Doubting Thomas: A Modest Defense of Transubstantiation
Thomas L. Humphries
The Catholic Church maintains that in the Eucharist the bread and wine are converted into the body and blood of Christ, and, furthermore, that this implies the entire or whole presence of Christ when the Eucharist is properly celebrated. The Thomistic formulation of the replacement of the bread and wine with the substance  of Christ remains an important explanation of the Catholic doctrine (explicitly formal teaching). Nevertheless, if the Thomistic position is incoherent or contradictory, it will not serve as a satisfactory explanation of the Eucharistic mystery. The doctrine seems to commit the believer to holding that a particular host  is identified with Christ, which is obviously problematic, as Christ has a set of properties that are different from a host. The doctrine also appears to commit one to assert that an accident is both a thing which inheres in a substance and a thing which does not inhere in a substance. In addition, believers also seem committed to asserting the multilocation of a material body, which is restricted to unilocation. In what follows, I shall articulate and defend the (Catholic) Thomistic formulation of transubstantiation.
I wish to make it clear from the outset, first, that I do not intend to offer a philosophical proof or argument that the real presence does occur; rather, I intend to defend the doctrine by showing that Thomas's position is not guilty of the contradictions mentioned above; and, secondly, that I will not attempt to resolve the mystery of the Eucharist, but only to defend Thomas's account as a possible explanation of this mystery. In this, I believe I have written in the spirit of Elizabeth Anscombe:
When we call something a mystery, we mean that we cannot iron out the difficulties about understanding it and demonstrate once for all that it is perfectly possible. Nevertheless we do not believe that contradictions and absurdities can be true, or that anything logically demonstrable from things known can be false. And so we believe that there are answers to supposed proofs of absurdity, whether or not we are clever enough to find them. 
This project will require a brief explication of the doctrine in preface to a discussion of seeming contradictions and logical impossibilities. In defining the doctrine, I will not focus on theological arguments against the Catholic understanding of Scripture. I will focus, instead, on defending Thomas's doctrine as logically possible.
II. The Doctrine
The first written account of the Eucharist is found in Paul's first letter to the Corinthians:
I received from the Lord what I handed on to you, namely, that the Lord Jesus on the night in which he was betrayed took bread, and after he had given thanks, broke it and said, "This is my body, which is for you. Do this in remembrance of me." In the same way, after the supper, he took the cup, saying, "This cup is the new covenant in my blood. Do this, whenever you drink it, in remembrance of me."…This means that whoever eats the bread or drinks the cup of the Lord unworthily sins against the body and blood of the Lord. 
The Catholic Church understands this teaching to mean "that in the sacrament of the most holy Eucharist are contained truly, really, and substantially, the body and blood together with the soul and divinity of our Lord Jesus Christ, and consequently the whole Christ." 
1 Christ's Real Presence
The first and most basic claim held by Catholic Eucharistic teaching is that (1) Christ's body is present in the Eucharist. In support of this "real presence," the words of institution, "This is my body," are taken as both a moral lesson and a metaphysical fact. The opposed, figurative position holds that the words of institution are intended as only a moral lesson. As I am defending transubstantiation as an explanation of the real presence, I will not consider theological arguments between the real and the figurative positions. The position, simply stated, is that when a priest consecrates the hosts, Christ's body is made present. 
"Real," however, is somewhat ambiguous in this discussion, as there are different ways of being really present. For instance, something is really present when it is partially present as well as when it is wholly present. I will mention some positions that hold a real, but not whole presence later. The Catholic position I am defending claims that Christ is wholly present in a sense that is opposed to only being only partially present. "Entirely" and "totally present" are also used to name this whole presence.
Aquinas argues that the real presence of Christ's body guarantees the presence of Christ in his entirety. This relies on two key teachings: (2) the presence of Christ's body necessitates the presence of his blood, soul, and divinity; and (3) when Christ is present in "body, blood, soul, and divinity," he is entirely present.
In support of (2), Aquinas argues that "from natural concomitance there is also in this sacrament that which is really united with [Christ's body]…For if any two things be really united, then wherever the one is really, there the other also be…[and] his soul is always really united with his body."  The Church teaches that Christ is truly human. The Church rejects the claim "that the Son of God 'came to be from things that were not.'" And, the Church rejects teachings that Christ was first a man who then became God.  Thus, the Church holds that "Christ…is to be acknowledged in two natures without confusion, change, division, or separation."  Christ's person, or "hypostasis," is an inseparable union of divinity and humanity. Therefore, the Church maintains that in the Eucharist, Christ's body is present, and, by nature of the person of Christ, the soul and divinity of Christ are present, as well. 
According to Church teaching, to be human is to have a body, blood, and a soul. To be God is to have divinity. As Christ is both man and God and nothing else, his complete nature involves body, blood, soul, and divinity. Thus, a presence of Christ in body, blood, soul, and divinity is rightly called "entire" or "whole" (claim (3)). In contrast, some hold a real presence of Christ's spirit but not his body in the Eucharist. 
One can interpret a "spiritual presence" of Christ to mean one of three things: (i) Christ is present only in his human soul; (ii) Christ is present only in his divinity; (iii) a combination of (i) and (ii). Each of these claims, however, is directly opposed to the nature of the person of Christ as elucidated in notion of the indissoluble hypostatic union. If one holds that Christ's nature is truly both God and man, a presence of only (i) Christ's human soul, (ii) his divinity, or (iii) his soul and divinity (and not his body and blood) is not a presence of Christ, but a presence of a part of Christ. But, according to the union of Christ's natures, these parts of Christ are inseparable. Moreover, the words of institution do not support a merely spiritual presence, as they specifically mention body and blood. Thus, the Church holds that Christ is really (and not figuratively) and wholly (and not partially) present in the Eucharist.
