by jhl

[a paper from fall 2012]:

            Among the several articles in the Summa theologiae on transubstantiation, the prominent role accorded to the little-used phrase ‘dimensive quantity’ is surprising—especially given that out of the one-hundred and forty or so times that it appears in all of Thomas’s corpus, almost half of those instances are found in a span of two questions on the eucharist in the Summa theologiae.[1] The important role that dimensive quantity plays is further highlighted by the radically different conception of Christ’s real presence resulting from the concept’s later rejection by prominent theologians like William of Ockham. The significance of dimensive quantity warrants a closer examination of what dimensive quantity is, its role as a philosophical concept within St. Thomas’s treatment of transubstantiation and, in the face of Ockham’s objections in particular, its philosophical viability.

I. Partes Extra Partes

            There are only a few places one might think to turn to in order to better understand what is meant by dimensive quantity. The most obvious place to begin is Aristotle’s Categories. After distinguishing between continuous and discrete quantities, Aristotle notes that some quantities consist of “parts which bear a relative position to each to each.”[2] Examples of this sort of quantity are lines, whose parts bear “a relative position to each other,” planes for which “it could similarly be stated what was the position of each and what sort of parts were contiguous,” as well as solids and space.[3] For quantities such as number (a discrete quantity) there is no way to show the relation of the parts,  for time (a continuous quantity) since “none of the parts of time has an abiding existence.”[4] We are left, then, with continuous quantities such as lines, planes, surfaces, solids, and space.

At this point, it is helpful to Joseph Bobik’s explication of the matter in order to get a firmer grasp of the nature of dimensive quantity.[5] After observing the distinction Aristotle makes between continuous and discrete quantities, Bobik further distinguishes among these examples quantities that are an intrinsic measure of a substance, e.g., lines, planes, and solids from the sort of quantity which is an extrinsic measure of substance, i.e., space.[6] Taking his cue from the spurious Summa Totius Logicae Aristotelis, Bobik provides a concise definition of dimensive quantity as “quantity having within itself partes extra partes. It has within itself distinguishable parts outside other distinguishable parts—partes distinguibiles (signabiles) extra partes distinguibiles.”[7] From this definition, Bobik highlights what he calls dimensive quantity’s “individuating vitality,” in that its character of partes extra partes allows for the multiplication of forms that would otherwise be indivisible. Thus, for example, a line has distinguishable parts which can be pointed out in distinction from other parts of the line and is potentially divisible.

The fact that each part is distinct from the other and cannot coincide allows for “a plurality of separated dimensive quantities,” and it is precisely by virtue of this potential for multiplication that something like whiteness, a quality, can also be multiplied.[8] As Bobik puts it, “Whiteness, as all accidents other than dimensive quantity, must be received in order to be multiplied. And this recipient must be dimensive quantity itself, or something having dimensive quantity.”[9] The role of dimensive quantity in the individuation of material things, including other accidents becomes fast apparent.

Without dimensive quantity, forms and specific natures would not be individuated but would be indivisible. Bobik writes, “without [dimensive quantity] individuals in the material universe would be like those of the angelic universe, in this that a same nature could never be multiplied.”[10] Moreover, not even prime matter is divisible apart from dimensive quantity. Joseph Owens writes concerning matter: “Alone in virtue of itself it has no individuating features. It has to be regarded first as parceled off by quantity into distinct portions if individuality is to be satisfactorily explained.”[11] Dimensive quantity is, in other words, the principle of individuation in the strictest sense because it is the principle of divisibility in matter. This is one reason why St. Thomas calls dimensive quantity “prima dispositio materiae,” the significance of which is made clearer in St. Thomas’s treatment of transubstantiation.[12]

II. Dimensive Quantity in St. Thomas’s Doctrine of Transubstantiation

            As stated, the phrase ‘dimensive quantity,’ appears most often in St. Thomas’s treatment of transubstantiation. Although the topic treated is primarily theological and pertains to the order of grace, philosophy remains relevant insofar as it is used by theology as a handmaiden—it is in this sense that St. Thomas speaks of theology as depending upon the philosophical sciences, “not as though it stood in need of them, but only in order to makes its teachings clearer.”[13] As will become apparent, a more accurate philosophical understanding of being, generally, and dimensive quantity in this particular case, enables the theologian to properly distinguish between the natural and the supernatural—leading to a more lucid and coherent account of Christ’s real presence in the Eucharist. Therefore a brief sketch of St. Thomas’s doctrine of transubstantiation highlighting the role of dimensive quantity is in order.

