The Hermes in the marble

A substance’s existence does not ontologically depend on the state of anything beyond the substance. But a typical artifact depends on absences of materials beyond itself. A classic example is a statue that comes into existence when the surrounding marble is removed. The statue’s existence is grounded in part in the absence of the surrounding marble. Similarly, even if a knife blade is made by forging rather than by removal of material, one can destroy the blade by encasing it in a block of steel: the existence of the knife is grounded in part in the absence of surrounding steel.

Thus, it seems, typical artifacts are not substances.

But this argument was too quick. What if the laws of nature are such that the following is true? When the sculptor chips away the surrounding marble to make the Hermes, a non-physical component, a form, of the Hermes comes into existence. That form is united with the Hermes’ matter. And what makes the statue be itself is not the absence of surrounding matter, but the presence of the form. It may be that by the laws of nature the form only comes into existence as a result of the removal of material, but it would be logically possible for the form to come into existence without any removal: the statue causally but not ontologically depends on the absence of surrounding material. God could make the statue within the block of marble, without any removal of material, simply by creating a form for a Hermes-arranged subset of marble molecules.

(One could also have a non-Aristotelian version of this account in terms of Markosian’s brute theory of composition.)

I think the above Aristotelian story is implausible. One reason is that the story conflicts with our intuitions as to the survival conditions for artifacts. A statue is essentially a statue. But the Hermes-shaped bundle of atoms in the block marble, even if distinguished by a metaphysical union with a form, are not a statue. Maybe God could make a form for these atoms, but it wouldn’t be the form of an artifact.

Substances and artefacts

Let us suppose that I am playing a nice game of Xiangqi with my daughter. The pieces are wooden, with painted red or black characters. As we play, we notice that one of the red catapult pieces has the character on its surface half warn off. So, I grab a laser pointer, and some motors, and a little processor, and program the motors to move the laser pointer rapidly so as to trace out the missing half of the character drawn on the piece, indeed to do so so rapidly that it looks like the character is all in place without any flicker. Moreover, I add a little camera that tracks the wooden disc, and continually repoints the whole assembly to follow the disc, so that when I move the disc, the character drawn on it moves with it. As we keep on playing (maybe the paint on the piece is of very low quality), more and more of the character wears off, and I am continually reprogramming the motors to replace more and more of the paint by the laser beam. Eventually, the disc has no paint on it, but has a laser image of the catapult character on it. I then take a bite out of the wooden disc itself. (Maybe I'm a beaver.) And I keep on taking more bites, while reprogramming the laser beam not to track what's left of the wooden disc, but to track my finger motions. Finally, I finish eating the wooden disc. I can now finish the game of Xiangqi with my daughter, except that now one of the red catapult pieces has become a pattern of laser light.

Suppose we were tempted to say that the initial red catapult piece was a substance.[note 1] Now, surely, a pattern of laser light isn't a substance. Light-spots aren't even processes, but quasi-processes. They can, after all, "move" faster than light.[note 2] So then we have the oddity that a substance became a non-substance. But it is plausible, for the same reasons for which it is plausible to suppose that the Ship of Theseus survives the replacement of its parts, that the red catapult piece survives its replacement with a light spot. Thus, if the red catapult piece initially was a substance, then one and the same thing is an existent substance at t₀ and an existent non-substance at t₁. Moreover, this didn't take any kind of miracle—all it took was a bit of skill with motors and electronics. If this seems absurd to you, then you may wish to conclude that the initial red catapult piece was not a substance.

Similarly, a painting could be restored with new paint, or it could be repaired piece by piece by projected light. A chair could be replaced, piece by piece, with force-fields, perhaps, or maybe even with carefully aimed jets of air. A computer could be replaced, piece by piece, with an emulation of itself (just replace the parts one-by-one with emulations). If these things survive this kind of replacement, and if we do not wish to accept that there can be change between categories—that a substance can change into a non-substance, say—at least without a miracle[note 3], then the conclusion to draw is that Xiangqi pieces (and by the same token international chess pieces), paintings, chairs and computers are not substances. In fact, it seems plausible to generalize this: perhaps no artefact is a substance, unless perhaps it is wholly composed of one non-artefactual substance (such as Peter van Inwagen's example of the hammock that is made out of one snake, weaved into a hammock like a rope).

Some of us want to go one step further, and deny that artefacts, except perhaps if wholly composed of one non-artefactual entity, exist. For it is not implausible to say that spots of light don't exist, and anything that can change into a spot of light doesn't exist either.

Another analogy for the Trinity?

A couple of months back, Ross Cameron offered a really nice example in favor of relative identity. I want to adapt Cameron's story, and use it as a putative analogy for the Trinity. So, Bob decides to make a non-representational statue out of clay, the statue being in the shape of a dodecahedron. Sara then makes a statue of Bob's statue. She makes her statue out of a lump of clay, and is so true to her subject that her statue is intrinsically just like Bob's. But of course her statue differs in representational properties from Bob's: Bob's statue is non-representational while Sara's statue represents Bob's statue.

Jacob decides to get all the fame, and notes that Bob and Sara's statues look exactly the same so one can save some clay. So he takes a single lump of clay and simultaneously makes three statues, each being made out of the whole lump: Statue₁ is a beautiful non-representational dodecahedron, Statue₂ is a statue of Statue₁ and Statue₃ is a statue of what Statue₁ and Statue₂ have in common. Physically, what we have is one dodecahedral lump of clay. But there are three statues that this lump of clay is: it is a non-representational dodecahedral statue, a representational statue of the non-representational statue, and a more abstract representational statue of what the first two statues have in common. They differ precisely in representational properties (and in the aesthetic properties that depend on these).

This analogy seems to work moderately well as an illustration of the Trinity. It really does seem that Statue₁ is the whole lump, that Statue₂ is also the whole lump, and that so is Statue₃, but that they are nonetheless the same statue. What's kind of neat about this example is that the distinctions between the three statues are grounded precisely in the mutual relations in which they stand—in this case, the representational relations. It is even the case that in some sense these relations are origination relations and yet they do not imply any temporal priority, again just as in the case of the Trinity.

On my own view of material constitution, this is an impossible example. For I think there really is at most one object made out of a lump of matter, and artifacts don't exist except in special cases (a hammock could be both an artifact and a snake[note 1], in which case the artifact exists because it is a snake). So on my view there is neither a lump, nor three statues. However, the analogy is still a useful one. For it analogizes the Trinity to what Jacob's work of art would be on metaphysical theories that support the above analysis. And one can do that even if one rejects these metaphysical theories, as long as one thinks that they are not flagrantly self-contradictory. (Moreover, I am partial to the view that something like relative identity holds in the case of God but only the case of God, for Thomistic reasons that are not, I think, ad hoc.)