Non-local real presence of Christ

Aquinas’s account of location for material substance is as follows. Ordinary material substances have a special accident—one more fundamental than all other matter-related accidents—he calls “dimensive quantity”, but which I will just call “dimensions”. This accident makes the object have a specific shape and size. The substance is then in a place provided that its dimensions are “commensurate with” that place—namely, provided that the dimensions are fitted into the place.

We can now say that a substance x is present in a place z in virtue of the following two presentness facts:

1. x is present in its dimensions D

2. the dimensions D are present in place z.

Furthermore, in the ordinary case, we can have an account of what “present” means in (a) and (b). A substance’s being present in dimensions D is just the substance’s having the dimensions D as an accident. And the dimensions being present in a place z is just their being commensurate with z. (This last one would bear more analysis, but that’s not my interest here.) When we have (a) and (b) with “present” grounded in this way—by having and commensuration respectively—we have what St Thomas call “local presence” or what we might call “ordinary physical location”.

Now, in the Eucharist the following happens according to Thomas. The substance of the bread turns into the body of Christ. The accidents of the bread miraculously remain in existence, but are no longer the accidents of any existing substance (whether bread or Christ). In particular, the dimensions D of the bread remain (and are a subject for the other accidents). And Christ’s body is present on the altar (say) because of the following two presentness facts:

3. Christ’s body is present in the dimensions D which are formerly of the bread

4. the dimensions D are present on the altar.

The ground of (d) just like that of an ordinary case of (b): the dimensions are commensurate with the place. But since Aquinas insists that Christ does not take on the accidents of the bread, the ground of (c) must be different from the ground of the ordinary case of (a): Christ does not have D. (In particular, Christ is not round and thin when transsubstantiation happens in a western Catholic Church.) Instead, Thomas says about (c) that Christ is “substantially” in the “foreign” dimensions D, but is not a subject of these dimensions, i.e., does not have them. As a result, we have the same structure of presence as in the ordinary case—it is mediated by dimensions—but because the grounds of the substance’s presence in the dimensions are different, this is not ordinary physical location any more.

In my 2008 paper, I gave up on figuring out what is meant by “substantial presence”, and indeed suggested that the problem is insoluble, and we should go for a different solution, one on which Christ has ordinary physical location on the altar. That solution may well be right, but I want to try out a more Thomistic solution—though the full story does not fit with everything Thomas says.

Consider the relationship between Seabiscuit and his accident of swiftness. This relationship has two features which make for interdependence:

1. Seabiscuit’s swiftness ontologically depends on Seabiscuit, i.e., Seabiscuit ontologically sustains his swiftness

2. Seabiscuit is qualified by his swiftness.

In all ordinary cases, the relations of ontologically sustaining and being qualified by between a substance and an accident are coextensive. Seabiscuit sustains all his accidents and they all qualify him, and similarly for all substances. To have an accident is then for the accident to ontologically depend on one and for one to be qualified by it.

Expanded out this way, we have a richer story as to what grounds an ordinary substance being present in its dimensions: the substance ontologically sustains the dimensions and is qualified by them.

Now, Thomas’s denial that Christ is “subject to” the dimensions of the bread means one aspect of the ordinary relationship between a substance and its accident is absent here—Christ is not qualified by the dimensions. However, that still leaves the possibility that the other aspect of the relationship is present. In other words, we can suppose that miraculously Christ’s body ontologically sustains “foreign” accidents that this body is not qualified by. This ontological sustenance relationship makes Christ’s body be substantially in the accidents, including in the dimensions.

Thus, the expanded account is:

1. Christ’s body is present in the dimensions D formerly of the bread by ontologically sustaining these dimensions in the way that a substance sustains its accidents but without D qualifying Christ’s body and hence without D becoming its accident.

2. The dimensions D are commensurate with a place, just as in ordinary physical location.

The presence in (1) is a special case of a type of presence that Thomas recognizes in his account of divine omnipresence. Thomas says that God is present to all things “by his essence”, namely by directly being their cause. This causation is, of course, divine sustenance. Thus, Christ’s body’s being “substantially” in the dimensions by sustaining them ontologically is like God’s being “by essence” present to all things by sustaining them. This is a recognized and metaphysically serious mode of presence, and hence it plausibly counts as a real presence.

At this point, it may seem that I have solved the problem of what Aquinas means by the substantial presence of Christ’s body in the dimensions of (the former) bread. But there is one hitch. I think Aquinas disagrees with my account. When Aquinas discusses how the accidents of bread and wine can remain without their substances, his answer is not that the body of Christ sustains them, but that God sustains them, because anything that can be done by creaturely causes can be done by God. St Thomas’s phrasing very much sounds like he thinks the sustenance of the accidents is done directly by the power of God.

The account I am offering requires that God miraculously bestow on Christ’s body the power to sustain accidents foreign to it (without being qualified by them). I don’t see any good reason to think this can’t happen. We thus have an extension of Thomas’s account, but it is one that I think is compatible with other aspects of his metaphysics and theology.