St. Thomas discusses dimensive quantity within two separate but closely related issues on transubstantiation. First, he discusses dimensive quantity as it belongs to Christ. This is important in order to clarify how it is that Christ who is truly human, and therefore who consists of dimensive quantity in His human nature, can be said to be present in bread and wine when, clearly, bread and wine are incommensurate to his bones and body. Secondly, dimensive quantity is discussed in the context of the bread and wine—namely, what happens to the dimensive quantity of the bread and wine once their former substances are converted into the body and blood of Christ. Given that accidents are understood as that to which it belongs to exist in a subject (which is usually substance), Thomas must give an account of how the accidents are able to remain when the substance is no longer present. Dimensive quantity figures largely, playing the role of subject of the other accidents, as we will see.

A. The Dimensive Quantity of Christ

Dimensive quantity makes its first explicit debut in the Summa Theologiae in  IIIa q. 76 a. 3. After answering in the affirmative both the first article, that the whole Christ is present in the sacrament, and the second article, that the entire Christ is under each species, St Thomas asks whether Christ is entire under every part of the species. The issue at hand pertains to the mode of Christ’s bodily presence. As the third objection of article three argues, if Christ’s body “always retains the true nature of a body, nor is [. . .] ever changed into a spirit,” then it follows under Aristotle’s definition of body as a “quantity having position,” that “the various parts [of Christ’s body] exist in various parts of place;” but “it is impossible for the entire Christ to be under every part of the species,” therefore Christ is not entire under every part of the bread and wine.[14]

The objection pertains specifically to whether Christ is present under the species by mode of dimensive quantity. Is what appears to be bread the body of Christ in such a way that to eat a part of the bread would be to eat a part of Christ’s body? If so, it is impossible for Christ to be present bodily since his entire body would have to be contained within the dimensions of the bread, which are usually far too small to contain any natural adult human body.[15] Unless the various parts are commensurate so that they are in a single, smaller space (e.g., the hands and feet might be said to be inhabiting the same place and therefore are no longer distinguishable from one another as partes extra partes), it is impossible for Christ to be present entire (totus) under every part of the eucharistic species without violating his bodily nature.

In the respondeo, St. Thomas affirms that Christ is, in fact, present entire under every part of the species. Yet he qualifies this saying that though Christ’s body, understood as “quantity having position” (i.e., his dimensive quantity) is in the sacrament, it is only “by reason of real concomitance.”[16] St. Thomas makes this move in order to maintain the integrity of Christ’s human nature and the reality of His presence in the sacrament. In his response to the third objection, St. Thomas notes that the objection “is based on the nature of a body, arising from dimensive quantity.”[17] However, it is not by dimensive quantity per se that Christ is said to be present, but rather, “Christ’s body is in this sacrament substantively, that is in the way in which substance is under dimensions, but not after the manner of dimensions, which means, not in the way in which the dimensive quantity of a body is under the dimensive quantity of place.”[18] In other words, Christ is present entire under every part of the species, not because he is present by means of dimensive quantity, but rather by mode of substance (per modum substantiae). And it is through his substance, which is inseparable via real concomitance from Christ’s actual dimensive quantity, that even his dimensive quantity can be said to be present.

In the next article, Thomas responds to the question whether the whole dimensive quantity of Christ’s body is in this sacrament.[19] The question naturally follows the previous one as a way of clarifying how, if Christ is present per modum substantiae, his dimensive quantity can be said to be present. His response highlights the inseparability of any material substance from dimensive quantity. As he states in the sed contra, “The existence of dimensive quantity of any body cannot be separated from the existence of its substance.”[20] He highlights, once again, that Christ’s dimensive quantity is present by real concomitance with the substance of his body by making a helpful distinction between how each are present: presence according to dimensive quantity would be “that the whole is in the whole and the individual parts in the individual parts,” whereas presence after the manner of substance “is for the whole to be in the whole and the whole in every part.”[21] Accordingly, in order for the substance of Christ’s body to be present totus it is not requisite that each individual part correspond to every individual part of Christ’s body since His body is not present by means of dimensive quantity; on the contrary, each part contains the whole substance. Thus, the physical size of the eucharistic species do not have to be commensurate with the physical size of Christ’s body in order for his substance to be contained under them.

            That Thomas can speak of Christ’s substantial presence as being direct, while the dimensive quantity of Christ’s body is present by real concomitance presupposes a real distinction between substance and dimensive quantity that is vital to Thomas’s account of transubstantiation. This distinction provides a way for him to make sense of Christ’s real presence in the sacrament while also respecting our sensible experience, “for the accidents which are discerned by the senses are truly present.”[22] To deny the real distinction between substance and quantity, as occurred in later scholastic theology, results in a drastically different doctrine of real presence as shall be seen below.

