns into doubt: first, with respect to the determination of quantity in the lesser; second, with respect to the determination of the same in the greater¹¹.

VII. Scotus, in II Sent., dist. II, qu. IX, endeavors to prove the opposite, and to maintain that there is no minimum in homogeneous substances capable of existing per se: but, given any quantity of water whatsoever, a smaller one can exist per se. And thus its form does not determine for itself a definite minimum quantity, as is said in the text.

He therefore argues from the reason of quantity (Metaphysics V), thus: It is no more essential to quantity that it be able to be divided into parts, than that each of the parts into which it is divided can be this something. Therefore each part of any quantity whatsoever of water can exist per se. — The antecedent is clear from Metaphysics V¹² The consequence, moreover, is manifest in itself. And nevertheless the consequent is confirmed in four ways. First, because the parts are of the same nature as the whole, as regards matter and form. Therefore to exist per se, which does not conflict with the whole, does not conflict with a part. — Second, because every part has a nature: hence it does not conflict with it to be an individual of the same species as the whole. Therefore it can be an individual; and consequently can exist per se. — Third, because the parts are naturally prior to the whole. Therefore it does not conflict with them to be prior in time, etc. — Fourth, because, given that least water, all corruption being set aside, even that of the container, if it is divided, then either after the division—whereas before there was one water in act and many in potency—there will be several waters in act, and the point is established; or not. And if not, then the water has been annihilated without a corruptive cause. This is proved: because division alone does not corrupt. This is proved: because it divides into homogeneous parts, out of which the whole is constituted; therefore it divides into waters; or else water is composed of non-waters, as integral parts. Nor, he says, is there any repugnance on the side of small quantity: because the form of water was already present with so small a quantity.

VIII. Against the determination of quantity upward¹³, an argument is drawn from reason and from authority. From reason, indeed: given any fire whatsoever, if combustible material properly disposed is placed near it, it is certain that it will burn. That fire, therefore, grows, insofar as it lies within itself, to infinity. — And this is confirmed by the authority of Aristotle, II On the Soul, text 41¹⁴: fire would be increased to infinity if combustible material were added to infinity. Therefore there is no greatest fire.

IX. To make this difficulty evident, note first that we do not intend here to treat of the maximum and minimum in its entirety, since that would be beyond our purpose; but only whether there is given a maximum and minimum from within. For this is what the reason assumed in the text requires, wishing that from within, namely from the substantial form, each natural substance claims for itself a definite quantity, both in excess and in deficiency. And therefore we have brought forward only these few reasons in this disputation. There will be, God willing, a special question on the maximum and minimum universally. — Note second that we have two reasons from Aristotle for this. One is in I Physics, text 36¹⁵, namely: the quantity of the whole arises from the quantities of the parts, etc. But this reason, as is clear, proceeds from a supposition: for it supposes that a maximum is given, and concludes that a minimum is given, otherwise the whole would not be of a definite quantity. The other is in II On the Soul, text 41¹⁶, namely: of all things constituted by nature the measure is determinate, etc. And this reason, as Scotus says¹⁷, speaks of ensouled things, in which alone there is a place for growth properly so called, of which the discussion there is concerned.

True, whatever may be said of that text, St. Thomas universalized it: and what is said there of the soul he took to hold of every substantial form, namely, that it claims for itself a certain quantity. And he proved it according to the doctrine handed down in V Metaphysics¹⁸ and II Physics¹⁹, namely, that causes are compared with their effects, and conversely, and are measured by them. For from this it follows that, if quantity follows naturally upon substantial form in general, then a determinate quantity follows a determinate form. But quantity is determined in no other way than according to its terms: for the corporeity of man and of water does not differ in species, so that one could not say that a determinate quantity follows a determinate form according to species. Therefore there follows a quantity determined according to its terms. — And even if quantities differed in species, the ground of the inference would still stand, from the fact that a determinate form is the power of a determinate act, and hence nothing consequent upon it can be infinite: for if it had an infinite heat, rarity, quantity, or any accident whatsoever, then from a finite form there would be an infinite power; which is unintelligible. Since therefore accidents follow physical form in general, it follows that certain accidents follow a certain form, and hence a thing of a certain power: not only such that these follow but not those; but also such that they follow in such a degree or term, highest or middle, and not in a greater or lesser one. — And thus we have the ground on which the inference of the text holds²⁰, not only concerning quantity, but concerning all accidents.

