## A Green Ball, a Blue ball, a Grue ball, and Transubstantiation

It is even more difficult to produce an angel from a stone than to produce it from nothing, because to make an angel from a stone, insofar as that can be done, the stone must first be annihilated and then the angel must be created, and nothing needs to be annihilated simply to create an angel.
~Nicholas Malebranche, the search after truth, chapter 3

Imagine that there is a green soccer ball which exists, and that a blue soccer ball of exactly the same size, shape, and, in short, with all the same properties comes into existence replacing the green soccer ball. Clearly that’s a violation of the Parmedian principle that out of nothing nothing comes, for the blue ball comes ex nihilo just as the green ball reduces to nihil. Now imagine that there is a grue soccer ball (a ball which is green at all times tn where tn<tx and which is blue at all times ti where ti≥tx). To all appearances, there is no difference between these two scenarios (no empirical difference whatsoever), but to reason there is clearly a significant difference, and it’s a revealing one.

In the case of the green soccer ball being annihilated and instantaneously being replaced with a blue soccer ball with all and only the same properties (not including the property of being x colour, and excluding all temporal properties such as existing at some particular set of times, etc.), there is the problem that some new thing is popping into the world uncaused. In the case of the grue soccer ball, we may have some concern about why it turned blue at tx, and our intuitions here lead us to think there must be some explanation of this odd fact (those intuitions are more general, and come from the Principle of Sufficient Reason). However, I think we feel, and rightly so, that there is less to be explained in the case of the Grue ball changing colour. To show this, I’ll need to make one of my suppositions explicit.

Let us say that even if a thing might be bilocated (extended in space at two non-overlapping regions A and B and not extended throughout any region C overlapping both A and B), that no two things can be simultaneously located, where simultaneously located will mean that at least two things x and y (presuming x≠y), are both extended throughout and not beyond some region A. So it is not possible for a blue ball and a green ball to both exist with all and only the properties forming an otherwise identical set of predicates (including predicates about location in space and location in time). Note: I think the intuition behind my rejection of local-simultaneity is informed by my intuition that the identity of indiscernibles is correct.

Now, if things cannot be simultaneously located, then it is not logically possible for one thing to be annihilated and for another thing to instantaneously take it’s place. To show this, we can take a set of times tn where at tn a Green ball exists, and another set of times ti at which a Blue ball exists. Now, suppose that no member of tn is a member of ti. There cannot be any time tx such that tn<tx<ti or else the Blue ball does not ‘instantaneously’ replace the Green ball (since there is a time at which neither the blue nor the green ball exist). Nor can there be a time tx between tn and ti, such that  tn<tx≤ti (or  tn≤tx<ti) because then tx would a member of ti (or of tn). There is no time between tn and ti, but there are no members shared by both tn and ti. Therefore, there is no time at which “Green ball is annihilated and Blue ball instantaneously replaces Green ball.”

One can avoid this conclusion only by arguing that time can be divided into discrete atomic parts or ‘chronons’, which would be to say that time is not continuous. I think that such a suggestion would violate the PSR, for it seems that there can be no reason for why chronons are only as long as they are. There are plenty of reasons for rejecting out of hand the view that time can be divided into chronons, not least of which is the Leibnizian argument that any moment of time can be divided into an infinite set of smaller moments, and there just is no unit of time (duration) which is so small as to be in principle indivisible. Unless one wants to accept that there are Chronons, one cannot accept as logically possible that a Green ball could be annihilated and simultaneously instantaneously replaced with a (nearly) identical Blue ball. Aristotle also has a powerful argument in the sixth book of the Physics for time not being divided into successive points. Thus, one should accept that time is continuous, like a line segment, and like a line segment, is not comprised of any set of points along the line.

Now, William of Occam once argued that if God had so willed he could have decided not to use the process of transubstantiation for the Eucharist, but could just as easily used the process of annihilating the substance of bread/wine and replacing it with the substance ‘Christ’. Now, the Catholic Church has been adamant about this point, that the substance ‘bread’ is not annihilated and the accidents adopted as ‘orphan properties’ by Christ, but rather that the substance ‘bread’ transforms into the substance ‘Christ’. That means that what happens to the bread at the confection is like what happens to the grue ball, except that it doesn’t simply change it’s properties (though, strictly speaking, on a B-theory of time, the grue ball doesn’t change any of it’s properties). It is similar insofar as both in the case of the grue ball and in the case of transubstantiation, a change takes place, and there is no annihilation of a substance. I note that the theological implications of God using a process of annihilating a substance would reflect a very different eschatology (possibly also lending support to the theologies which say that hell is a process/event of annihilation). However, since the case of annihilating bread and instantaneously and simultaneously instantiating ‘Christ’ in its place is like annihilating a green ball and instantaneously and simultaneously instantiating a blue ball in its place, and since the latter is impossible for the reasons already adduced, so too will the former be impossible.

For a substance to transform from one thing to another thing just means for it to take on a new essence; for it’s ‘form’ or substantial form to be different. This happens instantaneously. However, is this ‘instantaneously’ just as problematic as the case of one ball being annihilated and instantaneously replaced? I don’t think so. I said that no two things can be simultaneously located, but I don’t think that means that there can be no time at which “the Grue ball ceases to be Green and begins to be blue.” After all, we might imagine that some time at which the proposition “the Grue ball ceases to be Green and begins to be blue” is true is analogous to the point at which two lines meet. Even if lines can be divided into an infinite number of points, there may still be a point at which the conjunctive proposition above becomes true. In the case of transubstantiation, the substance instantaneously transforms, which means that one substance has a new substantial form; in other words the moment of confection is the moment at which “the substance whose substantial form makes it bread ceases to have that substantial form and receives the substantial form which makes it Christ.”

The difference is that no two things can be simultaneously located, but it is certainly possible for two propositions to simultaneously become true, and thus possible for a conjunctive proposition to become true instantaneously. So, there is a wisdom and a logic to ‘transubstantiation’ which sets it apart from other theses like the thesis that bread is annihilated and instantaneously Christ takes its place (i.e., adopts the accidents). By the way, I realize that if no two things can be simultaneously located then consubstantiation is dismissed as impossible out of hand, but I think it has to be dismissed out of hand anyways on theological grounds (for while Christ united himself to human nature, he did not incarnate himself so as to unite his nature with the nature of bread, or else two incarnations occur, and then a third with wine, and this is absurd, for neither bread nor wine need be saved). Thus, the hypothesis that Christ is ‘implanted’ into the Eucharist is absurd for other reasons, but then that means that the substance ‘bread’ will have nothing to do with (no communion with) the substance ‘Christ’, which makes one wonder why Christ would be communicable through bread, being neither in the substance of the bread, nor in-forming its accidents, nor having the accidents inhere him.

For more reading on the issue of transubstantiation being instantaneous (et al.), I would recommend taking a look at St. Thomas Aquinas’ Summa here.

[Edit-Note: I am presuming that for something to be annihilated at tn, it must exist at tn (for a thing cannot be annihilated at any time at which it no longer exists), and that for something to be instantaneously instantiated means that there is a time at which it exists, and there is no time prior to it at which it exists. Thus, for a Green ball to be annihilated at tn, it must exist at tn, and for a Blue ball to be instantaneously instantiated at tn, it must exist at tn.]