 B. The Dimensive Quantity of the Eucharistic Species

In addition to playing a key role in maintaining the integrity of Christ’s continuing bodily nature without sacrificing his entire presence in the eucharist by its relation to and distinction from substance, dimensive quantity also plays a notable part in relation to the accidents of the bread and wine that remain after they have been converted into that of the body and blood of Christ.[23] Once the substance of the bread and wine is converted their accidents still remain and this is apparent to the senses. “Even after the consecration,” writes Thomas, “we clearly perceive all the accidents of the bread and wine, namely, color, taste, smell, shape, quantity, and weight: and about these things we cannot be deceived, because the senses are not deceived about their proper sensible objects.”[24] Yet, it cannot be that they belong to the substance of Christ’s body and blood since it is not possible “for Christ’s glorious and impassible body to be altered so as to receive these qualities.”[25] Moreover, since accidents are individuated by the subject in which they inhere, it is not possible for an accident to simply pass from one subject to another. For these and other reasons, St. Thomas concludes that “the accidents continue in this sacrament without a subject.”[26]

The presence of accidents without a subject demands explanation. Appealing to divine power, St. Thomas argues that the accidents subsist without substance. God can do this as first cause of both substance and accident; thus, he can “by His unlimited power preserve an accident in existence when the substance is withdrawn whereby it was preserved in existence as by its proper cause.”[27] Clearly, that the accidents of the bread and wine exist without a proper subject is a miracle. “Thus then, in this sacrament, He upholds the accident in its being, although the subject that upheld it is no longer there.”[28]

The following question in the Summa Theologiae clarifies the nature of this miracle—it is at this juncture that dimensive quantity makes its second major appearance, arguably carrying a heavier weight philosophically than in the previous question on Christ’s substantial presence. It is asked “whether in this sacrament the dimensive quantity of the bread or wine is the subject of other accidents.”[29] Though it is the normally the case that an accident cannot be the subject of other accidents as Aristotle says in his Metaphysics, nevertheless, in transubstantiation God  supernaturally causes one accident to subsist, thereby enabling it to act as the subject of other accidents.[30] This subsisting accident is dimensive quantity; and it is the only accident that subsists without a subject.[31]

St. Thomas locates the miracle of transubstantiation in God’s causing the accident of dimensive quantity to subsist apart from its subject. The remaining accidents, however, “remain founded upon dimensive quantity.”[32] This is so, not because the absence of substance requires a re-ordering of the accidents, but because of dimensive quantity’s nature as the “first disposition of matter.”[33]

What does Thomas mean by this? Elsewhere he explains that “matter does not have division in virtue of the quiddity of substance, but in virtue of the corporeity upon which the dimensions of quantity follow in actuality.”[34] In other words, the divisibility of matter does not follow from substance, but dimensive quantity. As Owens comments, “Quantity with some accompanying accidents is in consequence required for matter to exercise its individuating function.”[35] Simply put, “Matter cannot be conceived as individuating the substantial form unless it is first conceived under quantitative dimensions.”[36] Thus, unlike any of the other accidents, dimensive quantity plays a central role in material substances; so much so that “[i]t appears to make the notion of individuation, which seems deeply rooted in substance and existence, depend ultimately upon an accident.”[37] Without dimensive quantity no material substance could be multiplied or be individuated. So to conceive of material substance  as individuated presupposes dimensive quantity; to think of the parts of any given substance requires that one think of those parts according to the dimensive quantity of a given thing. Even to think of the other accidents of material things is possible only through dimensive quantity.

Even though causing dimensive quantity to subsist per se is accomplished by divine power directly (i.e., a miracle), yet the dependence of other accidents upon dimensive quantity follows from the order of nature. So, in response to the objection that accident cannot be the subject of accident, St. Thomas responds that “inasmuch as an accident is received in another thing, one is said to be the subject of the other, inasmuch as one is received in a subject through another, as the surface is said to be the subject of color.”[38] What is significant about this response is that St. Thomas does not appeal to divine power or the order of grace to explain how dimensive quantity might be called the subject of other accidents. “Even as they were in the substance of the bread,” writes St. Thomas, “the other accidents [. . .] were individuated by means of dimensive quantity.”[39] It is true that normally an accident cannot be the subject of another accident since it does not subsist. Dimensive quantity, however, as it mediates other accidents (i.e., as when he says ‘one is received in a subject through another’), is a primary candidate for subsisting as a subject by divine power once the substance of the bread and wine are no longer present.

