Cursus Philosophicus Thomisticus, Secunda Pars Artis Logicae

Aristotle does not give a definition of quantity in this treatise on the Categories, but begins directly with the division of quantity into continuous and discrete. He does define quantity in Metaphysics V, text 18,¹ as follows: “A quantum is that which is divisible into the things present in it, each of which, or each taken singly, is naturally one thing and this particular thing.” St. Thomas explains this definition there, lecture 15.² The whole explanation comes down to this: Aristotle defines a quantum as divisible, not into physical parts, that is, matter and form; nor into potential parts, as the soul is divided into intellective and sensitive powers; nor into subjective parts, as a universal is divided into its inferiors; but into integral and quantitative parts, which are composed in such a way that, when division is made, each remains one thing, as is clear when water is divided into various parts. A quantified thing is divisible into these integral parts.

For the quiddity of a thing cannot be explained unless we first understand its separation from the other genera to be a real accident, distinct from substance and the other accidents, so that we may inquire only into its distinctive and proper account. Some Nominalists denied this. On the one hand, they thought that without quantity there are no parts or divisibility; on the other, they thought that the entity of anything whatever is nothing other than its parts. They therefore said that quantity is not really distinct from the thing having parts, whether it is a substance or an accident.

The most sacred mystery of the Eucharist, however, has shown us the opposite. Quantity remains there—the quantity that was formerly bread, as we see with our eyes—while the substance of bread does not remain, as faith teaches. Quantity, then, is distinguished and separated from the quantified thing. The Nominalists reply that the quantity of the substance does not remain, since the substance itself has vanished, but that the quantity of the qualities and other extended accidents remains. But there are several accidents there. Therefore, either each has its own distinct quantity, or there is some quantity common to all. If there is one quantity common to all, it is distinct from each accident, since it is common to several, and it is also distinct from the substance, which is not there; therefore, quantity is distinct from the quantified thing. If the first alternative is proposed, then those quantities are mutually penetrated, since all those accidents are in the same place. This penetration is either supernatural and miraculous, or natural and according to their nature. The first cannot be said, because those accidents have the same quantity after consecration as before, since they have the same entity, and quantity is not distinct from entity. Before consecration, moreover, they were also in the same place; therefore, they did not need a supernatural miracle in order to be penetrated. If the second alternative is proposed, then the quantity of such accidents naturally does not resist penetration, but admits it; thus it will be a quantity of another kind from the quantity we are discussing here, which experience itself shows us resists penetration. We say that this quantity is distinct from the quantified thing.

This also refutes a certain more recent opinion that quantity is a mode, not a real accident of the quantified thing. For a mode cannot be separated from the thing of which it is a mode. But in the Eucharist quantity is separated from substance. This opinion therefore concedes that the quantity of the substance vanishes with it, but says that another dimensional quantity remains. If this quantity is a mode of some accident that remains there, there will be as many modal quantities as there are accidents, and so the opinion falls into the view it set out to refute. If, however, it is not a mode but a reality, we have what we seek: quantity is a thing, not a mode. This view must then explain whose dimensional quantity it is.

We shall reply to the opposing basis by explaining St. Thomas’s view: quantity is said to provide a substance with integral parts, not by constituting those parts, but by ordering them among themselves. This ordering is accidental.

With these points presupposed, authors hold a varied and many-sided VIEW in assigning the formal constituent account of quantity. Most seek it in the effects introduced by quantity, some of which are separable from it and others not. Since everyone commonly understands the proper effect of quantity to be the extension of parts, from which several properties flow—such as the account of measure, divisibility, impenetrability, and filling a place—some assign quantitative extension, distinguishing it from the substantial extension of parts by its account of measure. For measure is common to continuous and discrete quantity, and St. Thomas teaches that Aristotle explained quantity in the Categories according to this account of measure in Metaphysics V, lecture 15.³

Others constitute the essence of quantity in divisibility itself: some in radical divisibility, others in formal and proximate divisibility.

