Jonathan Schaffer has proposed the Tiling Principle. Here’s a version of the principle, translated into Aristotelian terms:
Strong Tiling Principle
TPS1. Necessarily, no substance is a proper part of any other substance.
TPS2. Necessarily, the sum of all substances includes every real thing as a part.
I will call the conjunction of TPS1 and TPS2 the Strong Tiling Principle. The Weak Tiling Principle shall be the conjunction of TPS1 and TPA2:
Weak Tiling Principle
TPS1. Necessarily, no substance is a proper part of any other substance.
TPA2. Necessarily, the sum of all substances, surviving parts (remnants) of substances, boundaries (of substances and their parts), and accidents (of substances and their parts) includes every real thing as a part.
It might be helpful to re-state the principles in terms of fundamental and ontologically independent things:
Strong Tiling Principle
TPS1. Necessarily, no ontologically independent thing is a proper part of any other ontologically independent thing.
TPS2. Necessarily, the sum of all ontologically independent things includes every real thing as a part.
Weak Tiling Principle
TPS1. Necessarily, no ontologically independent thing is a proper part of any other ontologically independent thing.
TPA2. Necessarily, the sum of all fundamental things includes every real thing as a part.
Aristotelians who embrace the Strong Tiling Principle will either refuse to countenance individual accidents or will count a substance’s accidents among its “parts”. The Weak Tiling Principle opens up the option of treating individual accidents as real things while accepting the possible existence of accidents that are not parts of any existing substance. The case I’m most interested in is the possible existence of an accident after the demise of its substance.
Is there anything to be said on behalf of the Strong Tiling Principle?
There are four reasons that have been given for the Tiling Principle. First, we could appeal to Ockham’s Razor. Jonathan Schaffer has argued that OR should be applied only to fundamental entities. He claims that there should be no theoretical cost to postulating derived entities. In any case, if accidents and proper parts can exist in the absence of a containing substance, they must be fundamental entities. So, OR requires us to eliminate such fundamental things from our theory, unless they are explanatorily necessary. This is a fair point, but we have seen a number of cases that do seem to justify the postulation of such things.
Second, there is the worry about causal overdetermination that was raised by Trenton Merricks in Objects and Persons. If accidents and proper parts can survive, they must be fundamental. This means that we have more than one fundamental thing causing each effect, whenever an accident or part does belong to a complete substance. If the soccer player kicks the ball, the ball is caused to move by the soccer player, by his foot, and by the relevant accidents of location, momentum, and solidity, all of which are equally fundamental. I would respond that overdetermination of this kind is unobjectionable, because the substance causes the effects through the parts and accidents. Since the parts and accidents are s-essentially parts and accidents of the substance, this is sufficient to unify the cause.
Third, we might worry about the overdetermination of location. Each fundamental thing has an accident of spatial location at each moment. The location of the whole substance seems to be overdetermined, both by its own accident of location and by the location accidents of its proper parts. There are similar worries about overdetermination of the accidents of mass, momentum, and volume. Here again I would argue that the overdetermination involved is harmless. The whole substance has its location through the location of its s-essential parts.
Finally, there is a worry about an infinite regress of composition. If all proper parts are fundamental, and substances are infinitely divisible, then there will be an infinite regress of composition by fundamental entities. This would threaten to make the characteristics of the whole ultimately ungrounded. In response, I would rely on Aristotle’s distinction between actual and potential parts. Every substance has an infinite number of potential parts but only a finite number of actual ones.
The Analytic Thomist 