Value supervenes on being

Consider this thesis, which both Augustine and Aquinas would accept:

1. Value supervenes on being (VSB): How valuable reality is is determined by what entities exist.

However:

2. It is good to have a true belief and bad to have a false belief.

We now have an argument against presentism (only present things exist) and growing block (only present and past things exist). Among our beliefs, we have beliefs about contingent future events. Some of these beliefs are contingently true and others are contingently false. (I am assuming a bivalent temporal logic.) The value of these beliefs is determined by what entities exist. But present and past entities are insufficient to determine whether the beliefs are true, and hence what the value of the beliefs is. Thus, contrary to presentism and growing block, there must be future things.

A new Thomistic view of the Trinity

I think the historical Aquinas’ solution to how God is one in three persons is a relative identity view that posits two kinds of identity:

1. Individual identity: the lack of a real distinction, where real distinction might come from a difference of matter (as in material substances), a difference of form (as in angels) or an opposition of real relations (as in the Trinity).

2. Sameness of essence: having the numerically same substantial form.

While this is a relative identity account, it has an advantage over more standard relative identity accounts in that it nicely explains our intuitions about absolute identity. For on Aquinas’ solution, as far as we know, except where God is involved, the two identities are co-extensive. For Aquinas (like perhaps Aristotle) believes in individual forms of creatures, so all creatures that are distinct by individual identity have numerically distinct substantial forms, and conversely there are no mere creatures with two substantial forms. Thus when we are not dealing with God, we can afford to be ambiguous between the two kinds of identity, and hence talk as if there was absolute identity. (As far as I know, Thomas never makes this point.)

The point of this post, however, is to offer an alternative version of Aquinas’ two-identities account. The alternative is thoroughly Thomistic, but it’s not what Thomas has. Here it is. We have two kinds of identity. The first is individual identity, as in the historical Aquinas’ solution. The second is:

3. Sameness of esse: having the numerically same esse or act of being.

Just as in the historical Aquinas’ solution, the alternate account has the feature that apart from theological cases, the two kinds of identity are co-extensive. Distinct individual creatures have distinct acts of being, and no creature has two acts of being.

A disadvantage of this view is that “sameness of esse” doesn’t fit quite as well as “sameness of essence” with the Nicene Creed’s “homoousion”. But some things are worth noting. The previous English translation of the Nicene Creed in the Catholic Church actually had “sameness of being”. The word ousia is the abstract form of einai, to be. And in God essence and act of being are the same by divine simplicity. So I think the disadvantage can perhaps be overcome.

An advantage, however, is that sameness of esse seems even more identity-like and unifying than sameness of form. If x and y have the very same act of being, it is hard to deny that there is a real unity between x and y. Here is one way to see the point. On Platonist metaphysics, unlike on Thomastic metaphysics, you and I have sameness of form: we each have the numerically same Form of Humanity. Granted, Platonist metaphysics may be false. But the fact that you and I count as having sameness of form on Platonist metaphysics should make a little less happy about using that as an account of the unity in the Trinity. On the other hand, once we supplement Platonist metaphysics with an act of being, it is clear that you and I will get different acts of being, since each of us can exist without the other doing so.

Moreover, this account may help cast a light on the thorny question of why Aquinas at one point posits a human esse in the incarnate Christ distinct from the divine esse (though elsewhere he denies it). For suppose that there is only one esse in Christ and we accept the sameness-of-being account. Then we would be able say that the Jesus Christ as human is God, since the one and only esse in Jesus Christ, whether as human or as God, is the divine esse, and this we shouldn’t say (and indeed Aquinas denies it). Thus if we accept the sameness of esse account, we get an argument for the two esse view of the Incarnation. Of course, we can turn this around. We might say that the two esse view is false, and hence the sameness of esse account is false.