Others constituted the essence of quantity in an extension that fills space—not as regards actual filling, as some Nominalists thought, but as an aptitude or root, for quantity is a form that demands this filling. To make this account include every quantity, continuous, discrete, and successive, they distinguish three kinds of space: of place, duration, and discreteness. Extension of continuous quantity occurs according to the space of place, and is commensurated with different parts of place. Extension of successive quantity occurs according to the space of duration, corresponding to different parts of time or motion. Extension of discrete quantity occurs according to the space of discreteness, corresponding to different parts of number.

Others assign the essence of quantity to the extension of parts insofar as it is apt to resist penetration and to fill a place by its nature, although actual filling and commensuration can be separated from quantity. On these views see Carmelus, Course, here, disp. 13, qq. 2 and 3; Merinero, disputation on Quantity, qq. 1 and 2; Master Cabero, here, disp. 2, dub. 2; and Suarez, Metaphysics, disp. 40, sect. 4.

Finally, others constitute the essence of quantity in the extension of parts, not in relation to a place outside them, but in relation to the whole itself, so that without quantity a substance or subject would not have ordered parts, or one part outside another, which is what it means for them to be extended. The disciples of St. Thomas commonly follow this view, as may be seen in the cited authors, and in Vazquez, First Part, disp. 196, ch. 3; Toletus, Physics I, q. 7; and others.

Amid such a variety of opinions, I presuppose three points as certain and more generally agreed upon among authors; I find some doubt only in one.

THE FIRST is that the formal account of quantity cannot consist primarily and per se in formal measure or formal divisibility, actual filling of place, actual impenetration, or any actual extension in relation to place. For it is clear from the mysteries of faith that quantity is found without these properties. The body of Christ is in the Eucharist with its quantity as well as its other accidents, as St. Thomas proves in the Third Part, q. 76, a. 4; nevertheless, there it is not divisible in a divisible mode, nor measurable in relation to place by division, nor impenetrable in the ordinary mode. It is also clear that it was penetrated together with the tomb, when it came forth from the Virgin’s womb, and when it entered with the doors closed. Nor does it actually fill a place in the Eucharist, since the whole is in the whole and the whole is in each part. Therefore, the account of quantity does not consist in these things. If St. Thomas sometimes says quantity consists in measure, as in Opusculum 52,⁴ or in divisibility, as in 1 Sent., d. 19, q. 1, a. 1, ad 1,⁵ and Metaphysics V, lecture 15,⁶ he is speaking of measure and divisibility as roots.

THE SECOND is that quantitative extension, as the root and fundamental aptitude for these formalities and properties of extension in relation to place, belongs intrinsically to the very account of quantity. By its nature quantity demands to fill a place, not to be penetrated, to be formally divisible, and the like; for these modes are connatural to quantity. Hence the view that quantity consists in extension having an aptitude to fill a place and not to be penetrated is entirely correct. Quantity also consists in an aptitude for measure and divisibility, but that account is incomplete, because it explains the nature of the thing not by what it formally signifies, but by what it demands radically. The difficulty, however, is in what this root formally consists.

THE THIRD is that extension in relation to the whole presuppositionally signifies the entity of the parts, and then their union and ordering. It is clear that quantity does not give the entity of the parts, for the parts are entities substantial in kind. Union, moreover, is considered substantially or entitatively insofar as the united parts compose a substantial whole. It is also certain that quantity does not give union in this sense, because such composition is not accidental but substantial, since the resulting whole itself is substantial. Such union can also be taken accidentally, insofar as it signifies union not in just any way, but as ordered: it removes confusion by uniting one part to another, not as a whole to a whole, but according to some aspect of it, namely, according to an extremity. For this reason it is said to place one part after another, because some part extends outside another part and is not united to it as a whole. This is called the formality of an extended part, not insofar as it is the entity of a part, but insofar as it is distinct and ordered, or unconfused. This depends on extremities and indivisibles, without which the parts are not united in an orderly and unconfused way. It is doubtful whether this is the formal effect of quantity.

Resolution: LET THERE BE ONE CONCLUSION: In the view of St. Thomas, the proper and formal account of quantity is the extension of parts in relation to the whole, which makes the parts formal integrants. Hence, when quantity is removed, a substance does not have integral parts formally ordered and distinct in the account of part.