In the Summa Contra Gentiles, St. Thomas gives additional reasons why it is dimensive quantity that alone subsists without a subject. First, that dimensive quantity can be thought of as separate seems to indicate its potential separability from substance (and Thomas here notes that the Platonists held dimensive quantity to subsist of themselves—an erroneous view, but still indicative of the nature of dimensive quantity).[40] Second, only dimensive quantity, among all the other accidents, individualizes itself; “the reason being that position, i.e., the order of the parts in the whole, is included in the very notion thereof; since it is defined as quantity having position.”[41] Moreover, since any sort of multiplicity is dependent upon dimensive quantity, as indicated above, when the substance of bread is no longer present, dimensive quantity can act as the subject, enabling the other accidents to remain individualized apart from substance.[42]

Dimensive quantity acts as a safeguard, on the one hand, so that Christ’s presence in the Eucharist be properly conceived. It is necessary to posit that Christ’s dimensive quantity is present due to his physical human nature per modum substantiae in order to ensure that it is Christ the Incarnate Son of God rather than some logos asarkos.[43] Moreover, though the respective substances of the bread and wine are converted into the body and blood of Christ, the species of the bread and wine remain without their substance; instead, by the power of God, dimensive quantity is made to subsist per se and acts as subject to the rest of the accidents. This is fitting because, among other things, dimensive quantity naturally functions as a medium between substance and the other accidents. Given its major role, it is evident that a denial of dimensive quantity would undermine St. Thomas’s doctrine of transubstantiation.

III.William of Ockham

            Among the many scholastic thinkers to challenge St. Thomas’s understanding of dimensive quantity stands William of Ockham (c. 1285-1347).[44] As Marilyn McCord Adams notes, his opposition to the ‘common view’ of quantity was based on an a priori principle which “runs as deep as any philosophical disagreement can go.”[45] Though Ockham maintained that substance, quality, and quantity are distinct, but only in name. “Quantity,” he writes, “does not signify any absolute thing distinct from substance and quality. For they are distinct concepts and spoken sounds that signify the same thing in different ways; and because they signify them in different ways, they are not synonymous names.”[46] This view stands in stark contrast to that of St. Thomas for whom “ . . . the order of thought is based upon the order of reality and reflects it. Because words in turn reflect thoughts, by attending to distinctive modes of predication we may ultimately discern different modes of being.”[47] For Ockham, quantity does not represent anything distinct from substance and quality; as one might imagine, this results in a very different account of Christ’s real presence.

Ockham’s understanding of Christ’s presence in the eucharist is based upon his understanding of different ways that a thing can be said to be in a place. A thing may be in something circumscriptively or definitively. To be in circumscriptively means  “for something to be in the place in such a way that the whole is in the whole place and a part is in a part of the place.”[48] On the other hand, “to be in a place definitively is to be a whole in the whole place and a whole in each part of the place.”[49] The latter way of being in a place is likened to the way an angel is said to be in a place. It is interesting to compare Ockham’s understanding of place with Thomas’s understanding of substantial presence and presence by dimensive quantity, which was referenced earlier. The latter is worth quoting in whole:

. . . the dimensive quantity of Christ’s body is in this sacrament, not according to its proper manner (namely, that the whole is in the whole, and the individual parts in individual parts), but after the manner of substance, whose nature is for the whole to be in the whole, and the whole in every part.[50]

What Aquinas attributes to substantial presence, Ockham attributes to definitive presence; and the same seems to go for presence by dimensive quantity and circumscriptive presence. As we saw, for St. Thomas, Christ is said to be present per modum substantiae while the dimensive quantity of his body and blood are present by real concomitance. Ockham argues that the body and blood of Christ are present definitively, which would seem to coincide with St. Thomas’s understanding. Yet, the similarities are found to be purely superficial upon a deeper look.