Explanatory principlism

There are three views about ultimate explanations of reality:

1. Nihilism: There is no ultimate explanation of reality.

2. Onticism: The ultimate explanation of reality involves one or more beings.

3. Principlism: The ultimate explanation of reality involves principles rather than beings.

Nihilism is the standard view among atheists. Onticism is the standard view among theists. The main examples of principlism are axiarchism and optimalism, on which reality is explained by its having the kind of value it does. But other combinations are possible: Rescher was an principlist theist, since he thought that God’s existence could be explained by the fact that it’s for the best that God exists.

I want to say a little about what I think is wrong about principlism. Start with the observation that if truthmaker maximalism is true, principlism cannot get off the ground, because whatever principle helps explain the world is made true by the existence of some being, and if an explanatory proposition is made true by a being, that being is certainly “involved” in the explanation.

Truthmaker maximalism is false. However, I think that a neighboring grounding view is true:

4. Being grounds truth (BGT): All truths are grounded in a combination of what there isn’t, what there is and how what is is.

Given BGT, we have very good reason to reject principlism. For presumably all the principles involved in the explanation of reality are true. If any of them are grounded in what there is or how what is is, then we have onticism rather than principlism: onticism is compatible with principles being involved in explanation, as long as beings are also involved. Thus the only way to defend principlism is to say that what gives the ultimate explanation are principles made true solely by the nonexistence of certain entities. And it is very implausible that the nonexistence of certain entities is the ultimate explanation of our reality, rich in being as it is.

The one version of principlism I can think of that I can reconcile with BGT would be an explanation of our reality in terms of the non-existence of beings that would prevent this reality. (This is kind of like the idea in the Scotus argument that nothing can prevent the existence of God, so God exists.) But this is dubious. Mere lack of preventers of x is not enough to explain the existence of x. One would need some kind of basic principle of plenitude on which everything not prevented must exist.

The evanescent world of becoming

An old idea in philosophy, going back to Plato, is that things that are becoming are less beings than things that are timeless. This is a mysterious view, but I have just found that my own preferred four-dimensionalism implies a clear and unmysterious version of this view.

On my preferred four-dimensionalism, material substances are four-dimensional entities. Since they are substances, they are explanatorily prior to any parts or accidents they may have. This four-dimensionalism, thus, cannot hold that four-dimensional entities are constructed out of three-dimensional time slices, or even that the slices are somehow ontologically on par with the four-dimensional substances.

Nonetheless, it makes sense to talk of a three-dimensional time slices as a kind of derivative entity.

It may, for instance, turn out to be like the Thomist’s “virtual entities”. The Thomist does not think that the electrons that help make up my body are substances, but thinks that our scientific language can be saved: the electrons “virtually exist” in virtue of my pattern of (accidental) causal powers.

Or it might even be that three-dimensional time slices just are accidents: that the four-dimensional entity that I am has an accident corresponding to every time at which it exists, an accident which itself is the bearer of further accidents. Thus, the fact that I have a certain three-dimensional shape s at a time t could be analyzed in terms of me having an existence-at-t accident E_t, and E_t in turn having an s-shape accident.

Virtual entities and accidents are unmysteriously less beings than substances: for them to be is to qualify a substance.

So, now, here is a reconstruction of the Platonic insight. A lot of our ordinary talk about material substances is most straightforwardly construed as about time slices rather than four-dimensional substances. When we talk of the shape of a flower, we mean its three-dimensional shape with respect to a particular slice, and so on. Now, we identify something like the Platonic world of becoming as the world of three-dimensional time slices. These are completely evanescent entities—they exist literally only for a moment each—and their being is derivative from the being of substances.

Presentists have long complained that four-dimensional entities are not really becoming. We can embrace an aspect of that insight. There is a way in which the four-dimensional entities form a world where time is less important. Granted, they indeed are spatio temporal entities: they do exist in time as well as in space. But there is little reason to think that their very being is somehow ontologically tied to time in the way that the presenists think the world of becoming is. On the other hand, the time slices are very much time slices: their very being is tied to their temporality.

Of course, this reconstruction of the Platonic insight into a world of becoming is in the end quite unfaithful to Plato: for we, who are four-dimensional substances, end up not being in the world of becoming, though we ground it. We are almost like Kantian noumena, grounding a world of becoming phenomena.