Before the conclusion is proved, I observe that the term “distinct parts,” or “distinction of parts,” can be considered in two ways: in one way, as the term “distinction” is opposed to an altogether simple unity; in another way, as it is opposed to confusion. For distinction can remove unity when multiplicity comes about, and it can remove confusion when order comes about. Things are called confused when they are without order, and distinct when they are placed in an orderly and proper way. What we assert, then, is that quantity formally, insofar as it is quantity, does not constitute the parts of a substance with respect to their entity and intrinsic account, but with respect to their ordering, which removes confusion. This account of ordering is an accidental formality of the parts, which quantity constitutes as ordered and distinct.

That this is the EXPLICIT VIEW OF ST. THOMAS is proved. First, in Opusculum 42, ch. 16,⁷ he says “that part and part are in something by means of quantity, which is the first accident of a body, since it is its measure.” Likewise, in Opusculum 48, Treatise on Quantity, ch. 4,⁸ he says “that position is taken in one way as the order of parts in a place, and thus is one of the predicaments, called situs; in another way, position is the order of parts in a whole, and thus position is a difference of quantity.” He teaches the same there when discussing the predicament of situs, ch. 1,⁹ and in Physics IV, lecture 7.¹⁰ St. Thomas therefore holds that the order or extension of parts in a whole is the proper and distinctive account of quantity. He speaks in the same way in Sentences IV, d. 10, q. 1, a. 3, q. 3, ad 2,¹¹ where he says: “Although we cannot understand an order of the parts of Christ’s body according to a comparison with the parts of the host, we can nevertheless understand an order among the parts themselves in Christ’s body according to its proper quantity.” St. Thomas therefore holds that the order of parts in a whole pertains to quantity itself.

That when quantity is removed the substance remains indivisible, and thus quantity orders its parts first and per se, is proved from St. Thomas himself. In Opusculum 70, q. 5, a. 3, ad 3,¹² he says: “Matter cannot be divided except with quantity presupposed; when quantity is removed, all substance remains indivisible, and so the first account of diversifying things of one species is according to quantity. This pertains to quantity insofar as, in its account, it has position, as it were, for a constitutive difference; position is nothing other than the order of parts.” Here St. Thomas does not take position formally, but as a root; otherwise, how could he have been unaware that it is a predicament distinct from quantity and not its constitutive difference? Likewise, in Quodlibet 9, a. 6,¹³ he says “that a diversity of parts cannot be understood in matter without understanding division, nor can division be understood without understanding dimension, because when quantity is removed the substance remains indivisible, as is said in Physics I, text 18.”¹⁴ He says the same in the First Part, q. 50, a. 2, and in Contra Gentiles IV, ch. 65: “when quantity is removed, every substance is indivisible.” He adds that “quantity has this property among the other accidents: it is individuated according to itself. This is because position, which is the order of parts in a whole, is included in its account; for quantity is quantity having position.” See how clearly and consistently St. Thomas teaches both that quantity provides the order and account of parts in a whole, and that when quantity is removed the substance remains indivisible. Indeed, even when quantity is removed in relation to place, as in the body of Christ, the body nevertheless remains divisible and extended in relation to the whole by reason of quantity. St. Thomas therefore holds that when quantity is removed, substance remains indivisible both with respect to place and with respect to the whole; that is, it does not have parts formally as parts.

The BASIS of this view is often established by several arguments intended to destroy the entity-like extension of integral parts prior to quantity. The arguments, however, are most effective when reduced principally to two principles:

We cannot explain the first here; it must be presupposed and treated at length in the books on Generation,¹⁵ namely, that the individuation of corporeal things is taken from matter designated by quantity. It is taken from matter as a substantial principle, which individuates not formally but radically. Hence matter is not individuation itself, but the principle of individuation. Quantity is taken as a required condition, not as the per se principle of substantial individuation. This teaching is found explicitly in St. Thomas, Opusculum 70, q. 4, a. 2,¹⁶ and in many other places. From this principle it necessarily follows that if quantity designates matter with respect to individuation or the distinction of individuals, it will also do so with respect to the distinction of parts, because only by actual division do designated and extended parts become several individuals. Thus the designation of distinct parts and of individuals pertains to the same principle. Hence the Philosopher also calls a quantum “divisible into things, each of which is naturally one thing and this particular thing,” that is, something so designated that only by actual division does it become this or that individual.