I am still not completely convinced that I should abandon my account on which Christ’s body is present in the Eucharist by ordinary physical location. My account clearly makes Christ’s body by really present. The modified Thomistic account may do that, but it may not.

I want to end with a consideration in favor of the Thomistic view that Christ’s presence in the Eucharist is not ordinary physical location. Many Protestants think that Christ’s body is “spiritually present”, and historically the Reformed wing of the Protestant tradition has taken spiritual presence quite seriously—not just as symbol—while denying ordinary physical presence (I am grateful to one of my graduate students for pointing this out). An account of Christ’s real presence that makes Christ not be ordinary physically present thus has an advantage: it fits with the intuitions not only of many Catholic thinkers but also of many non-Catholic ones. Perhaps the modified Thomistic account just is what spiritual presence is, and hence we have a way of moving Catholics and some Protestants closer together through St Thomas.

A four-dimensional model of Eucharistic presence

In yesterday’s post, I discussed the Real Presence in the context of relativistic time. There, I made the assumption that when Christ is really present in the Eucharist, it is Christ at a specific time of life (intuitively, the current time, but that notion is tricky given Relativity). It is, in particular, an adult glorified Christ and not the toddler Christ who is present in the Eucharist.

But after discussion with my Aquinas seminar grad students, I think there is something rather appealing about denying that assumption. What if instead we say that the whole of the four-dimensional Christ is present in the Eucharist? Aquinas apparently thinks that the whole Christ is present in every potential “part” of the consecrated host. This suggests (but does not entail) the idea of a three-dimensional entity present at a single point in space. Why, then, can’t a four-dimensional entity be present at a single point of spacetime? This would require a distinction between internal and external time. During an instant of external time there would be a positive (indeed, infinite, in the case of a being that lives forever) length of internal time. This is just as the whole-presence of a three-dimensionally Christ in the Eucharist requires a distinction between internal and external space: there may be five feet (say) of internal space between Christ’s head and Christ’s toes, but both are present in the external space of two inches—or much less if Aquinas is right that Christ is present in every potential part.

Is there any point to such a supposition? Yes.

First, the Tradition holds that Christ is wholly present in the Eucharist. Given four-dimensionalism, a literal metaphysical reading of that requires the whole of the four-dimensional extent of Christ to be present. Granted, I think this is an overreading of the Tradition: even if four-dimensionalism is true, it is plausible that the doctrinal pronouncements on this only refer to the whole three-dimensional extent of Christ. But, still, supposing the four-dimensionalism, it is certainly in the spirit of the teaching on Christ being wholly present, even if not required by it, to suppose the whole four-dimensional extent of Christ to be present.

Second, in Q73.A4, Aquinas has a beautiful discussion of the threefold temporal signification of the Eucharist. With respect to the past, it commemorates Christ’s passion. With respect to the present, it brings all the members of the Church together. With respect to the future, it prefigures the enjoyment of God in heaven. If we think that we are united with Christ in his full four-dimensional extent, this deepens and underscores this threefold signification.

Third, the Catholic tradition holds that the Mass is a re-presentation of the sacrifice of Calvary. This is a mysterious doctrine, and a four-dimensional whole-presence model of the Eucharist gives us a precise account of that doctrine as well: Christ as hanging on the Cross is present in the Eucharist.

That said, there are three things that make me uncomfortable about this four-dimensional extension of the doctrine that the whole of Christ is present in the Eucharist. The first is simply that it is a new theological theory (as far as I know), and most new theological theories are heretical.

The second is that it feels important to me that it is the glorified Jesus who is present in the Eucharist. But perhaps I am wrong about this feeling, and in having this feeling I am underplaying the commemorative aspect of the past temporal aspect of the Eucharist. Perhaps a justification for my feeling of discomfort is given by the Church’s emphasis on the Eucharist as an unbloody re-presentation of the sacrifice of Christ—but if Christ’s mangled crucified body is present in the Eucharist, then this the unbloodiness is merely a matter of appearances.

The third is that it is difficult what to make of the period when Christ was dead. Aquinas thinks God was still incarnate in the dead body of Christ, and if the Apostles had celebrated the Eucharist then, a dead body would have come to be present. If Aquinas’s reasons are good ones, which I am not confident of, then on the four-dimensional whole presence model we should say that the dead body of Christ is present. But this doesn’t seem right. I worry both about the apparently unfitting gruesomeness of this, as well as about the idea that there is something in the Eucharist other than Christ’s body, blood, soul and divinity (a dead body is not a body!). That said, I am suspicious of Aquinas’s view of the Incarnation and the dead body of Christ. But even if Aquinas is wrong, we have another problem. If the whole temporal extent of Christ is to be present, the soul of Christ as it was when Christ was dead needs to be present. (Especially if, as I think, survivalism is correct.) But a soul is only present in a spatial location insofar as it is united to a body that is in that location. But the soul of Christ as it was when he was dead was not united to a body, so it seems that there is no way for it to be present in the Eucharist. If this problem cannot be solved, the account may yield the whole four-dimensional extent of Christ being present, but not the whole temporal extent of Christ being present (the soul is temporal but not spatial, and hence not four-dimensional). Thus, the account may not achieve quite as much as it seems to.