I don't know that the standard presentist can reconstruct the Platonist insight. For the standard presentist, to be is to be at present. The only difference between eternal things and things in the world of becoming is that eternal things were and will be in the same state, while things in the world of becoming were and/or will be in a different state. This is not a difference with respect to a way of being.

More on the privation theory of evil

Back in April, I suggested that there are two possible privation theories concerning evil:

1. every evil is a privation

2. for every evil, what makes it be evil is a privation.

Well, Aquinas essentially scooped me, in the first article of the De Malo, by distinguishing two senses of evil in the statement “evil is a privation”. If “evil” means the evil thing, the claim is false. But by “evil” we could mean the evilness of the evil thing, and then Aquinas holds the claim to be true. And it seems to me that the evilness of the evil thing is basically that which makes it evil, so Aquinas’ theory is basically my theory (2).

I think too much of our current literature on the privation theory of evil suffers from a failure to explicitly make the distinction between the evil thing and the evilness of the evil thing. As a result, some of the counterexamples in the literature are only counterexamples to (1). And indeed it’s not hard to find uncontroversial counterexamples to the claim that every evil entity is a privation. Josef Stalin was an evil entity (I hope he has repented since), but he was never a privation; an act of adultery is an evil thing, but it is not a privation.

Consider, for instance, the most discussed example in the literature: pain. It gets pointed out that pain is not a lack of pleasure or any other kind of privation. That is very likely true. But Aquinas’ version of the privation theory does not require him to hold that pain is a privation. He can just say that pain is an evil thing, but evil things don’t have to be privations. Rather, what makes the pain be an evil is a privation. Of course that still requires a privative theory as to what makes pain be an evil. But there are such theories. For instance, one might hold a modification of Mark Murphy’s theory about pain and say that what makes pain in paradigmatic cases bad is a privation of a correspondence between our mental states and our desires, given that in paradigmatic cases we desire not to be in pain (and it’s not much of a bullet to bite to say that pain isn’t bad when it doesn’t go against our desires).

The story about pain doesn’t end here. One might, and I think should, question whether the correct ontology of the world includes such entities as “matches” between mental states and desires for pain to be a privation of. I think what Aquinas would likely say is that because being is said analogically, “matches” do exist in an analogical sense, and hence we can correctly talk of their privation. I think this is problematic. For once we allow that “matches” exist analogically, we should equally allow for privations and other lacks to exist analogically—and Aquinas indeed does. And then we run into the problem that even positive things can count as lacks: for instance, sight could count as a lack of the lack of sight. And once we have gone this far, the privation theory becomes trivial.

But the point remains: once we have seen Aquinas’s distinction between the evil being a privation and the evilness of the evil being a privation, the critiques of the privation theory are apt to get a lot more complex.

Haecceity and esse

I wonder if the haecceity of a thing isn't identical with its esse.

A Thomistic argument for essentiality of origins

Here is a suggestive Thomistic line of thought in favor of the essentiality of origins—i.e., the principle that the causes of things are essential to them.

Consider two possible cases where a seed is produced in the same apple tree T:

1. A seed is produced at t because of the tree’s exercise of seed-producing powers together with God’s cooperative exercise of primary causation.

2. A seed is created directly at t by God and not by the exercise of the tree’s powers.

And suppose that the seeds in the two cases are exactly alike, occur in the same place on the tree, etc.

I will argue that the Thomist should say that these will be numerically different seeds, and the best explanation of their difference is given by essentiality of origins.

For the Thomist is committed to there being a genuine difference between the two cases. Cooperative divine-creaturely causality is metaphysically different from divine primary causality. But where does the difference lie? Well, in (1) the tree’s causal powers are activated, while in (2) they are not. But it is a standard scholastic maxim that the effect is the actuality of the cause qua cause. Thus it seems that the difference between cases (1) and (2) should be found in the effect, namely the seed.