The second principle to be explained here is taken from the proper account of integral parts. To be extended, unconfused, and ordered, they require some accident in addition to substance. This is proved because extension of parts in a whole is not just any union among them, but a union only at their extremities, so that one part is not united to another as a whole to a whole, penetrated and absorbed into it, as form is united with matter, which is purely substantial. For if one part is united with another in the whole by penetration and according to every part of itself, it is not united extensively—that is, one part is not outside the other. Therefore, for an extensive union in a whole, the parts must be united at their extremities and not as wholes, since otherwise they would be united by penetration, like matter and form. The mode of union among integral parts is distinct from the union of matter and form.

We therefore inquire: what causes the substance of one part, for example, a hand, to be prevented from uniting with the arm according to every part of itself, and to be united and joined to it only at the extremities? This cannot happen by virtue of the substance itself, since substance does not of itself have parts with extremities. Extremities are had only through indivisibles, but substance does not of itself have indivisibles, such as lines, surfaces, and points, since these are proper species of quantity.

If it is said that substance also has its own substantial indivisibles corresponding to the indivisibles of quantity, the following argument presses against this: these indivisibles are posited so that substantial parts may be united at their extremities, that is, extensively and not by penetration. For if they are not united at their extremities, then precisely by this fact they are united as wholes and by penetration, which means they remain confused and unordered among themselves, rather than one being after another. Therefore, if substantial parts are united before quantity by these indivisibles and extremities, they remain unpenetrated or extended in the very whole prior to quantity. Thus substance in itself has a sufficient principle to resist penetration in relation to place and to fill it. Consequently, it is pointless to posit the formal account of quantity as a principle of impenetration in relation to place, since the entity-like extension of substance in itself has this already.

The consequence is proved because the entity-like extension of substance occurs at extremities and indivisibles before quantity, in such a way that this union prevents one part from being penetrated with another in the whole as regards continuity. Therefore, it will also prevent it from being penetrated with the parts of an adjacent, contiguous body. For it is unintelligible that a principle sufficient to prevent the union and penetration of a continuous part would not prevent the union or penetration of a contiguous part. But authors of the opposing view call the principle that prevents penetration by a contiguous body quantitative extension, distinct from entity-like extension. Therefore, before quantity they posit in substance the formal account of quantity itself, precisely by positing that substantial parts are united in an orderly and unconfused way through substantial extremities and indivisibles. We must therefore hold that this extensive union in a whole is accidental and comes from quantity.

And if you say: In the sacramentally present body of Christ, there is quantitative extension in relation to the whole, such that one part is not penetrated with another in the union of the whole; and yet in relation to place it has no extension, but an indivisible mode. Therefore, this extension in relation to the whole comes from a principle other than the union of parts in relation to place. The reply is that the quantity of Christ’s body, which is in the whole itself, is a sufficient principle of impenetrability and extension in relation to place, unless this effect, which is secondary in quantity and properly pertains to circumscriptive location, is divinely impeded. This is why we place the whole force of the argument here: in substance itself, prior to quantity, there is a principle that repels penetration by a contiguous body, precisely because there is a principle that repels penetration of parts within a continuum. But if there is no principle that repels penetration in place, there is likewise no principle that repels penetration in the whole. Thus both effects come not from substance but from quantity, although one effect can be separated from the other by God’s absolute power, because one is primary and the other secondary.

THE ARGUMENTS ARE RESOLVED.

Nearly the whole difficulty and the arguments raised against this resolution depend on the principle that the parts of substance do not depend on quantity in their entity or distinction. Thus substance is considered without quantity and yet with parts. For example, if God were to remove quantity from a substance while preserving it, then either the substance would remain with distinct and extended parts, or without them and indivisible. If the first, we have what we seek; if the second, it follows that all the parts of substance converge to a point. This would occur either in an instant or over time. It cannot occur in an instant, because a flow or motion cannot take place in an instant. If it occurs over time, then those parts last as long as that time lasts, and yet there is no quantity. Nor is there more reason for that substance to converge to one part than to another; therefore it will remain as before.