One can resolve the second and third problems by supposing a moderate version of the view: Christ’s whole glorified four-dimensional self is present in the Eucharist—namely, Christ in the Eucharist is all of Christ from the time of his resurrection. This loses some of the advantages of the view, and it is not clear that what remains is sufficiently compelling. But, on the other hand, it’s also not clear that there is any serious disadvantage to that view over a three-dimensional-slice view of the Real Presence, except maybe the novelty. And it has the advantage of there not having to be a fact about the exact correlation of times between heaven and earth.

The Real Presence and Relativity Theory

Jesus Christ like all human beings has an internal clock. One can measure that clock in heartbeats or in lower level physical interactions or in some other way. Let’s measure it in “internal years”. If Jesus was born in 4 BC, then in 4 BC, his internal clock was at about a year (he was conceived about 0.75 years before he was born). In 1 BC, it was at 4 years, in 1 AD, it was at 5 years, and in 30 AD, it was at 34 years.

I don’t know what Jesus’s internal clock was at in 100 AD, and it’s not immediately obvious that the question makes sense. For it is not immediately obvious that there is a correlation between time on earth and time in heaven of such a sort it makes sense to ask “What is happening in heaven right now?” After all, according to Relativity Theory, it doesn’t make sense to ask “What is happening right now in the Andromeda Galaxy” without specifying a reference frame for the “right now”, and it’s not immediately clear that there is a common reference frame between heaven and earth.

However, the real presence of Jesus in the Eucharist does provide a temporal correlation between heaven and earth. Around 22:45 UTC today, Jesus will come to be present in our campus parish. Moreover, Jesus will be present as an adult glorified human, not as the three-year-old he was in 1 BC. There thus appears to be a fact of the matter as to what his internal clock will be showing when he comes to be present at 22:45 UTC in Waco today.

Interestingly, this gives a temporal ordering on events scattered across the earth apparently independent of our ordinary relativistic reference frames. For if the Eucharist is celebrated around 22:45 UTC in Waco and around 22:45 UTC in London, there is a fact of the matter whether Christ as present in Waco is older or younger or at the same age (according to his internal clock), and this fact provides a reference-frame independent temporal ordering between these two Eucharistic celebrations.

Indeed, since according to Catholic and Orthodox faith, Christ remains Eucharistically present in the tabernacles across the world, we constantly have a temporal ordering between events scattered spatially across the world. In principle, this defines a theologically privileged reference frame between scattered events—a Eucharistic reference frame. Events at locations z₁ and z₂ in spacetime are Eucharistically simultaneous, we might say, provided that Christ as Eucharistically present at z₁ and at z₂ has the same value of the internal clock.

Of course, some philosophers of time think there is an objective reference frame in the physical world. If they are right, then very likely the theologically privileged frame is the same as the objective one.

All that said, it is not completely clear to me that Christ as Eucharistically present has to have a well-defined value of his internal clock. But I suspect so, because of the intuition that it is the adult and not toddler Jesus who is Eucharistically present.

Sacraments and New Testament law

Christians believe that Jesus commanded us to baptize new Christians. However, there is a fundamental division in views: some Christians (such as Catholics and the Orthodox) have a sacramental view of baptism, on which baptism as such leads to an actual supernaturally-produced change in the person baptized, while others hold a symbolic view of it.

Here is an argument for the sacramental view. We learn from Paul that there is a radical change in God’s law from Old to New Testament times. I think our best account of that change is that we are no longer under divinely-commanded ceremonial and symbolic laws, but as we learn from the First Letter of John, we are clearly still under the moral law.

On the symbolic view, however, baptism is precisely a ceremonial and symbolic law—precisely the kind of thing that we are no longer under. On the sacramental view, however, it is easy to explain how baptism falls under the moral law. Love of neighbor morally enjoins on us that we provide effective medical treatment to our neighbor, and love of self requires us to seek such treatment for ourselves. Similarly, if baptism is crucial to the provision of grace for moral healing, then love of neighbor morally enjoins on us that we baptize and love of self requires us to seek baptism for ourselves.

The same kind of argument applies to the Eucharist: since it is commanded by God in New Testament times, it is not merely symbolic.

Eucharist talk and other YouTube things

I just noticed that a talk I gave on the Eucharist is available on YouTube. And there is a convenient playlist of a number of talks I've given.

Transsubstantiation and magnets

On Thomistic accounts of transsubstantiation, the accidents of bread and wine continue to exist even when the substance no longer does (having been turned into the substance of Christ’s body and blood). This seems problematic.

Here is an analogy that occurred to me. Consider a magnet. It’s not crazy to think of the magnet’s magnetic field as an accident of the magnet. But the magnetic field extends spatially beyond the magnet. Thus, it exists in places where the magnet does not.

Now, according to four-dimensionalism, time is rather like space. If so, then an accident existing when its substance does not is rather like an accident existing where its substance does not. Hence to the four-dimensionalist, the magnet analogy should be quite helpful.