On Ockham’s view, angels can exist in various places because they are incorporeal beings and are thus indivisible; however, any extended material substance is present to a place through its intrinsic parts circumscriptively.[51] Since Ockham does not posit a real distinction between substance and quantity, according to which a material thing’s substance might be present definitively (as angels are) while its dimensive quantity qua dimensive quantity would only be present in a place circumscriptively, he maintains that for Christ’s body and blood to be present definitively entails that “all of its parts will exist at the same place.”[52] What this means is that if the substance of Christ’s body and blood can exist in a place definitively, then a fortiori, they can be present in several places at once circumscriptively.[53] Thus, in addition to existing in several places at once, Ockham argues that a corporeal substance “can exist everywhere by divine power.”[54] And with regard to the eucharist, “even though the body and blood of Christ do exist in the Eucharist definitively, they could exist there circumscriptively without any logical difficulty.”[55] By identifying quantity with substance and quality, Ockham can consistently argue that the substance of Christ’s body and blood is present in terms of its ‘intrinsic parts,’ which is also to say, according to its dimensive quantity and quality (which are only conceptually distinct from substance) immediately by the power of God.[56]

Of course, some of Ockham’s more traditionally inclined contemporaries raised concerns about his identification of quantity with substance and quality. Pertinent to this discussion is Ockham’s argument which Adams summarizes well:

if quantity is not a thing distinct from substance and quality, which inheres in the substance directly and is the immediate subject of the qualities, then when the substance of the bread is converted into the substance of the body of Christ, the qualities of the bread would exist without inhering in any subject at all.[57]

Ockham’s response is formidable. He argues that, on the assumption that quantity is distinct from substance and quality, quantity’s dependence on substance is greater than that of quality on quantity.[58] If God can make dimensive quantity exist per se apart from substance, it should be less miraculous for God to cause quality to also subsist without inhering in quantity as subject. As Adams describes, “God can make one absolute accident exist without its subject as much as any other.”[59]

IV. Dimensive Quantity and Quality

            It is worthwhile to consider Ockham’s last noted objection regarding quantity’s fittingness as the subsisting subject of other accidents post-consecration; by doing this it may be possible to get a firmer grasp of Thomas’s rationale in identifying quantity as the subject of the other accidents. The question comes down to this: was Thomas’s prioritizing of dimensive quantity merely an arbitrary selection? Is Ockham right in thinking that quality could just as easily subsist per se? Or is there a fundamental philosophical reason that compels St. Thomas’s choice of dimensive quantity?

In the Summa Contra Gentiles Thomas notes:

Among these accidents a certain order is to be noted. Of all accidents, dimensive quantity adheres most closely to substance: afterwards, with quantity as a medium, the substance is affected with qualities: for instance with color by means of the surface. Hence the division of the other accidents is incidental to the division of quantity.[60]

Similarly, in the Summa Theologiae, St. Thomas notes explicitly that dimensive quantity is the subject of the accidents, “rather than the other way around.”[61] One reason for this was already stated above; it is because dimensive quantity individuates itself and because it can serve to individuate other accidents that it is caused to subsist per se in transubstantiation. Moreover, it was pointed out that dimensive quantity is an apt candidate inasmuch as it receives quality, according to which it can be called the subject of it, “as the surface is said to be the subject of color.”[62] St. Thomas is clearly intent on maintaining the priority of dimensive quantity, yet the reason why he chooses dimensive quantity as subject over any other accident is not always evident—especially in light of Ockham’s critique. Fortunately, there are places apart from his treatment on the Eucharist that prove helpful on this question.

St. Thomas’s treatment of the difference between abstraction and separation  in his commentary on Boethius’s De Trinitate provides a helpful angle from which to examine this issue more closely. In the process of answering a question concerning the proper subject matter of mathematics, Aquinas lays out the various ways in which the intellect abstracts.[63] He first distinguishes between the two operations of the intellect, apprehension and judgment. According to apprehension the intellect grasps a thing’s quiddity, and according to judgment the mind joins and divides. Due to the nature of the second operation of the intellect, i.e., of joining and dividing, it follows that it cannot abstract things that are united in reality since “the abstraction would signify a separation with regard to the very being of the thing.”[64] Through the first operation, however, it is possible to abstract things that are not separate or separable in reality. The intellect can abstract things either separated or united in reality as long as one can be understood without the other (i.e., “if one thing does not depend on another with regard to that which forms the definition of the nature”).[65] Accordingly a man might be understood apart from whiteness, even though he is a white man, but not vice versa.

Abstraction is further distinguished by two modes of union of the thing abstracted: either union of part and whole or union of form and matter. The latter distinction is important because the distinction between substance and accident falls into this category. Thomas writes, “. . . because all accidents are related to the underlying substance as form to matter, and because it is the nature of every accident to depend upon substance, no form of this kind can be separated from substance.”[66] Based upon what he has written here one might conclude that Thomas’s decision to view dimensive quantity as somehow unique among the accidents is at best arbitrary, or at worst misguided. Yet, St. Thomas adds an important qualification:

But accidents befall substance in a definite order. Quantity comes to it first, then quality, after that passivities and actions. So quantity can be thought though of in substance before the sensible qualities (because of which matter is called sensible) are considered in it. Quantity, then, according to its essential nature does not depend upon sensible matter but only upon intelligible matter.[67]

Such a qualification is significant because it clearly indicates the important role that quantity plays in relation to the other accidents (and it is possible that St. Thomas had transubstantiation in mind here); but the fact that quantity does not depend upon sensible matter offers grounds for the sort of abstraction in which one thing can be understood without the other.