It is confirmed: if two partial substances are united and newly acquired, as happens in nutrition, and God removes quantity from them, either those parts will remain one or distinct—that is, one part will not be the other. If the latter, we have what we seek. If the former, then they will lose their individuating principles and individual differences while those same principles remain, which is impossible. The same argument applies to two fires, one of which produced the other, if they are united with one another and God removes their quantity. Either the parts will remain distinct or they will not. If they remain, we have what we seek; if not, then when quantity is removed the producer and produced will be the same and one. Likewise, if God removes quantity from the two outer palms of a three-palm piece of wood while leaving quantity in the middle, then those two ends are distinct parts of the wood and without quantity. Therefore.

All these arguments press the same difficulty, and they are resolved by one principle: before quantity, substance does not have parts formally extended—that is, ordered and unconfused—but it does have parts radically, that is, a capacity to receive that ordering and distinction of parts. Without quantity, the parts remain penetrated and united as wholes, which is not to have one part outside another. This should not seem surprising, because when quantity is removed all indivisibles and extremities are removed, without which the parts are not united extensively—that is, at the extremity of one and the other—but by penetration and as wholes. Therefore, the entire entity of the parts remains when quantity is removed, but confused and in the manner of one thing. There is not, however, one integral part and another formally; there are parts only radically.

THEREFORE, AS TO THE FIRST CASE, we say that when quantity is removed substance would not converge to a point, but would lack all points and consequently every union of parts by way of extension. For, as St. Thomas rightly observes in 2 Sent., d. 3, q. 1, a. 1,¹⁷ substance without quantity is not indivisible because its parts are reduced to a point, which is a principle of quantity, but because it lacks all divisibility. Hence there would be no motion in that substance, just as there would be no physical place; rather, it would exist in the universe as a certain part of it, not as something located in a place. For all these imaginings must be set aside, since they follow quantity as located, as Cajetan rightly taught in the First Part, q. 52, a. 1, near the middle. Therefore, that substance is neither distant nor positively somewhere, but would have its existence without a place, like a thing outside the world or an angel not acting.

In reply to the confirmation, it is said that when quantity is removed from the parts, they do not remain actually distinct, but confused, as one entity with a radical capacity for partial distinction. When it is said that one part is not the other, and that the individual differences cannot be lost while the same things remain, we reply by denying the presupposition. For when quantity is removed, no part remains in act, but only radically and in potency. Hence every individual difference in the genus of part ceases, because no part is given in act. Nor do the same parts remain once their differences are removed, because, as we said, the parts do not remain in act; rather, a certain confused substance remains, capable of parts but not actually composed of parts. It is like matter without form: it would have no formal being in act, but only in capacity and potency, as will be said in Physics I.¹⁸

You will insist: Two individuals, for example, two stones, remain distinct according to their individual differences when quantity is removed, although their individuation depends on quantity. Therefore, substantial parts too will remain actually distinct according to substantial distinction, although that distinction depends on quantity.

The reply is to deny the consequence. The difference is that the distinction of individuals depends on quantity as dividing and separating them. Once division has taken place, if quantity is removed, since the substances themselves are not united again, they remain separate and not one; they have this by their order to quantity, although they are not informed by it. So a soul, individuated by its order to the body, is individuated by its order to the body even when separated from it; and the same is true of a separated accident in its order to its subject. But parts in the same whole are not distinguished by quantity as dividing and separating them—for in that way the parts would not remain; rather, the whole would—but by quantity as uniting them in an ordered way, that is, not as wholes and confusedly, but at their extremities, placing one outside another without dividing it from the other. When quantity is removed, this ordered and extended union is dissolved and another takes its place, by which those parts are united as wholes and confusedly, or rather become one in substance. Thus their distinction in the account of part is prevented, and this is to lose the individual differences of parts. For parts in the very whole do not have individual differences simply, which arise only through division, but in a qualified sense, since they truly compose one thing and are not simply distinct individuals. Hence their actual distinction in the genus of part does not remain in act when quantity is removed, but in potency, because the ordered union by which they were distinguished changes into another, confused union that prevents actual distinction.

As to the producer and product becoming the same in that case, we reply that the producer and product are never the same while production is being exercised. But when production ceases, the thing that produces can indeed pass into the substance of the product and be united to it, as if a son ate his father; and then, when quantity is removed, those parts are distinguished only virtually and radically. By absolute power, through transubstantiation, the producing things can be converted absolutely and wholly into the thing produced.