Actually, if we throw relativity into the mix, then we can get an even closer analogy, assuming still that a magnet’s field is an accident of the magnet. Imagine that the magnet is annihilated. The magnetic field disappears, but gradually, starting near the magnet, because all effects propagate at most at the speed of light. Thus, even when the magnet is destroyed, for a short period its magnetic field still exists.

That said, I don’t know if the magnet’s field is an accident of it. (Rob Koons in conversation suggested it might be.) But it’s comprehensible to think of it as such, and hence the analogy makes Thomistic transsubtantiaton comprehensible, I think.

A horizontal aspect to transsubstantiation

The Eucharist has the vertical dimension of our union with Christ and a horizontal dimension of our union with our fellow Christians. The doctrine of transsubstantiation ensures the vertical dimension in an obvious way. But yesterday, while at a Thomistic Institute retreat on the Eucharist, I was struck by the way that transsubstantiation also deeply enhances the horizontal dimension of the Eucharist as a common meal.

Normally, in a common meal we eat together. Sometimes we eat portions cut from one loaf or carved from one animal, and that makes the meal even more unifying. But according to transsubstantiation, in the Eucharist we have a common meal where miraculously we each eat not just a portion of the same food, but the numerically very same portion: the whole of Christ. That is as deep a unity as we can have in eating.

Consider how there is less unity on the main alternatives to transsubstantiation:

• On symbolic views, we eat and drink different portions of bread and wine with the same symbolism.

• On consubstantiation, we eat the same Christ along with different portions of bread and wine.

• On Leibnizian views (where the bread and wine becomes a part of Christ), we eat different parts of the same Christ.

The transsubstantiation view has as much substantial unity in what is eaten as is logically possible. (Though there is some accidental disunity, in that the accidents—shape, color, position—are different for different communicants.)

Real Presence and primitive locational relations

According to relationalism, space is constituted by the network of spatial relations, such as metric distance relations (e.g., being seven meters apart). If these relations are primitive, then there is a very easy way for God to ensure the Real Presence of Christ: he can simply make there be additional spatial relations between Christ and other material entities, spatial relations that are exactly like the relations that the bread and wine stood in to other material entities.

It might seem contradictory for Christ to stand in two distance relations: for instance, being one mile from me (in one church) and three miles from me (in another). But I doubt this is a contradiction. New York and London are both 5600 km and 34500 km apart, depending on which direction you go.

According to substantivalism, on the other hand, points or regions are real, and objects are in a location by standing in a relation to a point or region. If relations are primitive, again there should be no problem about God instituting additional such relations to make it be that Christ is present where the bread and wine were.

In other words, if location is constituted by a primitive relation—whether to other objects or to space—there is apt to be no difficulty in accounting for the Real Presence. The reason is that we expect, barring strong reason to the contrary, primitive relations to be arbitrarily recombinable.

If location, however, is constituted by a non-primitive relation, there might be more difficulties. For instance, as a toy theory, consider the variant of relationalism on which spatial relations are constituted by gravitational force relations (two objects have distance r if and only if they have masses m₁ and m₂ and there is a gravitational force Gm₁m₂/r² between them). In that case, for God to make Christ present in Waco would require God to make Christ stand in gravitational force relations of the sort that I stand in by virtue of being in Waco. For instance, the earth’s gravitational force on Christ would have to point from Waco to the center of the earth—but since the Eucharist is also in Rome, it would have to point from Rome to the center of the earth as well. And that might be thought impossible. But perhaps there could be two terrestrial gravitational forces on Christ: one along the Waco-geocenter vector and the other along the Rome-geocenter vector. This would require some sort of a realism about component forces, but that’s probably necessary for the gravitational toy theory. And then God would have to miraculously ensure that despite the forces, Christ is not affected in the way he would normally be by these forces. All this may be possible, but it’s less clear than if we have primitive relations.

Eucharist talk

I gave a Thomistic Institute talk on the Real Presence today. Here are the slides and here is the audio. I am particularly pleased with my argument against the purely symbolic view of the Eucharist.

Bilocation and the at-at theory of time

I was telling my teenage children about the at-at theory of motion: an object moves if and only if it is in one location at one time and in another location at another time. And then my son asked me a really cool question: How does this fit with the possibility of being multiply located at one time?

The answer is it doesn’t. Imagine that Alice is bilocated between disjoint locations A and B, and does not move at either location between times t₁ and t₂. Nonetheless, by the at-at theory, Alice counts as moving: for at t₁ she is in location A while at t₂ she is in location B.

My response to my son was that this was the best argument I heard against the at-at theory. My son responded that the argument doesn’t work if multilocation is impossible. That’s true. But there is good reason to think bilocation is possible. First, the real presence of Christ in the Eucharist appears to require multilocation. Second, God is present everywhere, but never moves. Third, there is testimonial evidence to saints bilocating. Fourth, the argument only needs the logical possibility of bilocation. Fifth, time-travel would make it possible to stand beside oneself.