3 Eucharistic Conversion
Because Christ is wholly present in the Eucharist, we may ask how he gets there. Aquinas offers three ways for a thing to be in a place: 1) by changing place, 2) by the conversion of another thing already in the place, or 3) creation of the thing from nothing.  He rejects the first manner of Christ's coming to be in the Eucharist for three reasons: i) "it would follow that [Christ's body] would cease to be in heaven," ii) "every body moved locally passes through all intermediary spaces," and iii) "because it is not possible for one movement of the same body moved locally to be terminated in different places at the one time [sic]."  He rejects the third way because it against the nature of Christ to be created. Thus, Aquinas's basic argument is that Christ must be present by one of three ways. But, two of those ways (my numbers 1 and 3) are unsatisfactory. Therefore, by a via negativa, Aquinas concludes that there must be a Eucharistic conversion.
"Adduction" is the name given to the notion that Christ's body descends from heaven into the Eucharist, and is explicitly rejected by the Apostolic Creed, which states that "[Christ] is seated at the right hand of the Father." The Creeds profess that the resurrected Christ is present in heaven; to provide an explanation of the Eucharist that requires Christ to leave heaven is problematic. Thus, a Catholic cannot accept i) that Christ's body ceases to be in heaven, and must deny 1) that Christ is present in the Eucharist by changing place. Closely related to this movement from heaven to the Eucharistic species is the notion that entails the movement of Christ through all intermediary spaces. In some way, we would say that Christ was present in heaven, then in the air around the Eucharistic species, and, finally, in the Eucharistic species. But, no one holds that Christ is really and wholly present in the air around the Eucharist directly before he is present in the Eucharist. Thus, Catholics deny ii) that Christ passes through each region of space between the host and his present location when coming to be in the Eucharist, and thus, must also deny 1) that Christ is present in the Eucharist by changing place.
The third notion Aquinas considers and rejects (my iii) in rejecting the notion that Christ is present in the Eucharist by changing place is related to many difficult problems of multilocation, which I shall discuss in more detail later. It should suffice to note here that if Christ becomes present in the Eucharist by changing place, he would have to move from each particular host to the next in order to be present in each host. One can easily see the compounding nature of the problem, as more than one host is consecrated at the same time. If Christ changes place from l1 to l2, he is no longer in l1, but he must be in l1 and l2 simultaneously. Accordingly, Catholics deny 1) that Christ is present in the Eucharist by changing place.
In regards to the claim 3) that Christ comes to be present in the Eucharist from nothing, Christ cannot come to be really and entirely present in a place from nothing, for that would entail that he be created from nothing (ex nihilo), and Christ cannot both be created and remain God. According to early Trinitarian theology, Christ is "eternally begotten of the Father,"  and the Christian must be wary of falling into the Arian heresy of denying Christ's divinity.  Furthermore, Christ already exists, and, therefore, cannot be created from nothing.
Aquinas, therefore, concludes that the second way of being present must be the manner in which Christ becomes present; (4) there is a conversion of the bread and wine into the body and blood of Christ. This conversion, however, is not of the ordinary sort. Usually, change implies that one subject is F at time t1 and not-F at t2. Aquinas argues that (5) this conversion is from the whole substance of the bread and wine into the whole substance of Christ. Thomas calls this change a type of "substantial change."
I should note here that in a very technical sense, bread and wine are probably not substances; they are artifacts or "types of stuff," but they are not particular individuals. Nevertheless, Thomas speaks of the "substance of bread and wine" throughout his discussion of the Eucharist. I do not think that he means to argue that bread and wine are substances in the very technical sense. Moreover, nothing is lost in the doctrine if bread and wine are not technical substances. Instead of one substance being replaced by another, one mass of stuff (i.e. bread) is replaced by a substance (i.e. Christ). Nevertheless, I will continue to speak of bread and wine as though they were substances with the note that if they are not, nothing will be lost for the doctrine.
As Anthony Kenny explains, "according to scholastic theory, substance is not an imperceptible part of a particular individual. It is not a part of an individual; it is that individual."  He notes that this is not to be confused with Locke's notion of substance: "some thing, we know not what, which supports the sensible qualities we find united in things."  For Aquinas, substance is not a part of some thing, as Locke is commonly thought to have argued. John Wippel notes that "Aquinas refers to first substance as the particular or individual substance of which all else is predicated,"  and, thus, substance can be thought of as a particular subject. In the Eucharist, the bread and wine are converted into Christ; there is no part of the Eucharistic species  that becomes some part of the body and blood.
Following Aristotle, Aquinas divides the world into matter and form. Brian Davies notes, "[Aquinas] calls the capacity (or 'potentiality') a thing has for changing substantially its 'matter…A form is that by which something actually is what it is, whether substantially or accidentally."  The meaning of the doctrine of transubstantiation is that there is a change at the level of substance, which is a matter/form composite. Transubstantiation, then, is a very unique "change,"  for it claims not only that the substantial form changes, but that the matter (potentiality to change) changes as well. If the change is merely formal, that is, the same matter remains, then it would be true to say of the bread that it naturally has the potentiality to be Christ, as matter is the potential for change. This, however, is absurd. Therefore, if there is a substantial change, it is a change of the entire substance, both matter and form. Thus, the Church holds that (5) this conversion is from the whole substance of the bread and wine into the whole substance of Christ.