As to the final case, it is said that when quantity is removed from the two ends while quantity remains in the middle, the quantity itself is consequently divided, and those ends remain separated from the whole and become individuals by their order to the divided quantity; they are no longer parts. But if God keeps them united to the intermediate substance, they will not remain parts formally, but radically, as confused and united as wholes with the intermediate substance.

And if you ask what it means for a substance to have parts radically, and how it differs from an indivisible substance such as an angel, the reply is that it differs from a spiritual substance because a spirit lacks parts negatively and by incapacity, whereas a body deprived of quantity lacks parts privatively, while retaining a capacity for them. It is not said to have those parts actually, because it does not have them distinct and multiplied by extension, that is, one outside another; rather, through confusion they are reduced within it to the manner of one thing, and not merely with respect to place. Thus the entity remains ordered toward an extension of parts, but it does not itself have an ordered extension of parts.

Second it is argued: When substance is under quantity, it has distinct parts not only accidentally but also substantially; therefore, even when quantity is removed, that substantial distinction can remain.

The antecedent is proved: the distinction of a hand from an arm now does not occur through quantity alone. For if they differed through quantity alone, they would not be two parts of a substance; just as Christ’s body placed under the Sacrament and in heaven is not two bodies, although its place accidents vary. Therefore, likewise, if those parts differ substantially, they are not distinguished through quantity alone.

It is further confirmed that unity or division follows the being of a thing. But every substantial part has being as a substance not from quantity but from itself; therefore, it will also have substantial unity and distinction from itself, not from quantity. The major premise is clear, because unity is a property of being, and there are as many unities as beings. Therefore, substantial unity or distinction is a property of substance and thus does not depend on quantity. Hence St. Thomas says in Metaphysics V, lecture 15,¹⁹ that only quantity has division into proper parts after substance. Therefore, St. Thomas presupposes that substance has proper parts.

It is confirmed a second time: the quantity of a hand is not in the foot, or vice versa. Therefore, the quantity of one part is not received in another. Therefore, a distinct account of the parts of hand and foot is presupposed before quantity, since the quantity received in one is not received in the other. Again, when quantity is removed, the entity of the hand, the entity of the foot, and the other parts remains in that substance. But the entity of the hand is not the whole entity of that substance; therefore, it is a part. Nor can it be said to be reduced to an indivisible entity, as a spiritual substance is, since a spiritual entity does not contain the entity of a hand and foot as a corporeal substance does when quantity is removed.

THE REPLY to the principal argument is that substance under quantity has parts distinct in two ways, namely substantially and accidentally. But substantial distinction cannot be reduced to act except dependently on quantity as a condition, without which that distinction of substance does not come into act. Just as substance does not come into act in influencing and acting unless a quality is posited as the instrument by which it acts, and when the quality is removed it remains an agent only radically, so without quantity confusion and indistinction remain. When this is posited, substance cannot proceed to the act of substantial distinction through an extension of parts that removes this confusion; rather, the whole remains radically distinguishable through quantity. Thus from substance comes the account of constituting parts; from quantity comes the account of ordering and removing confusion through extension; and substantial distinction itself depends on this ordering as a required condition.

In reply to the first confirmation, it is said that unity or division follows entity, but not always absolutely; it may depend on something extrinsic, without which distinction does not follow in act but remains in potency. Thus unity follows being without abstracting from a state, because sometimes unity involves a state, for example, the unity of individuation, universality, order, and so on. These states can depend on accidents at least as conditions, without which that state does not exist. For example, the state of individuation depends on a collection of properties belonging to one individual rather than another, and on the designation of matter, which occurs through quantity. Likewise, the distinction of integral parts depends on quantity because it does not occur without an order that removes their confusion. For this reason, St. Thomas calls those parts material and accidental in the cited Opusculum 70.²⁰ As to the passage from Metaphysics V, we reply that substance has proper parts radically from itself, but formally and in an ordered way from quantity. It also has proper physical parts, namely matter and form, but not extended and integral parts.