(The time-travel case is probably the least compelling, though, as an argument against the at-at theory. For the at-at theorist could say that the times in the definition of motion are internal times rather than external ones, and time travel only allows one to be in two places at one external time.)

I’ve been inclining to think the at-at theory is inadequate. Now I am pretty much convinced, but I am not sure what alternative to embrace.

One might just try to tweak the at-at theory. Perhaps we say that an object moves if and only if the set of its locations is different between times. But that isn’t right. Suppose Alice is bilocated between locations A and B at t₁, but at t₂ she ceases to bilocate, defaulting to being in location A. Then the set of locations at t₁ is {A, B} while at t₂ it is {A}. But Alice hasn’t moved: cessation of bilocation isn’t motion. Nor will it help to require that the sets of locations at the two times have the same cardinalities. For imagine that Alice is bilocated at locations A and B at t₁, and then she ceases to be located at B, defaulting to A, and walks over to location A′ at t₂. Then Alice has moved, but the sets of locations at t₁ and t₂ have different cardinalities. I don’t know that there is no tweak to the at-at theory that might do the job, but I haven’t found one.

Leibniz's idealistic transsubstantiation

I’ve been thinking how much nicer Leibnizian idealism is than the Berkeleyan sort, because you get this nice dose of realism from unconscious perception.

For instance, in one of his letters to Des Bosses, Leibniz offers a neat idealistic account of transsubstantiation: the unconscious perception of the micro-structure of the bread and wine perishes and is replaced with the unconscious perception of the micro-structure of Christ’s body, while the conscious perception of the macro-structure of the bread and wine remains. Material substance is better identified with micro-structure than macro-structure, and the macro-structure is more accident-like, so this counts as a replacement of the material substances in the bread and wine with the material substance of Christ’s body and blood.

Clever! But I am not sure what Leibniz can do with issues about size. The phenomenal perception of the micro-structure of Christ’s body presumably covers a larger volume of perceptual space than the macro-structure of the host. But Christ’s body is supposed to be where the host is.

Leibniz doesn’t say that this account of transsubstantiation is good. He suggests it’s the best one that can be adopted by Jesuits who don’t believe in composite substances.

Change in transubstantiation

The two main parts of the doctrine of transubstantiation that get philosophically discussed are that after consecration we have:

• Real Presence: Christ's body and blood is really there.
• Real Absence: bread and wine is no longer there.

But there may be another part: that the bread and wine change into the body and blood rather than simply being replaced by the body and blood. Certainly the Council of Trent uses the language of "conversion" of bread and bread wine, but it is not completely clear to me that they mean to define there to be something more than replacement. Aquinas talks unclearly (to me) of the substantial change as a kind of "order" in the two substances.

Besides the general puzzle of how change differs from replacement, there are at least two philosophical difficulties about the change. The first is that on some versions--not mine--of Aristotelian metaphysics, what makes substantial change be a change is the persistence of matter. But there is no matter persisting here (indeed, Aquinas' remark emphasizes this). The second is that what the bread and wine change into, namely Christ's body, is already there. But it seems that if x changes into y, then y doesn't exist prior to the change.

Leibniz considers a theory on which the bread and wine change into new parts of Christ's body. This solves the second problem, but at the expense of having to say that the bread changes into a mere part of Christ's body, which does not appear to be what the Church means. Trent does say that whole Christ comes to be present. I suppose one could have a hybrid theory on which the bread and wine change into new parts of Christ's body, and the rest of Christ's body then additionally comes to be present, but not by conversion. While I do not have decisive textual evidence, this does not seem to me to be what Trent means. And it is grotesque to think that Christ gets fatter at transubstantiation.

While it could well be that the Council doesn't mean anything beefy about the "conversion", and perhaps all it is an "order" between the two substances (cf. Aquinas), an order constituted by by non-coincidental replacement in the same location. That would simplify things metaphysically. But I want to try for something metaphysically thicker.

Here's the thought. On my Aristotelian metaphysics, nothing persists in substantial change. But when a change of substance x into substance y, a rather special causal power is triggered in x, the causal power of giving rise to y while perishing. The exercise of such a causal power is what makes it be the case that x has changed into y. There isn't any matter persisting in the change, so the first of the two philosophical problems with the Eucharistic change disappears. What about the second? Here's my suggestion. Normally, the existence of Christ's body at later times is caused by its existence at earlier times. But what if we say that the bread miraculously gets a special causal power, the power of causing Christ's body to exist just as the bread perishes? Then the existence of Christ's body after consecration will be causally overdetermined by two things: the bread's exercising that causal power and Christ's body exercising its ordinary causal power to make itself persist.

The bread in perishing is an overdetermining cause of the existence of Christ's body, and that is exactly how substantial change happens on my view. The main metaphysical difference here is that normally substantial change is not overdetermined, while here it is.