According to St. Thomas, quantity clearly does not depend upon quality (i.e., matter as sensible) but only upon intelligible matter. The parallel example to this would be snub and nose, which is given in the context of abstractions of things of dependence (where the dependence clearly goes one way). Thus, just as snub cannot be known apart from nose, though nose can be known apart from snub, so quantity can be known apart from quality, but not vice versa; there is, in other words, a relation of dependence for quality, but not for quantity. This one-way dependence of quality upon quantity is made even more clear when St. Thomas explains that “sensible matter cannot be abstracted by the intellect, because sensible qualities cannot be understood unless quantity is presupposed.”[68] So, clearly, between quantity and quality the former takes precedence.

If one were to stop here it might seem that, at most, the relationship between quantity and quality might, at best, be analogous to the relationship of substance and quantity. Yet, as St. Thomas clarifies, while quantity might be known through abstraction apart from quality, the relation between substance and quantity is of a different nature. “Substance,” he writes, “which is the intelligible matter of quantity, can exist without quantity. Consequently, the consideration of substance without quantity belongs to the order of separation rather than to that of abstraction.”[69] Substance considered without quantity follows the second operation of the intellect by which it joins and divides—that is, substance not only is able to be thought of apart from quantity, but it can also exist apart from it.

Since substance is separable from quantity,  it follows that the two can be considered independently from one another. On the other hand, while quantity may be considered in abstraction from quality (just as nose can be considered apart from snubness), it does not work the other way; i.e., since ‘snub’ includes nose in its definition it is not intelligible apart from it. Therefore, it seems that St. Thomas’s choice of dimensive quantity as the subject for the other accidents rests in a more general concern to respect the order of knowing since for quality to subsist per se apart from quantity would posit something which is absolutely non-intelligible rather than something that is coherent without being natural or normal.[70]

V. Conclusion

            Dimensive quantity clearly plays an essential role, not only in St. Thomas’s account of the eucharist, but also in his view of matter. Without dimensive quantity, it becomes very difficult to account for Christ’s continuing human nature as he is present in the Eucharist or the bread and wine’s remaining accidents without their substance. The importance of dimensive quantity was further highlighted by showing how Ockham’s philosophy, one that denies dimensive quantity as something distinct from substance and quality, stemmed from a number of contrary philosophical assumptions and resulted in an upheaval of St. Thomas’s doctrine of transubstantiation, as well as his more general view of material substance. After a brief overview of Ockham’s position, St. Thomas’s view was revisited in order to shed light upon the rationale behind his stance, thereby emphasizing just how fundamental dimensive quantity is to the Common Doctor.

Though there are quite obviously a number of unaddressed issues with regard to Ockham’s objections, this paper has aimed at least to shed a small amount of light on the importance of the matter.

[1] Of the 141 cases of dimensive quantity, 62 are found in questions 76-77 of the tertia pars. The only other concentrated appearance of the phrase appears in Summa Contra Gentiles IV, cc., 63, 65, which is, not surprisingly, on the Eucharist. Apart from these two cases, there is a brief mention of dimensive quantity in relation to glorified bodies in the Scriptum super Sententiis, lib. 4 d. 44 q. 2 aa. 2, 3 as well as in d. 49 q. 2, on whether the saints seeing God, comprehend him.

[2] Categories VI.

[3] Ibid.

[4] Ibid.

[5] Joseph Bobik, “Dimensions in the Individuation of Bodily Substances,” Philosophical Studies Vol. 4, 1954: 60-79.

[6] Bobik, “Dimensions,” 60.

[7] Bobik, “Dimensions” 62. Regarding the spurious nature of the work, Bobik writes, “Though this work has been attributed to St. Thomas, it is now generally admitted to be spurious. This is not to say that it has no value in philosophical inquiries,” 62, n.5.

[8] Bobik, “Dimensions,” 62.

[9] Bobik, “Dimensions,” 63-64.

[10] Bobik, “Dimensions,” 65.

[11] Joseph Owens, “Thomas Aquinas: Dimensive Quantity as Individuating Principle,” Medieaval Studies, Vol, 50. Pontifical Institute of Medieval Studies, 1988, 280.