Thus, the Church has condemned the explanation of substantial transformation, as this change is at the level of form or "kind," and not a replacement of one substance with another. Or, as I have mentioned before, if the bread is not technically a substance, "transubstantiation" is the replacement of some stuff, namely bread, with the substance, Christ. That is to say that the Eucharistic conversion is not only a change in form or kind, but a change of particular subject. Luther seems to have grasped the difficulty of this notion of "change" of substance with his suggestion of consubstantiation: the substance of Christ exists along with the substance and accidents of the Eucharistic species. This formulation of an explanation of the real and substantial presence of Christ in the Eucharist has the major appeal of not having to explain how an entire substance could be converted into another completely different substance. There is no need to posit a mysterious and supernatural conversion; yet, consubstantiation still retains something of a mystery as Christ is really and wholly present. Indeed, because consubstantiation retains this mysterious aspect, but does not rely on a substantial "change" or conversion, consubstantiation is a strong position.
Consubstantiation, however, requires either that Christ is created from nothing or that he moves from Heaven to the host, both of which are impossible for the Christian to coherently hold as discussed before. Also, the words of institution follow a pattern more conducive to transubstantiation than consubstantiation. "This is my body" follows a pattern expressing transubstantiation. "This bread contains my body" follows a pattern expressing consubstantiation, of which it is true to say that the bread entirely remains bread, though it is infused with the substance of Christ as well.
4 Bread and Wine
Another major point in the Catholic doctrines concerning the Eucharist follows from the previous, as stated by the Council of Trent: "What is beheld by the eyes, or perceived by the other senses is in a wonderful and unspeakable manner, without any subject matter."  This is stated in the Thomistic sense as (6) the accidents of the bread and wine exist without a subject, and raises the controversy of the existence of accidents without inhering in a substance. Furthermore, one will note that the properties (accidents) of Christ are not present in a perceivable manner in the Eucharist (e.g. Christ does not appear like a human in the Eucharist). I shall discuss both issues later.
When the Eucharistic species are changed into Christ, only the accidents of bread and wine remain. One would expect the accidents to be replaced along with the substance. A common way of explaining this assumes some principle of illusion, as if the senses are fooled into thinking that the accidents of bread and wine are present. Aquinas rejects this notion, "for the accidents which are discerned by the senses are truly present."  The issue is not whether the accidents actually exist, but how they exist. They certainly do not inhere in the bread and wine. Using "change" in the sense of "substantial change" outlined above (meaning that the bread and wine are replaced by Christ), Aquinas notes the obvious: "What is changed into another thing no longer remains after such change. "Furthermore, they do not inhere in Christ as Christ does not have the properties of bread (e.g. he is not one inch in diameter, white, and round).
There is one, final, very important point about the Eucharistic doctrines of the Church: the Eucharist is a sacrament. According to Catholic belief, a sacrament is an outward sign of an inward grace instituted by Christ for the sanctification of man. In this sense, a sign is a physical reality that expresses the action of God to make one holy: the physical sign causes the spiritual grace.
The words of institution clearly mark Christ's institution of the sacrament of the Eucharist. The outward sign is the consecrated host, which causes the inward grace of Christ, which, when consumed, gives eternal life.  As such, (7) the Eucharist is an efficacious sign. An efficacious sign is simply a thing which causes what it signifies. A coronation serves as an example: the crown is the sign of the king, and, by virtue of the crown placed on his head, the man becomes king: the crown causes what it signifies. Military rank works in the same fashion. In a similar manner, sacraments are believed to cause what they signify. The consecrated host is the efficacious sign of Christ's real and whole presence. Where the consecrated host is present, there also is Christ.
6 The (Real) Position
I may now restate the list of propositions that are important to this paper concerning the Catholic, Thomistic doctrines about the Eucharist:
(1) Christ's Body is present in the Eucharist.
(2) The presence of Christ's body necessitates the presence of his soul and his divinity.
(3) When Christ is present in "body, blood, soul, and divinity," he is entirely present.
(4) There is a conversion of the bread and wine into the body and blood of Christ.
(5) This conversion is from the whole substance of the bread and wine into the whole substance of Christ.
(6) The accidents of the bread and wine exist without a subject.
(7) The Eucharist is an efficacious sign.
III Logical Possibility
Having explained relevant parts of the doctrine, I may now turn to a defense of the Thomistic position of transubstantiation. Specifically, I will reject Kenny's defense of how accidents could exist without inhering in a substance and, then, argue that the argument from the definition of an accident fails to grasp Aquinas's position. I will argue that the doctrine of transubstantiation does not force one to claim that Christ is small, white, and round in considering identity claims in the Eucharist. Finally, I will address the problem of multilocation and offer suggestions for understanding the Thomistic position.
One key problem many have cited with the Thomistic explanation of transubstantiation is the existence of accidents without a substance, as stated in (6) above. As Anthony Kenny explains, "If we take the Aristotelian notion of accidents, there is clearly an incoherence in the notion of an accident inhering in no substance: there cannot be any such thing as A's being F if there is no such thing as A."  Most agree that Aristotle could not speak of accidents existing without inhering in a substance. But, Kenny argues that Aquinas has two senses of accident: one is the strict Aristotelian notion; the other is the popular notion. As uses of accident in the popular sense, Kenny cites the examples of the smell of an onion existing after the onion has been removed and the color of a rainbow. Succinctly stated, Kenny's position is that "the popular notion, since it allows a variety of relationships to be indicated by the 'of' in the 'the F-ness of A', can allow for the F-ness to exist after the demise of A."  Kenny calls this process "nominalization." Nominalization, thus, is Kenny's response to this problem of the impossibility of accidents existing without inhering in a subject.