Location, causation and transsubstantiation

Here’s a fun thought experiment. By a miracle (say) I am sitting in my armchair in Waco but my causal interaction with my environment at the boundaries of my body would be as if I were in Paris. There is a region of space in Paris shaped like my body. When a photon hits the boundary of that region, it causally interacts with me as if I were in Paris: I have the causal power to act at a distance to reflect Parisian photons as if I were in that region in Paris. Alternately, that photon might be absorbed by me: I have the causal power to absorb Parisian photons. As a result, it looks to Parisians like I am in Paris, and as I look around, it looks to me like Paris is all around me. The same is true for other interactions. When my vocal cords vibrate, instead of causing pressure changes in Texan air, they cause pressure changes in chilly France. As I walk, the region of space shaped like my body in Paris that is the locus of my interaction with Parisians moves in the usual way that bodies move.

Furthermore, my body does not interact with the environment in Waco at all. Wacoan photons aimed at my body go right through it and so I am invisible. In fact, not just photons do that: you could walk right through my body in Waco without noticing. My body is unaffected by Texan gravity. It is simply suspended over my sofa. As I wave my hand, my hand does in fact wave in Texas, but does not cause any movement of the air in Texas—but in Paris, the region of space in which I interact with the Parisians changes through the wave, and the air moves as a result. When I eat, it is by means of Parisian food particles that come to be incorporated into my Wacoan body.

To me, to Wacoans and to Parisians it looks in all respects like I am in Paris. But I am in Waco.

Or am I? There is a view on which the causal facts that I’ve described imply that I am in Paris, namely the view that spatial relationships reduce to causal relationships. It is an attractive view to those like me who like reductions.

But this attractive view threatens to be heretical. Christ’s body is here on earth in the Eucharist, as well as in heaven in the more normal way for a body to be. But while the body is surely visible in heaven and interacts with Mary and any other embodied persons in heaven, it does not interact physically with anything on earth. Granted, there is spiritual interaction: Christ’s presence in the Eucharist is a means of grace to recipients. But that probably isn’t the sort of interaction that would ground spatial location.

There is, however, a way to modify the causal reduction of location that handles the case of the Eucharist. Actual causal interactions do not seem to be enough to ground location. The reduction very likely needs needs dispositional causal interactions that typically ground causal counterfactuals like:

1. If Parisians were to shine a flashlight into that dark alley, they’d see me.

However, dispositions can be masked. For instance, sugar is still soluble even if God has promised to miraculously keep it from dissolving when it is placed in water. In such a case, the sugar still has the disposition to dissolve in water, but fails to ground the counterfactual:

2. The lump would be dissolved were it placed in water.

We might, thus, suppose that when the Mass is being celebrated in Waco, Christ comes to have the dispositional causal properties that would ordinarily be contitutive of his being present in Waco, such as the disposition to reflect Texan photons, and so on. But by miracle, all these dispositions are masked and do not result in actual causal interaction. The unmasked dispositions are those corresponding to spiritual interaction.

Here’s an interesting lesson. The kind of causal-reductive view of location that I’ve just considered seems to be one of the least transsubstantiation-congenial views of location. But, nonetheless, the transsubstantiation can still be made sense of on that view when the view is refined. This gives us evidence that transsubstantiation makes sense.

And we can now go back to the story of my being in Waco while interacting in Paris. The story was underspecified. I didn’t say whether I have the dispositions that go with being in Waco. If I do, these dispositions are being miraculously masked. But they may be enough to make me count as being in Waco. So on the story as I’ve told it, I might actually be both in Waco and in Paris.

Final question: Can external temporal location be similarly causally grounded? (Cf. this interesting paper.)

Materiality and spatiality

I’ve been fond of the theory that materiality is just the occupation of space. But here is a problem for that view.

I have argued previously that we should distinguish between the internal space (or geometry) of an object and external space. Here is quartet of considerations:

• Imagine a snake one light-year in length out in empty space arranged in a square. Then imagine that God creates a star in the middle of the square. The star instantly disturbs the geometry of space and makes the distances between parts on opposite sides of the square be different from what they previously where. But this does not make any intrinsic change to the snake until physical influence can reach the snake from the star, which will take about 1/8 of a year (the sides of the square will be 1/4 light-years, so the closest any part of the snake is to the center is 1/8 light years). The internal geometry of the snake differs from the external one.

• We have no difficulty imagining a magical house whose inside is larger than its outside.

• Christ in the Eucharist has very different (larger!) internal size and geometry from the external size and geometry of where he is Eucharistically located.

• Thought experiments about time travel and the twin paradox suggest that we should distinguish internal time from external time. But space is like time.

Now, if internal and external space can come apart so much, then it is plausible that an object could have internal space or geometry in the absence of any connection to external space. Furthermore, if a material object ceased to have an occupation relation to external space but retained its internal geometry, it would surely still be material. Only a material object can be a cube. But a cubical object could remain a cube in internal geometry even after losing all relation to external space. But if so, then materiality is not the occupation of external space.

In fact, even independently of the above considerations about internal and external space, it just doesn’t seem that objects are material in virtue of a relation to something beyond them—like external space.