In reply to the second confirmation, it is said that although the quantity of the hand is not received in the foot, it does not follow that before quantity the hand and foot are formally distinct parts. Rather, there is only something capable of and receptive to the quantity of a hand and the quantity of a foot. This is to precede those parts radically and in capacity, as things that can be ordered, not as already ordered. Thus different quantities are received in different parts, not parts that are presupposed to be different, but parts that quantity makes different. This is like the view that distinguishes existence from essence and posits matter as inseparable from every form: existence is received in an existing subject and form in existing matter, not by an existence that it presupposes, but one that it provides; it presupposes only a capacity for existing. Similarly, regarding what is added—that the entity of the hand is not the whole substance when quantity is removed—we say it is not the whole adequately. It does not follow, however, that it is formally a part, but only radically, because it is not capable of the same quantity and ordering that is in the whole; in itself, however, it does not have another ordering and distinction of a part in act. Nor does it follow that this entity becomes spiritual, because it remains with a capacity for quantity, which a spirit does not have; nevertheless, it has a certain mode of spirituality, like Christ’s body in the Sacrament.

Finally it is argued: Substance acquires parts not all at once but successively, so that when one is produced, it is not the same part that existed before, but a distinct one. What is produced is not merely new quantity but new substance, since it is produced through nutrition, which is an action distinct from increase; increase formally concerns a greater quantity. Therefore, if nutrition or generation of an added part is distinct from increase, it must have a distinct formal terminus in the account of substance. But it does not terminate in the whole substance, since that pertains to generation itself; therefore, it terminates in a part. Thus before quantity there is a part in substance.

It is confirmed that the parts of substance are united substantially; therefore, diversity is given according to substance, not only according to quantity, for a union is between distinct extremes. Likewise, when quantity is removed, if the parts are confused, they must be united in a different way from how they were united before, under quantity. Why, then, could God not prevent this new union, so that they remain unconfused without quantity?

Finally, it is not impossible in the Eucharist for one half of the host to remain unconsecrated when the other half has been consecrated. Then it is not distinguished from the consumed half by quantity, because the quantity of that half remains there. Therefore, it is distinguished without quantity and, consequently, one half could be preserved by God in this way without quantity, as could the other.

THE REPLY is that nutrition and every successive acquisition of parts formally terminate in substance, but do so under the condition of quantity, by reason of which the substance is formally a distinct part. Increase, on the contrary, formally terminates in quantity, but in quantity inhering in substance; this serves as a condition with respect to increase. Hence nutrition and generation of an added part are distinguished from increase on the side of the formal terminus, because the terminus of nutrition is substance, not total substance but partial substance. Yet the formal character of part does not come from the formality of the terminus of nutrition, but from the added condition of quantity. Thus if it terminated in substance stripped of all quantity, it would not terminate in a part formally but radically.

In reply to the confirmation, it is said that this substantial union of parts cannot occur independently of quantity, which is a condition required for the ordering and designation of parts. Once this designation is presupposed, the substance of the parts themselves is also united. In the view of St. Thomas, designated matter is likewise a principle of substantial individuation, with quantity as a required condition; for without the designation of matter, it is a principle of confusion rather than of division and individuation. Likewise, since substance without quantity presupposes no ordering of parts, it cannot exercise a substantial union among them as ordered; rather, it is said to remain confused, and consequently without substantial union between formally distinct extremes, but only radically.

As to what is added—that when quantity is removed the confusion of parts occurs through a new union—we reply that this is not necessary; rather, only the removal of every union is necessary. For when quantity is removed, parts are not replicated, penetrated, or reduced to a point, all of which would require a positive union. Rather, they are left in the negation of all divisibility, as St. Thomas says in 2 Sent., d. 30, q. 2, a. 1.²¹ A positive union is not necessary for this negation; for parts do not remain to be united through a positive confusion, but only an entity capable of parts and partibility remains, and this is a negative confusion.

As to the case of the consecration of half the host, we reply that the half that is consumed is distinguished from this half not as a part coordinated and distinct from it, but as a certain whole, because it has been converted into the body of Christ, which has its own distinct quantity. If God were to separate that half without converting it into some other substance, while its quantity remained with the other half of the host, then it would be distinguished from the other half by separation as a whole, not by an ordered union as a part; and it would have an order to the divided and distinct quantity that it demands by virtue of this separation.