Furthermore, suppose that the difference between the cases is solely located in the cause, namely that in case (1) the tree’s causal powers are activated but not in (2), and that this activation is an accident A of the tree. The difference between cases (1) and (2) then is that in case (1), A occurs in the tree and in case (2) it does not. But for any accident of the tree, God could miraculously suppress any effects of that accident. Thus, there will be a case where A occurs in the tree and no seed results. And we could, further, imagine that:

3. Not only does God suppress the effects of A but he additionally directly miraculously produces an effect exactly like the one that A would have produced.

The difference between (3) and (1) can’t be in the activation of the tree’s causal power, since that is still there in (3). So we really should suppose a difference in the effects between (3) and (1). But a similar difference should exist between (2) and (1).

Note that the Thomist cannot say that there is a difference on the side of the causes lies in God, namely that in case (1), God’s causal power is unactivated but it is activated in (2) and (3). For an intrinsic difference in God between possible worlds would violate divine simplicity.

Thus, it is the effects, namely the seeds, that are numerically different, and they are different precisely because their causes are different. But the seeds are exactly alike. So the difference must be a metaphysical difference between the seeds. And this strongly suggests essentiality of origins. Indeed, it suggests that entities have encoded within them the identity of their cause.

Objection: The argument at most suggests that there has to be a numerical difference when something is produced by a finite cause (with God cooperating) and when something is produced directly by God. But why think there is also a difference when the effect is produced by one finite cause rather than another?

Response: The simplest metaphysical explanation of why it makes a difference whether God produces the effect or it is produced by finite causes is that the effect has metaphysically encoded in it what its cause was. In fact, my own view is that this may be found in the effect’s esse: perhaps an effect’s esse is to be caused by this-and-that.

Moreover, suppose that there need be no numerical difference between effects of different finite causes, but there is a numerical difference between direct effects of divine causation and the effects of finite causes. Then in principle scientists could have directly made the numerically same seed that the tree made in (1), but God couldn’t have directly made the numerically same seed. That seems unacceptable. (Of course, one might rejoin that essentiality of origins is unacceptable as it implies that God couldn’t directly make the numerically same seed that the tree could make. But when, as I suppose, an effect of necessity encodes in itself what its cause is, the impossibility of something’s being made by a different cause does not seem to be a limitation on that cause.)

Ways of being and quantifying

Pluralists about ways of being say that there are multiple ways to be (e.g., substance and accident, divine being and finite being, the ten categories, or maybe even some indefinitely extendible list) and there is no such thing as being apart from being according to one of the ways of being. Each way of being comes with its own quantifiers, and there is no overarching quantifier.

A part of the theory is that everything that exists exists in a way of being. But it seems we cannot state this in the theory, because the "everything" seems to be a quantifier transcending the quantifiers over the particular ways of being. (Merricks, for instance, makes this criticism.)

I think there is a simple solution. The pluralist can concede that there are overarching unrestricted quantifiers ∀ and ∃, but they are not fundamental. They are, instead, defined in terms of more fundamental way-of-being-restricted quantifiers in the system:

1. ∀xF(x) if and only if ∀_BWoBb∀_bxF(x)

2. ∃xF(x) if and only if ∃_BWoBb∃_bxF(x).

The idea here is that for each way of being b, there are ∀_b and ∃_b quantifiers. But, the pluralist can say, one of the ways of being is being a way of being (BWoB). So, to use Merricks’ example, to say that there are no unicorns at all, one can just say that no way of being b is such that a unicorn b-exists.

Note that being a way of a being is itself a way of being, and hence BWoB itself BWoB-exists.

The claim that everything that exists exists in a way of being can now be put as follows:

3. ∀x(x = x → ∃_BWoBb∃_by(x = y)).

Of course, (3) will be a theorem of the appropriate ways-of-being logic if we expand out "∀x" in accordance with (1). So (3) may seem trivial. But the objection of triviality seems exactly parallel to worrying that it is trivial on the JTB+ account of knowledge that if you know something, you believe it. Whether we have triviality depends on whether the account of generic existence or knowledge, respectively, is stipulative or meant to be a genuine account of a pre-theoretic notion. And nothing constrains the pluralist to making (1) and (2) be merely stipulative.