X. Against Scotus's argument,²¹, the antecedent is granted, but the consequence is denied. And the reason is that both things—namely, being divisible into parts, and those parts being able to be a this-something—if understood really, do not belong to quantity through itself positively, but non-repugnantly, as is clear in the case of the quantity of the heavens: for that quantity can neither be divided by actual division, nor can any part of it exist separately, and yet it is truly a quantity. Both conditions, therefore, posited in the definition of quantity, can be impeded from being exercised by the natural form to which the quantity is joined. Hence that definition belongs to quantity as such: and yet it is repugnant to some quantity. — And if against this Scotus's argument be brought forward: Whenever two things follow from something through itself, they are impossible, and those two things are impossible; but the conditions of quantity and of a minimal form are incompossible; therefore quantity and a minimal form are incompossible: — the answer is, first, by applying the whole argument to the nature of the heavens, which does not admit division. Second (since to multiply is not to solve), that that major premise is true of things following through themselves positively: but not non-repugnantly. Hence the capacity for infinite speed belongs to motion through itself non-repugnantly, and is even demonstrated of it; yet it is repugnant to any natural motion, as is clear in II On the Heavens, text. 39²²: and therefore motion and naturalness are not incompossible.

It could nevertheless be said otherwise, that those conditions are not understood according to actual division, but according to designation: and that thus every quantum is divisible, and any part can be this something, according to designation. And then nothing follows against our thesis.

XI. To the first confirmation, the inference is denied. For the form of water requires some condition in that which is perfectible per se in the first way, which it does not require as part of it: and one of these conditions is such a quantity. And the same judgment holds for so much heat, etc.

To the second, likewise, it is said: that communicating in a nature is not sufficient for being able to be an individual of the same species; but one must add the conditions required for existing of oneself. For whatever has the nature of water together with the conditions necessary for existing of itself can be an individual of water; and not otherwise.

To the third, the consequence is denied, insofar as it concerns only the non-existent parts.

To the last argument it is said that, if the smallest fire alone were posited and divided, it would not only be corrupted but annihilated; although both the antecedent and the consequent are impossible. Nor need one seek any other destructive cause than division: since even if division as such is not corruptive, yet division of such a thing, namely of a natural minimum, is universally corruptive; and in such a case annihilative. Nor is the minimum fire one in act and many in potency, except in the way in which parts are said to be in potency in the whole: namely because they are by an esse that is not their own but the whole's; just as the parts of the heavens are in potency in the whole.

XII. To the things objected against the maximum²³, it is answered that a maximum fire can be understood to be given in two ways: in one way, speaking of an individual of fire that is one per se; in another way, of one that is one as it were by aggregation. And I say that a maximum and minimum fire is given intrinsically in an individual that is one per se; although a maximum that is one as it were by aggregation is not given, except from without (namely, because the nature of the universe does not allow fire to surpass the other elements, etc.). Now that is called an individual of fire one per se which is constituted of one thing necessarily in act both in form and in matter, such that by mere division it could not become two fires. Nor does this consist in the indivisible: but the whole breadth from the minimum quantity of fire to the quantity of two minima, exclusively, constitutes a fire that is one per se and one in number. But the quantity of two minima, and greater, makes one as it were by aggregation. And the same judgment holds concerning water and the other elements, and homogeneous things of this kind. – Nor, moved by these considerations, should you understand that a plant is not one per se, which is one in act and many in potency: since the parts of a plant are organic, and for the natural completion of its individual there is required that it have all its parts, etc. It is not so in homogeneous things of this kind, as is evident. – Therefore, when combustible material is added to any fire, etc., it must be granted that it would burn, and that it would grow infinitely: but it would not be one fire per se and one in number. – And thus the answer to the authority of Aristotle is clear.

XIII. Concerning the proof of the second consequence²⁴, a doubt arises: because something false is assumed, namely that quantity is one of the accidents following the substantial form; since it is evident that quantity is an accident consequent upon matter. – Nor does it avail to say that quantity is considered in two ways, namely absolutely and as terminated; and that although absolutely it is consequent upon matter, its termination nevertheless follows the form. For these things, although true, are nevertheless not to the point. Because the text, from the fact that quantity follows the form, infers that therefore it is terminated: whence, if it were assumed that quantity with respect to its termination follows the form, there would be a begging of the question.

XIV. To this it seems one should reply that quantity can be taken in two ways. In one way, according to what is in it of act: and thus it follows form. In another way, according to what is in it of potency: and thus it follows matter. And since most of what pertains to it belongs to the potency of matter, as is clear from the definition of the quantitative given in Book V Metaphysics²⁵, therefore absolutely speaking it is posited as an accident consequent upon the composite by reason of matter. And since the discussion at hand concerns quantity in act, because it concerns the infinite in act; therefore in the passage at hand, using "quantity" with respect to act, he attributes it to form; and from the fact that it, insofar as it is in act, follows form, he infers: therefore it is terminated, like the other things consequent upon form.