So, it seems, objects aren’t material in virtue of the occupation of external space. Could they be material in virtue of the occupation of internal space? Not substances! A substance does not occupy its internal space. It has that internal space, and is qualified by it, but it seems wrong to say that it is in it in the sense of occupation. (Perhaps the proper parts of material substances do occupy the substance’s internal space.) But some substances, say pigs or electrons, are material. So materiality isn’t a function of the occupation of internal space, either. And unless we find some third sort of space, we can’t say that materiality is a function of the occupation of space.

Perhaps, though, we can say this. Materiality is the possession or occupation of space. Then material substances are material by possessing internal space, and the proper parts of material substances are material by occupying the substance’s internal space. On this view, the materiality of me and my heart are analogically related—a fine Aristotelian idea.

But I have a worry. Point particles may not exist, but they seem conceivable. And they would be material. But a point particle doesn’t seem to have an internal space or geometry. I am not sure what to say. Perhaps, a point particle can be said to be material by occupying external space (in my proposed account of materiality, I didn’t specify that the space was internal). If so, then a point particle, unlike a square snake, would cease to be material if it came to be unrelated to external space. Or maybe a point particle does have an internal zero-dimensional space. It is hard to see what the spatiality of this “space” would consist in, but then we don’t have a good account of the spatiality of space anyway. (Maybe the spatiality of an internal space consists in a potentiality to be aligned with external space?) And, finally, maybe point particles that are points both externally and internally (particles that have non-trivial internal geometry but that are externally point-like aren’t a problem for the view) either aren’t material or aren’t possible.

Of balloons and transubstantiation

Our three-dimensional space is curved, say, like the surface of a balloon--except that the surface of a balloon is two-dimensional while space is three-dimensional.

Now imagine you have an inflated balloon. Draw two circles, an inch in diameter, on opposite sides, one red and one blue. Put your left thumb in the middle of the red circle and your right thumb in the middle of the blue circle. Press the thumbs towards each other, until they meet, with two layers of rubber between them. The balloon now looks kind of like a donut, but with no hole all the way through. Imagine now that you press so hard that the two layers of rubber between your thumbs coalesce into a single layer of rubber.

Now the single layer of rubber between your thumbs is at the center of the red circle and at the center of the blue circle. We can think of each circle as defining a place, and the coalesced rubber inside it is found in both of these places.

Replace the red circle with a drawing of a church and the blue circle with a drawing of heaven. The same coalesced layer of rubber is both inside (a drawing of) a church and inside (a drawing of) heaven. Suppose now that the rubber is infinitely thin, and that there is a space that coincides with this rubber, and little two-dimensional people, animals, plants and other objects inhabiting this space, much as in Abbott’s novel Flatland . Suppose that the pictures of the church and heaven are replaced with two-dimensional realities. Then the space of the church and the space of heaven literally overlap, so that there is a place that is located in both. An object found in that place will be literally and physically located both in the church and in heaven. In one sense, that object is physically located in two places at once. In another sense, it is located in a single place, but that single place is simultaneously located both in heaven and in the church.

There is no serious additional conceptual difficulty in three-dimensional space curving in on itself similarly.

(This is largely taken from a forthcoming piece by Beckwith and Pruss.)

A Catholic argument against presentism

1. If Catholic teaching on the Eucharist is true, then there is a time t such that an accident of bread exists-at-t and no substance of which it is an accident exists-at-t.
2. It is metaphysically impossible that an accident exists and no substance of which it is an accident exists.
3. If presentism is true and x exists-at-t, then it is true at t that x exists.
4. Catholic teaching on the Eucharist is true.
5. If presentism is true and Catholic teaching on the Eucharist is true, then it is true at some time t that an accident of bread exists and no substance of which it is an accident exists. (By 1 and 3)
6. There is no time t such at that time it is true that an accident of bread exists and no substance of which it is an accident exists. (By 2)
7. So at least one of presentism and Catholic teaching on the Eucharist is false. (By 5 and 6)
8. So presentism is false. (By 4 and 7)

Traditionally, Catholic philosophers have denied (2). But (2) is very plausible, so we have a good argument against presentism.

Christianity and paradox

Suppose we have a religion whose central tenets are paradoxical, verging on the contradictory. What would we expect? We might predict that the religion would be unsuccessful. But that would be too quick. The religion could be successful by adopting strategies like the following:

1. Hiding the central tenets from the bulk of the members.
2. Obscuring the paradoxical nature of the central tenets from the bulk of the members.
3. Downplaying the central tenets as unimportant.
4. Appealing almost only to the uneducated and ignorant.
5. Denigrating reason, and thus appealing to anti-intellectual impulses among uneducated and anti-rational impulses among the educated.