Kenny's onion example, however, fails as an appropriate example. Science holds that smell is perception of things present to the olfactory nerves. Were there no small particles of onion floating around in one's nose, he would not smell onion, unless he has an olfactory hallucination. Because the common understanding of smell is simply that smell is one type of perception of an object that is really present to the senses, this example does not seem satisfactory: one may respond that the substance and accidents of onion are present to the nose in small quantities. Furthermore, hallucination-type events cannot provide examples for transubstantiation, as Aquinas is clear that there is no deception and no fooling of the senses in the Sacrament. 
Nevertheless, this nominalization claim seems potentially powerful in understanding Aquinas. Kenny argues that "the 'of' that occurs in expressions such as 'the shape of…' [and] 'the smell of…' covers many other relationships besides that of an accident's inherence in a currently existing substance."  He provides the examples of "the effect of the explosion" and "the story of King Arthur." These examples, however, are not the same type as in the Eucharist, indicated by the form of "the F-ness of A," in which F is an accident and A is a substance that ceases to exist. Kenny's position is intended to show that it is possible for "the F-ness to exist after the demise of A."  These Fs appear to be concrete things of their own accord, and not cases of predication (A's being F). We may say "King Arthur's story," which has the form "A's F," but we can make no sense of "the story-ness of King Arthur," which has the form "the F-ness of A." Ultimately, these F's (effect and story) are not accidents of some substance. Thus, Kenny's suggestion of defending Aquinas by posing two senses of accident does not seem pertinent to transubstantiation, specifically, the claim that (6) the accidents of the bread and wine exist without a subject.
Yet, we often refer to the color of a rainbow, and a rainbow is not a substance. A rainbow is an appearance. The example "the rainbow is curved" has the form "A is F," where F is an accidental predicate. "The rainbow is curved" is not explained by Kenny's nominalization, though it is very similar. Kenny's position applies only to cases in which A is a substance (that ceases to exist) and F is an accidental predicate (which continues to exist). A rainbow is neither a substance nor ceasing to exist. Nevertheless, we accord meaning to the "F-ness of A," namely, "the curvature (curve-ness) of the rainbow." If we are correct in assigning "curved" to the category of accidental predication and in noting that "rainbow" is not a substance, this is an example of an accident existing without inhering in that of which it is predicated. In addition, we speak of the "shade of blue," which also has the form the "F-ness of A," and blue is not a substance; it is a color property (accident). But, providing examples of the existence of some accidents without inhering in a substance is not Aquinas's way of arguing for transubstantiation. It does, however, lend credence to the notion of accidents existing without inhering in a substance.
It is helpful to consider Thomas' position in light of property instances.  Newtonian physics describes a body as a region of space that has been given or infused with certain properties by God.  According to this conception, God may cause a region of space to have properties F, G, and H. Locke seems to have endorsed this notion, as well as contemporary philosophers.  While I do not wish to endorse this metaphysical system in its entirety, it is relevant and important to note that several philosophers consider the notion of certain properties existing solely on God's power as logically possible. Furthermore, such properties can include properties that we normally consider as belonging to, or existing "according to," something other than God's direct power.
While Aristotle was not in a position to speak of accidents existing without inhering in a substance, Aquinas does seem to be in such a position. Aristotle's system is rooted in observation of the universe, from which he infers several "rules." Aquinas picks up where Aristotle left off, so to speak. For Aquinas, observation of the universe is not complete unless it includes God. Aquinas, therefore, admits a distinction between natural impossibility and logical impossibility. Aquinas certainly holds that God cannot do what is logically impossible (e.g. God could never make a square circle, because, by definition, it is not logically possible). However, there are things God can do that nature  cannot. Aquinas argues that this class of things includes the Eucharistic mysteries. Therefore, the claim that transubstantiation is incoherent because of the impossibility of the existence of accidents without inhering in a substance must be a claim of logical impossibility  and not simply one of natural impossibility. In order to defend Thomas, I will argue that (6) is not logically impossible on account of this argument. In support of this, I have already noted the example of the curvature of a rainbow as a logical possibility. But, Aquinas does not argue for the existence of accidents without inhering in a substance by analogy to other examples. Thus, I have mentioned other philosophers who argue that it is logically possible for God to uphold some properties that do not inhere in a substance.
2 The Definition of "Accident"
The argument from the definition of an accident is the most formidable argument supporting the claim of the logical impossibility of (6) the accidents of the bread and wine existing without a subject. According to the definition argument, an accident is "that which inheres in a substance." As (6) is inconsistent with the definition of an accident, (6) is logically impossible by definition.  We may use the example of the "married bachelor." It is logically impossible for a bachelor to be married because, by definition,
No persons who are unmarried men are persons who are married.
All persons who are bachelors are persons who are unmarried men.
No persons who are bachelors are persons who are married.
This argument follows a valid syllogistic form (EAE-1) and argues for the logical impossibility of (6). The parallel argument from definition,
No things which inhere in a substance are things which do not inhere in a substance.
All things which are accidents are things which inhere in a substance.
