Here’s an interesting thought experiment I came up with recently. First I should briefly explain what substance realism is, and next I should provide an account of localization.
The substance-accident distinction, which has been standard since Aristotle, distinguishes the accidents or ‘appearances’ of some thing, and the thing itself. Paradigm cases are usually living things (trees, dogs, flowers, apples). Most philosophers today recognize a distinction between substances, which are things in which accidents inhere, and bundles of accidents we refer to ostensibly but which are not substances. For instance, William Lane Craig and J.P. Moreland refer to these as property-things (philosophical foundations for a Christian worldview p.219-20). The sorites paradox (and others like it) illustrates why this new distinction is necessary. Simply put, a substance is a thing in itself, apart from the way it is presented to us by our five senses. If I have an apple which is red, and later it turns moldy, it is the very same apple even if its accidents have changed.
To be localized is simply to stand in some relation to other objects extended in space-time. For instance some object A1 may stand at a relation of D1 from some other object B1, and object A1 stands at another relation D2 from some other object B2… and object A1 stands at some relation Dn from Bn. (These relations must be thought of not in terms of our regular units such as Kilometers or Miles, but must be thought of as three dimensional distances thus including something like distance and direction-from, otherwise A would stand in the same relation Dn from Bx, By, etc). This seems a clear enough sketch to me. So some object ‘the city of Montreal’ stands at some relation of 7050.46 Km Bearing NE from some other object ‘Moscow’ (obviously the city of Montreal is an example of a property-thing, and not a substance).
Now, consider the example of the Christian belief in the Eucharist, where Christ is. For simplicity, I will mean by the Eucharist specifically Transubstantiation. The belief in the Eucharist implies that Christ is present in the liturgy by way of a transformation of the substances (bread and wine) into the body, blood, soul and divinity of Christ, as outlined clearly by the council of Trent among others. This seems to me to imply that Christ becomes fully presented in the gifts after the confection (specifically the epiclesus I believe). This, however, implies that, while Christ’s resurrected body (or at least the accidents of that bundle of properties properly belonging by nature to Christ) does not stand in any localized relation to any object in our space-time, having ascended, nevertheless Christ himself is not only localized in the Eucharist, but is localized wherever the Eucharist is. This implies, however, that multi-location is instantiated as a reality for some object ‘Christ’, such that ‘Christ’ stands at some various relations (Dq,Dw,De, etc) from any other object Bs. Note also that the whole Christ is present in the smallest molecule of the Eucharist, so that a Lutheran-Leibnizian account of Transubstantiation (where the Eucharist as an aggregate of monads becomes yet another ‘part’ of Christ, like an ever extending toe nail) does not satisfy the Catholic doctrine which I am presuming for this thought experiment.
Crazy physics thought experiment
Now, people often find themselves having some measure of difficulty either understanding and/or accepting this queer and central Christian belief. However, dodging the theological debate entirely, I want to propose that the belief is not logically incoherent. Imagine that a physicist came up with the wild idea (unrealistic given their track record, I know, but indulge me) that some particle here before us was actually identical with a particle on the other side of our galaxy, such that if something were to appear to happen to the particle here, it would appear to happen to that other particle as well. The physicist then posits that this particle exists in ‘two places’. That is, this same object P1 stands in at least two relations Dx and Dy from any other object within space (ie it is bilocal). Now, quite apart from whether the physicist is in her right mind, or whether she is correct (those are two different things I suppose), the point is this: as far as I can tell, they haven’t suggested anything which is logically incoherent either because it is self-referentially defeating (such as positing a married bachelor implies a contradiction in terms), or because the proposition doesn’t properly relate the subject to its predicate (such as 2+2=Giraffe).
It seems to me, then, that what is proposed in either case is logically possible. Another useful way to express this is to say with Leibniz that it is true in some logically possible world (or more technically that it obtains at some logically possible world). So, to say that it is logically possible for some particle to be bilocal is just to say that at some logically possible world it is the case that some particle is bilocal. The same could be said for the Eucharist. Neither of these ideas are incoherent, because we all understand what it would mean for it to be true (with the exception of non-cognitivists concerning substances who already see where I am going). Even with Hume’s constraints on what is logically possible then (such that if I can imagine it without incoherence) it seems that for any of us who at least understand what it would mean for some object to be bilocal or multi-local it is logically possible.
Now, here’s the catch. The only way for either of these ideas or any like them to be logically possible is if we refer to objects (or at least some objects) not as property-things (like a heap of grains), but as substances. In other words, we understand what it would mean to refer to a thing which stands behind its accidents.
Thus, if multi-location is logically possible, substance realism is a necessary truth which governs logical possibility (governs the imagination), and thus is a necessary feature (or a feature which obtains at all logically possible worlds, call it a trans-world feature). It may be a nomologically necessary truth (psychologically necessary, such that we are simply hard-wired to think in terms of substance realism regardless of whether it is true). The non-cognitivist (or more appropriately the extreme nominalist) may object that this thought experiment is question begging, but that must be because they have no idea what it would mean for something to stand in multiple relations to any/every other object extended in space. It is obviously incoherent to say that substance-realism is in all forms false, and that it is logically possible for some single object to be bi-localized. More, it is not possible to imagine that substance realism holds in a subset of all logically possible worlds, since if substance realism is true it is not true about particular logically possible worlds, but true about the way we construct models of logically possible worlds.
The point is, for anybody who can coherently imagine even provisionally that at some logically possible world some object A stands in multiple relations from every other object with which it is related, it must be admitted that substance realism is true. Minimally that it is psychologically possible for us to think that substance realism is true, which given the Humean constraints on logic make it logically possible. Maximally that it is a necessary truth which governs all the models of logically possible worlds which we can entertain.
Therefore, substance realism is proved to be true by the success of this thought experiment.