[12] The description of dimensive quantity as the first disposition of matter appears in ST Ia q. 3 a. 2, where St. Thomas writes, “quantitas enim dimensiva est quae primo inhaeret materiae,” in IIIa q. 77 a. 2, where he writes, “quia prima dispositio materiae est quantitas dimensiva,” and finally in his commentary on the Metaphysics Bk. VII, l. 2, n. 14: “Quantitas enim dimensiva videtur inesse materiae immediate, cum materia non dividatur ad recipiendum diversas formas in diversis suis partibus, nisi per huiusmodi quantitatem.”

[13] ST Ia q.1 a. 5 ad. 2.

[14] IIIa q. 76 a. 3 ob. 3.

[15] As St. Thomas writes in the Summa Contra Gentiles IV, c. 52: “And yet it is evident that Christ’s body is greater in quantity than the bread that is offered on the altar. Therefore, seemingly, it is impossible for Christ’s body to be truly present in this sacrament: unless one were to say that one part of Him is here, and another part there.”

[16] IIIa q. 76 a. 3.

[17] IIIa q. 76 a. 3 ad. 3.

[18] IIIa q. 76 a. 3. The definition of dimensive quantity as “quantitas habens situm” is repeated in SCG IV, c. 65 and Super Sent., lib. 4 d. 44 q. 2 a. 2 qc. 2 co.

[19] IIIa q. 76 a. 4.

[20] IIIa q. 76 a. 4. In the next section, we will discuss the subsistence of the accidents of the bread and wine, which obviously includes the dimensive quantity, apart from the substance of the bread and wine. St. Thomas’s response here might be taken to contradict what he will later say concerning the bread and wine. One must remember that at this particular juncture he is concerned to maintain the presence of Christ’s human person (i.e., the substance of body and blood) in all His fullness. In order to do so, it is necessary that Christ’s dimensive quantity be present through substance. The bread and wine, on the other hand, are not substantially present and the accidents are said to subsist by the power of God. If the substance of a material thing is to be present, it is necessary that dimensive quantity follow; it is not necessary, however, for substance to be present if dimensive quantity is subsistent. The existence of material substance is tied to dimensive quantity in a non-reciprocal way. The dimensive quantity of a thing might be separated from its substance by divine power, but a material substance cannot even be conceived apart from its dimensive quantity—in other words, the latter, because it is a contradiction, is simply not possible.

[21] IIIa q. 76 a. 4 ad. 1.

[22] IIIa q. 75 a. 5 ad. 2.

[23] Dimensive quantity also plays an important role in the question of place and movement, IIIa q. 76 aa. 5-6, “Whether the body of Christ is in this sacrament locally.” Since a body is said to be in a place “according to the manner of dimensive quantity, namely, inasmuch as it is commensurate with the place according to its dimensive quantity,” Christ is said to be present where his dimensive quantity is per se, i.e., in heaven. And since Christ’s body is not in the sacrament according to place but is “at rest in heaven” it follows that it is not movably in the sacrament.

[24] SCG IV, c. 52. Aristotle speaks similarly in De anima II.6, 14-17: “Each sense has one kind of object which it discerns, and never errs in reporting that what is before it is color or sound.”

[25] IIIa q. 77 a. 1.

[26] IIIa q. 77 a. 1.

[27] IIIa q. 77 a. 1. Thomas likens this to the virgin birth, “. . . even as He formed a human body in the Virgin’s womb, ‘without the seed of man’ (Hymn for Christmas, First Vespers).” He explains this also in IIIa q. 75 a. 5 ad. 1: “As is said in the book De Causis, an effect depends more on the first cause than on the second. And therefore by God’s power, which is the first cause of all things, it is possible for that which follows to remain, while that which is first is taken away.”

[28] SCG IV, c. 55. Similar to his explanation in ST IIIa q. 77 a. 1, Thomas here writes, “Now the divine power can produce the effects of any second causes whatsoever, without these second causes, even as it could fashion man without seed, and cure a fever without the operation of nature. This is because God’s power is infinite, and because He bestows on every second cause its active energy; so that He can uphold the existence of the effects of second causes, without the second causes themselves.”

[29] IIIa q. 77 a. 2.

[30] Cited in IIIa q. 75 a. 5 obj. 4. “But this is impossible; for ‘an accident cannot have an accident’ (Metaph. iii).”

[31] SCG IV c. 55, “only dimensive quantity subsists without a subject, and affords a support to the other accidents.”