No things which are accidents are things which do not inhere in a substance.
notes that (6), which requires "Some things which are accidents are things which do not inhere in a substance," must be logically impossible. Claim (6) is inconsistent with the conclusion of the argument. Thus, if Thomas can be defended, it will be by countering one of the premises. Indeed, he specifically considers the second premise in his discussion of the Eucharist. 
Aquinas relies on his distinction between being and essence to show exactly how the definition applies. Essence, quiddity, or nature, for Aquinas, is "what something is:" esse is "that something is." Briefly, Aquinas notes that we can know a thing's nature without knowing its esse. Consider unicorns: Aquinas argues that it is entirely possible to know what a unicorn is without knowing that it is. Also, we may note that "it is not part of the nature [quiddity] of a dog to exist,"  but a dog has a nature and exists. Furthermore, Aquinas argues that there can only be one thing whose nature is to exist, namely, God. All other things must be a composite of esse and quiddity. Thus, Aquinas argues for a real distinction between esse (a thing's existence) and quiddity (a thing's nature).
Thomas denies that an accident is a being which inheres in a subject. "The definition of accident [is not] a being in a subject; but it belongs to the quiddity or essence of…accident to have existence in a subject. But in this sacrament it is not in virtue of their essence [nature] that accidents are not in a subject, but through the Divine power sustaining them."  An accident is a mode of being, and not a being itself. To inhere in a substance belongs to the nature of an accident. Only by virtue of God do accidents exist without inhering in a substance.  The accidents do not cease to be accidents, as their nature (definition) is not taken from them. It still belongs to the nature of the accidents of the consecrated host to inhere in a subject; they exist without inhering in a subject by God's power. If they existed without inhering in a substance by their own nature, they would have a different nature, and, thus, be something other than an accident in the proper sense. 
Considering accidents as property instances, God has at least two ways of instantiating the set of property instances F, G, and H: 1) he may create a substance in which F, G, and H inhere according to their nature, or 2) he may "infuse a certain region of space" with F, G, and H according to the Divine First cause. In both cases, F, G, and H are accidents. This is simply a specific instance of the general principle that 1) God may cause something to exist according to its created nature, or 2) God may cause something to exist according to his power as first cause.
3 Accidental Causes
The Thomistic theory of causation makes use of first and second causes. When Larry hits a baseball with a bat, most agree that the bat's hitting the ball is the cause of the ball's moving out of the ballpark. In this way, we might call the bat the cause of the ball's movement. But, it also seems natural to say that Larry, who swung the bat, is also causally related to the ball's moving out of the ballpark. In this way, Larry is the β-cause of the ball's moving out of the park. Furthermore, without the cause, the cause could not effect the ball's moving out of the park, but the α-cause is still an effective cause of the ball's movement out of the park.
Aquinas argues that God is the first cause of everything. God allows created things to have causal power as well, so that we may call created things "secondary causes." Indeed, the oddity of this particular facet of Aquinas's position is not that there is a first cause, but that there could be a second, or intermediary cause. In his arguments for secondary causes as efficacious, Aquinas argues that "Divine Providence works through intermediaries."  God, in effect, gives created things the power to be efficacious. If God were not working through secondary causes, all our activity associated with secondary activities would be useless. When Larry swung the bat and hit the ball, if the ball moved directly on the cause of God, swinging the bat at the ball would be useless. With this distinction between primary and secondary causes, Aquinas notes that a substance is the secondary cause of an accident. In the consecrated host, the accidents of bread do not exist according to their second cause (or in virtue of their nature), but by virtue of their first cause, Divine Providence. "For since an effect depends more upon the first cause than on the second, God Who is the first cause both of the substance and accident, can by His unlimited power preserve an accident in existence when the substance is withdrawn."  It is not logically impossible for an effect to rely directly on its primary cause without the intermediary, second cause. Since "nature" is the term that applies to second, or intermediate causes, it is naturally impossible, but not logically impossible, for a thing to exist but not according to its nature (second cause). Thus, the accidents of bread and wine really do exist as accidents, but not as accidents of a substance.
Transubstantiation appears to commit the believer to holding that Christ both has the properties of the host and does not have the properties of the host. Simply stated,
i. The consecrated host is small, white, and round.
ii. The consecrated host is Christ.
iii. Christ is not small, white, and round.
are taken to be an inconsistent set. By the transitive property of identity, if we assume i (O is F, G, and H,) and iii (C is not F, G, and H), ii (O = C), should be O ≠ C. It is true that the accidents of Christ are not the accidents of the consecrated host, as iii notes. The accidents of the consecrated host do include smallness, whiteness, and roundness. But, the accidents of the consecrated host do not inhere in the substance of Christ, according to (6), "the accidents of the bread and wine exist without a subject. Two things with different properties cannot share the relation of identity: because H and C have different properties, we must reject ii, the claim that "the consecrated host is Christ" (O = C). But, ii seems to be a statement of the belief of transubstantiation. Thus, this problem of identity is taken to demonstrate the logical impossibility of transubstantiation.
The referent of "consecrated host" is, however, a set of properties. Transubstantiation could not require a relation of identity between a set of property instances (accidents) and the substance of Christ, as ii claims. When the believer says, "This is Christ," he could not mean that "these properties are Christ," for Christ is not a set of properties. The claim made in ii, therefore, must be rejected as meaning O=C; no such relation could exist. If it is to make sense, it must be understood in light of (1), "Christ's Body is present in the Eucharist." Christ is present, but he is not identified with the host. Thus, it is correct to point to the host and say "The Body of Christ"  because Christ is present; but, this cannot mean that "this host (set of properties) is Christ." Pointing to the host and claiming "this is Christ" is a statement of Christ's location (presence); that is, it means "Christ is here," and not "This set of properties is an individual, namely, Christ."