But now consider Christianity. It has central paradoxical doctrines, including Trinity, Incarnation and Real Presence. It does not hide them from the members. Nor is there any attempt to hide the paradoxical nature of these doctrines: that paradoxicality is plain to see, and if anything it is gloried in. Through much of the history of Christianity, the central tenets have been insisted on very publicly and are central to the liturgy. While Christianity has always had a special love for the downtrodden, its appeal has always also included many men and women of very high intellectual stature. Finally, while there are occasional instances of Christians denigrating reasons in history, the main thread of Christianity has been a defender of the importance of reason, even to the point of a significant part of the tradition embracing the Greek idea of humans as distinctively rational animals. How did it do it? Well, in addition to the five strategies above (and perhaps some others) there is also a sixth possibility:

6. Having true central tenets and having God work in the hearts and minds of members and nonmembers.

Accidents outlasting their substance

At least as traditionally philosophically understood, the Catholic understanding of transsubstantiation insists on the persistence of (at least some) of the accidents of bread and wine after the bread and wine have ceased to exist. But how can accidents exist without their substance?

Well, imagine a very long rattlesnake—say, a billion kilometers long—all stretched out in space. Suppose that the snake rattles its rattle at noon for a second, and one second after the end of the rattling a prearranged array of blasters simultaneously annihilates the whole snake.

Let R be the accident of the snake's rattling. A simple relativistic calculation shows that there is an inertial reference frame in which the rattling occurs after the vast majority of the snake—including all of the snake's vital organs (which I assume are placed much as in a normal snake)—has been annihilated. But an animal is dead, and hence non-existent (barring afterlife for animals; let's stipulate there is none), after all its vital organs have been annihilated. Thus, there is a reference frame in which the accident R exists after the substance S of the snake has been annihilated.

So special relativity gives us good reason to think that accidents can survive the destruction of the substance, at least in some inertial reference frames. But all inertial reference frames are supposed to be on par.

I suppose an opponent of transsubstantiation could insist that while an accident can survive the destruction of a substance in some reference frames, it cannot survive the destruction of the substance in all reference frames (as it would have to in the case of the Eucharist). But that requirement sounds a little ad hoc.

So, relativity theory gives us good reason to reject one of the most famous objections to transsubstantiation.

Eternalism and accidents without a subject

A classic objection to transubstatiation, famously pressed by Wycliffe, is that according to the Catholic understanding of the doctrine, the accidents of bread and wine persist even though the substance of bread and wine no longer exists. But in Aristotelian metaphysics, accidents are essentially dependent on their substance.

Eternalism—the view that past and future and present things all exist—provides a neat way for the Catholic to respond to Wycliffe. One can, if one so wishes, hold on to the idea that it is metaphysically necessary that a subject exists if an accident exists. But one denies that it is metaphysically necessary that the subject exists at the same time as the accident. The eternalist then holds that even if the bread and wine have perished at a time t₁ after transubstantation, nonetheless it is true at t₁ that the bread and wine exist, where the "exist" is tenseless. On this view, every accident has a subject in the same world but not always at the same time.

Impanation

The doctrine of transubstantiation has two primary components:

• The real presence of Christ's body and blood
• The real absence of bread and wine.

Some objections center on the Real Absence. After all, it looks like bread and wine are present—why would God make our senses deceitful? And why would God destroy the bread and wine? Doesn't nature build on grace? (Quick answers: Senses give prima facie reasons to believe, but in the context of the liturgy as a whole there is no deceit as it is explicitly stated that this is Christ's body and blood. And we are built out of our food, even though our food is destroyed when we eat it.)

One theory that attempts to avoid the Real Absence is impanation. Analogously to how Christ became a human, he now becomes bread and wine. But here is a curious fact about impanation. While it does hold that bread and wine exist after consecration, it has to say that the bread and wine cease to exist after consecration. In other words, the particular piece of bread and the particular sample of wine that were present before consecration cease to exist given consecration, and what we have after consecration is a new piece of bread and a new sample of wine. But if this is right, then impanation really doesn't help much with the two objections to Real Absence. We still have cessation of the existence of bread and wine. And while our sense that bread and wine are present is not mistaken, our sense that it's the same bread and wine as before consecration is mistaken. So impanation doesn't offer much of an advantage with respect to the objections.

But am I right? Does impanation imply that the old bread and wine are absent after consecration? I think so. First, consider the analogy with the Incarnation. The thought was that just as Christ came to be a human being, so too Christ came to be bread and wine. But the human being that Christ came to be did not preexist the incarnation. By analogy, the bread and wine that Christ came to be should not preexist the impanation.

Second, let's call the post-impanation bread B, and the pre-impanation bread A. Then B is Christ (just as the post-incarnation human, Jesus, is Christ). But identity is transitive. So if B is Christ, and A is identical with B, then A is Christ. Which is absurd. So the impanationist needs to deny that A is B.

But perhaps my arguments are a misunderstanding of impanation. For maybe the impanationist doesn't say that Christ becomes bread in the same way that Christ becomes human, but that Christ becomes bread in the same way that Christ becomes flesh. When Christ becomes flesh, there isn't a piece of flesh that is Christ. Rather, Christ comes to be a composite of flesh and soul. Now the analogy between impanation and incarnation forces the idea that there be a Y such that Christ comes to be a composite of bread and Y, analogously to his coming to be a composite of flesh and soul. But it is far from clear what Y would be.