I will assume that individual accidents have real definitions, but that these definitions are shared by all the members of an infima species of quality, quantity, or whatever. These definitions include some predication of properties to an external entity (the substance in which an accident must inhere). But the definition won’t include any particular substance – only the relevant species of substance.
If a thing x has real definition D(x), must x satisfy this definition at every moment at which x exists, or only at some moment? In other words, if P is an essential property of x, must x have P at every instant in every world? Most Aristotelian philosophers assume that essential properties are necessary, contingent on the thing’s existence, but I’m not convinced. It’s true that x cannot be complete in a state in which it does not fully satisfy its own real definition, but it’s not obvious that it can’t exist in a somewhat abnormal or truncated form while only partially satisfying the definition. For example, Thomists who are “survivalists” hold that a human being can exist post-death with only a soul, even though both soul and body are included in the real definition of a human being.
Here is an example of a persistent accident: the accident of action. Suppose that a bowler bowls a strike at the bowling alley. The action of bowling strike exists at the moment at which the tenth pin topples over. It is possible for a bowler to tie between releasing the ball and bowling the strike. In such a case, the accident of action exists at an instant at which the bowler no longer exists. It is nonetheless an accident of the bowler. The definition of the accident of bowling a strike refers to certain intentions and motions on the part of a bowler. This is a case where the real definition of the accident is fully realized, even though the substance and accident do not coexist in time.
A similar example involves our seeing the light from distant stars and galaxies. When I see a star, the star is at that moment acting on my eyes. This is true even if the star no longer exists.
Thomas Aquinas accepted the possible persistence of accidents for a purely theological reason: the Catholic doctrine of transubstantiation. In Thomas’s account of that doctrine, the qualities and quantities of the bread and wine persist, even though the substances have been annihilated. In my view, the persistence of accidents need not involve a miracle (although in this case they clearly do).
There are also cases in which essential parts of substances seem to survive the demise of the substance. Cells from an organism can be kept alive in laboratory cultures indefinitely — The Immoral Life of Henrietta Lacks. Organ transplants provide another plausible case.
Aristotle embraces what is known as the Homonymy Principle. A hand or an eye that have been separated from a living human being are not truly hands or eyes anymore: to call them ‘hands’ or ‘eyes’ is to indulge in a kind of equivocation. This would support the idea that such parts are indeed essential parts. It is part of the very definition of a hand that it belong as a part to some human being. It also seems to exclude the possibility of a hand surviving as a hand after the death of the hand’s owner. However, it could be that Aristotle is talking about a hand or an eye that are truly dead, as opposed to being merely separated from the body. In the milieu in which he was writing, it was of course impossible to sustain such separated organs.
Persistence of essential parts. Transplants. The Immortal Life of Henrietta Lacks. The Homonymy principle.
Can parts and even accidents be transferable from one substance to another. Clearly not in cases in which the two substances belong to different infimae species. A pig heart is essentially the heart of a pig and could never become the heart of a human being.
At this point, we need to revisit the question of essential parts. I defined essential part in this way:
EP1. A thing x is an essential part of y iff it is essential to x that it be a part of y.
However, there is an alternative way of thinking about essential parts, one that goes through the notion of the infima species:
EP2. A thing x is an essential part of y iff x is a part of y, and it is essential to x that it be a part of exactly one thing belonging to y’s infima species[1], and that it not be a part of anything belonging to any other infima species.
To make clear which meaning I’m using, I’ll use the terms ‘s-essential’ to correspond to definition EP2 and ‘p-essential’ to correspond to EP1.
Can a fundamental thing, like a substance, have parts that are not p-essential, so long as all of its parts are s-essential parts? I think so. There is still a very intimate connection between a whole and its s-essential parts. They are still in a sense an extension of the whole. There is a profound unity to a whole that has only s-essential parts.
Now suppose we transplant a human heart from one human being to another. If the heart survives as a heart through the excision, is there any reason to deny that it becomes part of the recipient? Doesn’t the recipient simply acquire a heart in an unusual way? So long as the heart was only an s-essential part of the donor, there is no reason why it cannot become an s-essential part of the recipient.
Are accidents transferable? The most salient case would be the corruption of living organisms. Do any of the qualities or quantities qualifying parts of the body become qualities or quantities qualifying parts of the corpse? Of course, the corpse and the living organism do not belong to the same infimae species, but it doesn’t follow that some of the accidents could not belong to the same species. Brownness is essentially a quality of a surface, and both the cow and the carcass have surfaces.
We do pay some price for admitting the possibility of transferable accidents and parts: we can no longer use the accident as the truthmaker for the substance’s being qualified in the appropriate way, nor can we use the proper part as the truthmaker for the substance’s having a part of that kind. If the accidents and parts are transferable, they can exist even though they no longer belong to their current owner.
Even if we want to retain truthmaker theory without exceptions, we might be able to find something else that can act as the truthmaker in these cases. For example, it may be that each accident and each proper part has its own act of existence (actus essendi), and that it must acquire a new act of existence when it is transferred to a new substance. In other words, we could reify some sort of tie or connection between the accident or part and its substance and use that tie as the truthmaker of the relevant predications.
[1] We might have to make an exception here for extraordinary cases like conjoined twins.
The Analytic Thomist 
Wh
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