The objection of multilocation in the Eucharist can be related to the problem mentioned above. Arguments of multilocation are based on the principle that a body is restricted to one location in space-time. This is called "unilocation." A thing with spatial extent may be wholly present in only one location at a given time.  This principle is widely accepted by philosophers and seemingly unquestionable; thus, the problem of multilocation is premised on strong ground. Transubstantiation, which claims that Christ is wholly present in multiple consecrated hosts,  necessarily holds the multilocation of Christ: Christ is really and wholly present in heaven, in consecrated host A, consecrated host B, and in each part of consecrated host A. Thus, transubstantiation might be rejected because multilocation of a body is not possible. The two basic claims that seem to be made by transubstantiation appear contradictory:
iv. Consecrated host A and consecrated host B are both Christ.
v. Consecrated host A is in (location) l1 at (time) t1 and consecrated host B is in l2 at t1.
If (iv) consecrated host A and consecrated host B are both Christ, they cannot have an inconsistent set of properties. Specifically, A and B cannot be in two distinct locations at the same time, as v claims.
The mistake in this series is the same as above. The supposed identity between consecrated host A, consecrated host B, and Christ (made in iv) equivocates from substantial identity to possession of a set of accidental properties. This is to say that the referent of "host A" and "host B" is a set of properties. It is not possible for Christ, a substance, to be identical with a set of properties. The incompatibility upon which this formulation of the problem rests, however, relies on this (false) identity. Thus, it misrepresents the doctrine, attempting to force it into making an (impossible) identity claim between a set of accidental properties and a substance.
While this diverts the thrust of arguments that rely on the identity of a consecrated host with Christ, I must discuss the manner in which Christ is present in each host. If Christ is wholly present in two hosts, and the two hosts are in different locations at the same time, then Christ is wholly present in at least three locations (host A, host B, and heaven) at the same time. Furthermore, if Christ is wholly present in each part of a particular host, he is wholly present in multiple locations. This formulation of multilocation does not rely on a mistaken identity between Christ and a set of accidents. It is important to note that this multilocation in the Eucharist claims that the location of Christ in space is multiplied. It does not claim that there are several "Christs." The doctrine does not claim that Christ1 is present in l1 and Christ2 is present in l2. Christ is wholly present in l1 and l2 at t1. This formulation of the problem attacks the nature of the real bodily presence of Christ. Bodies have spatial extent, and it is logically impossible for spatially extended things to multilocate.
For ease of articulation, I will refer to the presence of a body, which is a spatially extended thing, as "material presence." Aquinas notes that material presence is described as "whole in the whole and part in the part." Things that are materially present can be wholly present in only one place at one time, thus, multilocation is impossible for things materially present. Material presence is juxtaposed with immaterial presence, which Aquinas describes as "whole in the whole and whole in the part." Immaterial things, such as angels, do not have spatial extent. Furthermore, they are wholly present in each part. Because they are present wholly in every part, things that are present immaterially are necessarily wholly present in multiple locations. Aquinas argues that Christ is immaterially present in the Eucharist. Thus, the problem lies in defending the claim that a body could be immaterially (without dimension and "whole in the part") present.
6 Bodies, but not according to dimension
Aquinas articulates a subtle observation about the Eucharistic conversion: the dimensive quantity of the host remains after the substance of bread is replaced by Christ. The host has spatial extent at a certain location. Since two spatially extended things cannot occupy the same location at the same time, Aquinas argues that the believer is committed to holding that Christ is not present in his normal, spatially extended manner. For Aquinas, then, the dimensive quantity (spatial extent) of Christ is not present by the replacement of the bread with Christ; rather, the dimensive quantity is present by concomitance. I discussed this issue before with the union of Christ's soul to his body and his divinity to this humanity starting on page 3.
Since, then, the substance of Christ's body is present on the altar by the power of this sacrament, while its dimensive quantity is there concomitantly and as it were accidentally, therefore 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 [an immaterial] substance, whose nature is for the whole to be in the whole, and the whole in every part. 
Thus, Aquinas introduces the notion that Christ is present in the Sacrament wholly, but not as "in a place."  "In a place," as a technical Thomistic phrase means "materially present," as I am using the phrase. It, however, seems logically impossible for a body to be present, but not "in a place," because, by definition, a body is a thing with spatial extent. Thus, we may pose the question of the possibility of the immaterial presence of the body; that is, is it possible for the body of Christ to be present, but not according to its normal manner or nature. Before turning to Aquinas' technical language, I wish to consider a few examples.
There does not seem to be a logical problem with God causing thing X to be invisible. By "invisible" I do not mean simply out of sight, as we might say about something that "disappeared around a corner." I mean that X could be present right before our eyes and in the right lighting for us to see, but it would be impossible for us to see X because God had made X invisible. Furthermore, it is possible that X could be white. God could make a white X invisible.
Moreover, I should note that Christians have long held that immaterial substances can be present in a given location. For instance, Christian Scripture records that the angel Gabriel, an immaterial substance, was present to Mary when he visited her to speak to her about the incarnation.  Something seems odd about something without spatial extent (an immaterial presence) being present in a location. Nevertheless, a point has location without spatial extent. It is not logically impossible for something without spatial extent, or dimension, to be present in a location. That is, an immaterial presence is in a location, but not in the same way as a material presence, namely, without dimension.