XV. Secondly, the conclusion is proved²⁶ from the notion of mobility. Every natural body has some natural motion, as is shown in I On the Heavens, text 5²⁷; no infinite body is naturally movable: therefore. – The minor is proved by using the distinction of natural motion made in I On the Heavens²⁸. For it cannot be moved by rectilinear motion, because every such body can be outside its own place, at least as to its parts. Nor by circular motion, because lines drawn from the center of a circle, the farther they are drawn out, the more they diverge from one another; therefore in an infinite body they would diverge from one another infinitely; therefore one would never reach the place of another; therefore one part of an infinite circular body could never come to the place where another is; therefore it implies that it be moved. And this argument is taken from I On the Heavens, text 35²⁹.

XVI. The second conclusion³⁰ is: No mathematical body can be infinite in act. – It is proved. If it is a body in act, therefore it has a form; therefore a figure; therefore a limit. Therefore it is not infinite. – The first consequence is proved: because nothing is in act except through its form. The second, however: because the form of a body, of the genus of quantity as such, is figure. The third, moreover, follows from the definition of figure. And this argument is taken from Book III Physics, text 40³¹.

XVII. In response to the second objection, note that, if it is examined carefully, he denies that the infinite is a passion of quantity, although he concedes that it is not repugnant to it. And if against this the fifteenth text of Book I Physic.³² is adduced, namely, that the notion of finite and infinite befits quantity, the answer is ready at hand: that this is not said because quantity lays claim to infinity for itself; but conversely, because infinity lays claim to quantity for itself, since the infinite is not intelligible except as a quantum: just as it is also said that the notion of void befits place. For by this the philosophers intend that if these are found to exist, they must be found in quantity and place, etc.

XVIII. In response to the third objection, note that, although the response is taken from Book III of the Physics, from which the other responses are also taken (the first indeed from text 71³³, the fourth from text 74³⁴, and this one from text 66³⁵): although, I say, this is so, nevertheless the words of St. Thomas in the Third Part, question VII, article 12³⁶; and in Book III of the Sentences, distinction XIII, question I, article 2, question III, ad 1, stand against this response; indeed even here, in the following article, in the reply to the second objection, by conceding the multiplication of figures to infinity. Likewise in Book III of the Physics³⁷, Aristotle expressly concedes, in texts 59 and 60, that magnitude is increased to infinity, just as it is divided.

XIX. To this it is briefly answered, with Aristotle in the same place, that magnitude's being increased to infinity can be understood in two ways. First, on the ground that an addition can always be made to it according to proportional parts. And thus it is said there that it can be increased to infinity: but by such increase a certain determinate magnitude will never be exceeded. Second, because addition can always be made simply, so as to exceed every determinate quantity. And thus a distinction must be drawn. For we speak either of magnitude considered within the limits of the continuous, or of it as taking on the character of the discrete. In the first way, the continuum is not augmentable to infinity, whether by natural or by intellectual augmentation: and the cause of this is assigned in the text. In the second way, however, it is augmentable to infinity, just as number is: and to this belongs the increase of figures to infinity. – That the continuous as such is said not to be augmentable to infinity even by intelligible augmentation is not because the intellect cannot, given any magnitude whatever, imagine a greater one, and so on to infinity; but because in the nature of the continuum as such there is no potency for an increase of this kind. Yet in the nature of material number there is; and likewise in the nature of the continuum there is a potency for diminution to infinity, as is clear from its definition. And thus all things are consonant, when understood according to their diverse modes.

XX. Concerning the reason assigned in the text³⁸, a doubt arises from Scotus, in Book III Sentences, distinction XIII, question I. For he attacks it as follows. Every number is one in itself formally, as is said in Book VIII of the Metaphysics³⁹: therefore, when number is increased, something is added to the form; therefore, an approach to the form does not prevent increase to infinity. Therefore it is wrongly said in the text that magnitude is not increased to infinity because one approaches the whole and the form.

XXI. To this it is said that, since the number augmentable to infinity is not any number whatsoever, but the number of continua, as is clear from III Physics, text. 68⁴⁰, the augmentation of number does not accrue to number simply, but to such a number, namely that of the parts of a continuum: and hence what is clearly augmented is not the whole but the part; just as also the division of the continuum, from which it is caused. But the augmentation of the continuum accrues to the whole simply. – Therefore Scotus's first consequence must be denied: for he argues from number to such a number, that is, a material one. Which is not permissible in the matter at hand: because the term material diminishes the ratio of number with respect to its formality, since it adds materiality to the form, and mixes act with potency, as is evident.