Suppose, however, your motivations for pluralism are theological: you don’t want to say that God and humans exist in the same way. You might then have the following further theological thought: Let G be a fundamental way of being that God is in. Then by transcendence, G has to be a category that is special to God, having only God in it. Moreover, by simplicity, G has to be God. Thus, the only way of being that God can be in is God. But this means there cannot be a fundamental category of ways of being that includes divine and non-divine ways of being.

However, note that even apart from theological considerations, the BWoB-quantifiers need not be fundamental. For instance, perhaps, among the ways of being there might be being an abstract object, and one could hold that ways of being are abstract objects. If so, then ∀_BWoBbG(b) could be defined as ∀_BAb(WoB(b)→G(b)), where BA is being abstract and WoB(x) says that x is a way of being.

Coming back to the theological considerations, one could suppose there is a fundamental category of being a finite way of being (BFWoB) and a fundamental category of being a divine way of being (BDWoB). By simplicity, BDWoB=God. And then we could define:

4. ∀_BWoBbF(b) if and only if ∀_BDWoBbF(b) and ∀_BFWoBbF(b).

5. ∃_BWoBbF(b) if and only if ∃_BDWoBbF(b) or ∃_BFWoBbF(b).

Note that we can rewrite ∀_BDWoBbF(b) and ∃_BDWoBbF(b) as just F(God).

Existence, causation and individuation

Suppose a cause C produces horses, in the following way:

• When C produces a horse, a horse instantly comes into existence made out of some mass of non-equine matter M.

• The genetic makeup of the resulting horse is randomly distributed over all DNA compatible with being a horse.

(Imagine lightning striking a bog and randomly turning the bog mass into a horse.)

So now suppose that in world w₁, a female Arabian, Green Lightning, comes into existence as a result of C, while in w₂, a male Exmoor pony, Tigger, comes into existence as a result of C.

Presumably, Green Lightning and Tigger are numerically distinct horses. Why are they distinct? Presumably because they are qualitatively different—specifically, because their DNA is different. If in w₁ and w₂, C respectively produced horses that were exactly alike out of M, those horses would have to have been numerically identical. (Haecceitists will disagree.)

But now we have a puzzle for Aristotelians. Both Green Lightning and Tigger are of the same species. (If you think that breeds or sexes make for different metaphysical species, modify the example and make them be of the same sex and breed, but still very different from each other.) Let the Fs be the qualitative features that Green Lightning and Tigger initially differ in.

1. The Fs in are accidents in the Aristotelian sense: they are accidental to their horsehood, which is their form.

(They may not be accidents in the contemporary modal sense. It may be that it is impossible for a horse to be of another sex than it is.)

But:

2. The Fs make Green Lightning be distinct from Tigger.

3. If what makes Green Lightning be distinct from Tigger are the Fs, then the Fs help make Green Lightning be Green Lightning.

4. Nothing that helps make x be x can be explanatorily posterior to x.

5. So, the Fs are not explanatorily posterior to Green Lightning. (2-4)

6. The accidents of x are explanatorily posterior to x.

7. So, the Fs are explanatorily posterior to Green Lightning. (1,6)

8. Contradiction! (5,7)

The case where C makes a horse come into existence from non-equine matter makes the above argument a bit more vivid. In the ordinary case of equine reproduction, a sperm and egg contribute their DNA and give rise to the DNA of the offspring. There it could be argued that the relevant thing that helps make the resulting horse be the horse it is is the DNA in the sperm and the DNA in the egg.

One could conclude that a horse can’t come into existence from matter that doesn’t already contain implicit in it the DNA of the horse. But that is implausible, especially since God could create a horse even without any matter.

This puzzle worries me a lot. I initially thought it was a special puzzle for four-dimensionalist temporal-parts Aristotelianism, because it showed that the first temporal part of the horse was explanatorily prior to the whole, whereas Aristotelianism forbids parts to be prior to wholes. But then I realizes that the same point could be made about accidents without reference to four-dimensionalism.