My first example is a case of something existing without, or not according to, one of its properties. Namely, X, which is white, existed, though it was invisible. The latter pair of examples demonstrate that neither Christian Scripture and Tradition nor geometry hold that an immaterial presence has no location, even though an immaterial presence is without dimension.
The question is whether God could cause a body with dimension to be present immaterially. I submit that if it is possible for God to make an X with color invisible, he can make a Y with dimension present immaterially. Thus, it does not appear that it is logically impossible for God to cause Christ to be present immaterially. That is, Christ can be present in the Eucharist "whole in the whole and whole in the part," and, thus, wholly present in multiple locations, though this must be according to the divine first cause and not by virtue of his spatial extent.
One might make an appeal to a definition argument concerning a body: a body is that which has dimension, but Christ has no dimension in the Eucharist. This discussion, however, can be refuted on the same grounds that the definition argument was refuted for accidents existing without inhering in a substance. Just as before, the nature (definition) of a body does not change: it retains its nature as having dimensive quantity. The body exists in the Eucharist by virtue of God's miraculous power, and not according to its own nature. If it did exist according to its own spatial extent, that is, if it were materially present, Christ could not multilocate.
In the case of Christ's presence in the Eucharist, Thomas claims that a substance is present without its normal accidents. In the case of the presence of bread and wine, Thomas argues that the accidents remain without inhering in a substance. I noted earlier that God had two ways of instantiating a property: 1) by creating the secondary cause of the property, namely, a substance and 2) by causing the property to exist by virtue of the divine first cause. In similar terminology, God has two ways of preventing a property (accident) from existing: 1) to remove its secondary cause, or substance, or 2) to uphold the existence of the substance, but prevent the existence of the property (accident). The Eucharist happens by the divine first cause, and this is not logically impossible.
7 Can we be assured of Christ's presence?
In several essays, Anthony Kenny argues that transubstantiation is possible, though only on the power of God. Kenny is careful to point out many misunderstandings about the doctrine, especially the notion that the accidents of the bread and wine inhere in Christ. After carefully arriving at the point that the accidents do not inhere in Christ, he notes one final problem, with which I shall also conclude.
The principle that the accidents inhere in no substance, however, leaves one problem… Among the accidental categories of Aristotle is the category of place '…is on the altar', for instance, is an accidental predicate. But if the accidents which once belonged to the bread do not inhere after consecration in the substance of Christ's body, then it appears that it by no means follows from the presence of the host upon the altar that Christ is present on the altar. Thus the doctrine of transubstantiation appears in the end to fail to secure that for which alone it was originally introduced, namely the real presence of Christ's body under the sacramental species. 
If, as Aquinas argues, the accidents of the bread do not inhere in Christ, then we cannot ascribe them to Christ. It does seem that the sacrament does not assure one of the real and whole presence of Christ.
I find two basic problems Kenny could be raising. The first seems to rely on some principle that the sacramental elements (i.e. consecrated host) do not guarantee the sacrament (i.e. body of Christ). The second is that the immaterial (i.e. non-dimensive) presence Christ has in the Eucharist cannot have a location because the accident of location applies to what remains of the bread and wine. The first principle, that the sacramental elements do not guarantee the sacrament, is strictly rejected by the doctrine, as stated in (7); "the Eucharist is an efficacious sign." The second principle is refuted by the examples of a non-dimensive point and an (immaterial) angel having location.
The doctrine claims that a sacrament is an efficacious sign: the bread and wine are physical realities that express the grace of Christ's presence. Thus, on account of the Eucharist as an efficacious sign, one is assured of the real presence of Christ. The consecrated host causes what it signifies, Christ, who is wholly present where the accidents of the bread and wine are. Christ has the location of the host not because the accidents of the host belong to Christ, but because the host signifies where Christ is present.
IV Concluding Remarks
I have defended the Thomistic account of transubstantiation against claims that it is logically impossible on account of problems of accidents, identity, multilocation, and the nature of Christ's presence in the Eucharist. In making these arguments, I have not taken the mystery out of the Eucharist. Indeed, I have merely outlined where part of the mystery lies in this wonderful and beautiful Sacrament. In this, I believe I have followed the spirit of Anscombe and Aquinas. I, therefore, do not intend these arguments to explain the Eucharist in a way that makes it perfectly intelligible, but simply to defend transubstantiation.
Anscombe, Elizabeth. Ethics, Religion, and Politics . On Transubstantiation. V3, pp 107-112. University of Minnesota Press. Minneapolis. 1981.
Aquinas, Thomas. Summa Theologica. Fathers of the English Dominican Province (trls.). Christian Classics. Westminster, Maryland. 1981.
The Cambridge Companion to Aquinas. Kretzmann, Norman, and Eleonore Stump, (eds.). Cambridge University Press. 1993.
Catechism of the Catholic Church. Paulist Press. Mahwah, NJ. 1994.
Catechism of the Council of Trent. Eucharist. Art. 3, §1322-§1419. http://www.albertusmagnus.org/religion/theotokos/eucharist.html
Conn, Christopher. "Two Arguments for Lockean Four-Dimensionalism." British Journal for the History of Philosophy. 7(3) pp. 429-446. 1999.
Council of Trent, Cannons on the Eucharist. http://history.hanover.edu/early/trent/ct13.htm.
Davies, Brian, OP. The Thought of Thomas Aquinas. Clarendon Press: Oxford. 1992.
