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.

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.)

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.