[32] IIIa q. 77 a. 2.

[33] IIIa q. 77 a. 2.

[34] Super Sent., lib. 1 d. 8 q. 5 a. 2 co. quoted in Owens, “Dimensive Quantity as Individuating Principle,” 283.

[35] Owens, “Dimensive Quantity as individuating Principles,” 284.

[36] Owens, “Dimensive Quantity as Individuating Principle,” 284.

[37] Owens, “Dimensive Quantity as Individuating Principle,” 281.

[38] IIIa q. 77 a. 2 ad. 1.

[39] IIIa q. 77 a. 2 ad. 2.

[40] SCG IV c. 55.

[41] SCG IV c. 55.

[42] IIIa q. 77 a. 2 ad. 2.

[43] IIIa q. 75 a. 1.

[44] Others, according to David Burr’s historical account, were a number of Franciscans: William de la Mare, Matthew of Aquasparta, John Pecham, Peter Olivi, Roger Marston, and William of Falgar. Cf., Burr, “Eucharistic Presence and Conversion in Late Thirteenth-Century Franciscan Thought,” Transactions of the American Philosophical Society, New Series, Vol. 74, No. 3 (1984): 1-113.

[45] Marilyn McCord Adams, William Ockham (Notre Dame, IN: University of Notre Dame Press, 1987), 1:175. As she writes elsewhere, “Ockham agrees that, in the natural order of things material substances are hylomorphic composites that are located in place. Otherwise he rejects virtually every aspect of Aquinas’s picture, not least the notion that quantity is ‘a skin’ between material substance and its qualities, and reconceives their metaphysical structure from the ground up,” Some Later Theories of the Eucharist: Thomas Aquinas, Giles of Rome, Duns Scotus, and William of Ockham (Oxford: Oxford University Press, 2010), 152.

[46] Quodlibet IV, q.27 quoted in Adams, Ockham, 1:175.

[47] John F. Wippel, The Metaphysical Thought of Thomas Aquinas: From Finite Being to Uncreated Being (Washington, DC: The Catholic University of America Press, 2000), 216.

[48] Quodlibet IV, q. 21.

[49] Quodlibet IV, q. 21.

[50] IIIa q. 76 a. 4 ad. 1.

[51] Quodlibet IV, q. 21. A thing’s ‘intrinsic parts,’ are, according to Ockham, ‘parts’ of the substance. Adams provides a concise description of Ockham’s view, “material substance and its essential parts prime matter and substantial form are divided into integral parts of themselves,” Some Later Theories of the Eucharist, 153.

[52] Adams, Ockham, 1:189. The discussion is, of course, much more complex and convoluted than this simple presentation that I give and takes place in the context of the question of whether several things can exist in the same place, which is related to the question of dimensive quantity but far too involved for this paper. For a more thorough account of Ockham’s view on quantity cf., Adams, Ockham, 1:169-213, 2:671-95, Some Later Theories of the Eucharist, 152-76, and Quodlibet IV, qq. 18-35.

[53] Cf., Adams discusses this in great depth in Ockham, 1:190.

[54] Rep. IV, q. 6 quoted in Adams, Ockham, 1:190.

[55] Adams, Ockham, 1:190.

[56] Cf., Quodlibet IV, q. 20, “Is an extended material substance immediately present to a place through its intrinsic parts?” Where, as one might guess, he answers in the affirmative.

[57] Adams, Ockham, 1: 191.

[58] Adams, Ockham, 1:192.

[59] Adams, Some Later Theories of the Eucharist, 221. Ockham posits several other arguments against quantity acting as subsisting subject for quantity, but it is beyond the purview of this paper. Cf., Adams, Ockham, 192.

[60] SCG IV, c. 53.

[61] IIIa q. 77 a. 2.

[62] IIIa q. 77 a. 2 ad. 1.

[63] Super Boethium de Trinitate 5.3 (hereafter In DT), trans Rose E. Brennan, S.H.N. and Armand Mauer, http://www.josephkenny.joyeurs.com/CDtexts/BoethiusDeTr.htm (accessed December 8, 2012).

[64] In DT 5.3.

[65] In DT 5.3.

[66] In DT 5.3.

[67] In DT 5.3.

[68] In DT 5.3.

[69] In DT 5.3.

[70] Cf., In DT 4.3 ad. 1 where St. Thomas distinguishes between two types of non-intelligibility. The first that is based upon deficiency of intellect and therefore does not contain any contradiction; and the second which is on the part of the proposition which does imply a contradiction. To have quality without quantity would be non-intelligible in this second absolute sense.