Kenny, Anthony. Aquinas. Being. Pp. 32-41. Hill and Wang. New York, NY. 1980.
Kenny, Anthony. Reason and Religion. Basil Blackwell Inc., New York, NY. 1987.
The New American Bible for Catholics. Thomas Nelson Publishers: Nashville, TN. 1983.
I would like to express deep gratitude to my teachers, especially those professors who helped me in formulating my thoughts and significantly revising them in this essay, Dr. D. Huber, Dr. D. Richardson, and Dr. J. Peters, and my philosophy advisor, Dr. C. Conn.
 The doctrine uses the term "transubstantiation," for which St. Thomas Aquinas gives a detailed explanation. The doctrine itself is not necessarily committed to Aquinas's formulation, though I am specifically defending Aquinas.
 A host is a piece of bread used in the Eucharist.
 Anscombe, E. Ethics, Religion, and Politics. On Transubstantiation, 109.
 I Cor. 11:23-25, 27. The Gospel accounts are found in Mt. 26:26ff, Mk. 14:26ff, Lk. 22:18ff, and Jn. 6:25ff.
 Council of Trent on the Eucharist, Cannon I.
 "Consecration" is the term used for invoking God's power to convert the bread or "hosts" into Christ's body. The same happens with the wine, which is converted into Christ's blood.
 Aquinas, Summa Theologica, III Q76 A1.
 "Gnostic Docetism," (2nd and 3rd centuries); Catechism of the Catholic Church, § 465, citing the Council of Nicaea I (325) against Arianism; and the Nestorian and Monophysite position, respectively.
 Council of Chalcedon.
 The doctrine does not consider what is entailed by a part of Christ's body being present somewhere, as the words of institution make present Christ's body, and not a part of his body.
 Such an position might attempt to find support in Jn. 6:63: "It is the spirit that gives life; the flesh I useless. The words I spoke to you are spirit and life."
 "Now a thing cannot be in any place, where it was not previously, except by change of place, or by the conversion of another thing into itself." (III Q75 A2 reply) The third is considered elsewhere, but I have added it here.
 Nicean Creed.
 The Arian heresy was mentioned on pg.3.
 Kenny, Reason and Religion, 16.
 As described in Kenny, Reason and Religion, 11.
 Cambridge Companion to Thomas Aquinas, 107.
 "Eucharistic species" refers to both the bread and the wine.
 Davies, The Thought of Thomas Aquinas, 46, 47.
 I have already noted something of this odd sense of change on pg. 6.
 Catechism of the Council of Trent, English Ed. of 1687, pg. 208, as cited in Kenny, Reason and Religion, pg. 9.
 Aquinas, III Q75 A5 ad 2.
 Cf. Jn. 5:53ff.
 Kenny, Aquinas, 38.
 "There is no deception in this sacrament; for the accidents which are discerned by the senses are truly present." Aquinas, III Q75 A5.
 Ibid Kenny, 37.
 Property instances of kind (second substance) quantity, quality, relation, habitus, time when, place where, posture or position, action, and passio are accidental categories for Aristotle and Aquinas.
 Newton, De gravitatione et aequipondia fluidorum, as discussed in Conn, "Two Arguments for Lockean Four-Dimensionalism."
 See Conn, for one part of this discussion as well as references to pertinent work from other contemporary philosophers such as Bennett and Remnant.
 By this use of "nature" I mean the world without God. I do not mean to imply a dichotomy between nature and God, suggesting that God is unnatural. Instead, "natural," in the sense I am using it here, has the common meaning akin to "mother nature" or "the laws of science."
 i.e. "The existence of accidents without inhering in a substance is a logical impossibility."
 One may consider the situation from the other perspective: a substance is the proper cause of an accident.
All things that are accidents are things that are caused by a substance.
No things that are caused by a substance are things that are not caused by a substance.
No things that are not caused by a substance are things that are accidents.
As there is no substance causing the accidents according to (6), transubstantiation is logically impossible. Aquinas considers this as a separate objection. I will discuss causality in the Eucharist later in this paper in resolving the argument from definition.
 Aquinas, III, Q77 A1 obj 2.
 Davies, 32.
 Aquinas, III, Q 77 A1 ad 2.
 A case of accidents existing without inhering in a substance is a case of accidents existing, but not according to, or by virtue of, their nature.
 This, it seems to me, is Kenny's suggestion with nominalization. Kenny understands that an accident existing according to its own nature without inhering in a substance is a different sort of accident from an accident existing according to its own nature as inhering in a substance. Aquinas argues precisely against Kenny's position that there are two classes of accident.
 Aquinas, I Q22 A3, as in Davies, pg 163.
 Aquinas III Q77 A1 reply.
 This is the form used in Roman Catholic Masses when giving the Eucharist to the faithful.
 Such things can also be in several different locations at several different times, and one location at several times. The case of multilocation is presence in several locations at the same time.
 The argument is also extended to the multilocation of Christ on the altar and Christ in Heaven. Obviously, a resolution of multilocation among altars will extend to multilocation between Heaven and altars in earth. Nevertheless, there are some unique and interesting differences I will not be able to explore in this paper, such as the non-spatial relation between Heaven and Earth: that is, Heaven is not spatially distant from the earth.
 Aquinas, III Q76 A4 ad 1.
 Aquinas, III, Q76 A5: "Hence it remains that Christs' body is not in this sacrament as in a place, but after the manner of substance, that is to say, in that way in which substance is contained by dimensions."
 Lk. 1:26ff.
 Kenny, Reason and Religion, 19-20.
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