Here is my best solution. There is something about Green Lightning that is prior to her being Green Lightning. It is her being caused by C to exist with the Fs (i.e., her being caused by C to exist as a female Arabian, etc.). Admittedly, that sounds just as much as an accident of Green Lightning as the Fs are. It’s not Green Lightning’s form, so what else could it be but an accident? There is no answer in Aristotle, but there is a potential answer in Aquinas: this could be Green Lightning’s act of being, her esse. And it is not crazy to take Green Lightning’s esse to be something that (a) is prior to Green Lightning, (b) Green Lightning could not exist without, and (c) an individuator of Green Lightning.

This reminds me of a line of thought in the Principle of Sufficient Reason book where I argued that the esse of a contingent being is its being caused. If my present solution is correct, that was only a partial description of the esse of a contingent being. And I think there may well be an argument for the principle that ex nihilo nihil fit in the vicinity, just as in the PSR book—for it is absurd to think that anything contingent could be prior to x if x has no cause, while this esse is something contingent.

A puzzle about being and being-caused

These claims are really plausible:

1. I exist because I was caused by my parents.
2. My having been caused by my parents is a fact about me.
3. My existence is explanatorily prior to all other facts about me.
4. There are no loops of explanatory priority.

But they seem to be contradictory. My being caused by my parents is explanatorily prior to my existence, but my existence is explanatorily prior to that, and that surely looks like a loop.

But actually there is no contradiction. To get the claim that my existence is explanatorily prior to my being caused out of (3), we need to add the premise that my being caused is a different fact about me from my existing. But why add a premise that makes for a contradiction? We should instead conclude that the fact of my existence is the same fact as my being caused by my parents.

But if it's the same fact, then we have an interesting ontological conclusion: My existing is my being caused by my parents (and presumably by all the other causes cooperating with them, including especially God). I've argued for something like this conclusion here, but this is a much neater argument.

There may be another corollary. It seems that my esse, my existence, is modally essential to me--I couldn't exist with a different esse. But if my esse is my being caused by my parents, then I couldn't have had other parents.

Objection 1: We should restrict (3) to facts about the present time. But my having been caused by my parents isn't like that.

Response: Run the argument in the first moment of my existence (assuming there is one; if not, run it for some creature which has a first moment of existence; presumably if the ontological thesis I am arguing for is true for some creature, it's true for them all).

Objection 2: If my existing is the same as my being caused by my parents, how can (1) be true: isn't (1), then, a claim that I exist because I exist?

Response: Even if the fact (or state of affairs or event--there are multiple ways to formulate the argument) of my existence is the same as the fact of my being caused by my parents, the proposition that I exist is not the same as the proposition that I am caused by my parents.

Theologians who say "God doesn't exist"

Some theologians say that God doesn't exist--God is beyond being. Here is one way to make sense of their claim: Non-relational claims with "God" as the subject term have the word "God" functioning like the "It" in "It's raining" (we should think of "It's raining" on this reading as a nullary predicate). In other words, what we are really expressing are subjectless claims. When the vulgar believer says "God doesn't exist", that's not literally true. What is literally true is something like: "It's Godding". And when the vulgar believer says "God is wise", what's literally true is: "It's Godding wisely" just as "The rain is intense" really means that it's raining intensely. Relational claims can be similarly handled. "The rain falls on me" is more precisely expressed as "It's raining on me", and "God creates the earth" is better said as "It's Godding creatively with respect to the earth." A theologian of this stripe can then talk with the vulgar, but she has a preferred explication of what is being said.

I think this story fails when we talk about love between God and humans. For love is essentially relational. An account of love that eliminates either the subject term or the object term is automatically not an account of love in the proper sense. (There is an extended sense in which someone might be said love a non-existent person. But I think it's more proper to say that she seems to love. If presentism and no-afterlife are true, then in this example, Sally does not love Fred—she only thinks she does.)

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.