An Aristotelian argument for Causal Finitism

The Aristotelian account of individuation for beings in the same species proceeds by matter. But to fill out this account, we may need to talk about the times at which the matter is different.

One reason for talking about this is the possibility on some versions of Aristotelianism that a chunk of matter can survive substantial change, and hence can compose different substances—albeit at different times. If one wolf kills and eats another, there is in principle no reason why eventually the cannibal wolf’s matter might not entirely be the same as the matter of the victim, then.

So, perhaps, we may want to say that what distinguishes members x and y of the same material species is that they have different matter at the same time. But that’s not quite right. For it could be that x and y don’t ever exist at the same time! We might thus want to say that what grounds the distinction between x and y is:

1. at some time t, either x exists and y doesn’t or x doesn’t exist and y does or x and y both exist and have different matter.

This has at least two problems. First, if I travel backwards in time to a time when I already existed, then I will have different matter from my past self at the same time (since I’ve changed some cells in the meanwhile).

But the second is probably the more serious. According to the story in (1), past, present and future differences in matter all ground the distinction between x and y. But it is implausible that future differences in matter be relevant to my present distinction from you. So we should minimally restrict (1) to talking of past and present times t. But if we do that, then what grounds our difference changes over time, and does so pointlessly, because as soon as our distinction has once been established, that’s surely all we need. In fact, the last point is particularly important given the soul’s survival past death: what makes your soul past death different from mine is presumably the past difference in matter. This suggests that if we want to get at what truly grounds our distinction, we have to go back in time as far as we can, to the very beginnings of our existence, and say:

2. either x and y differ in the time at which they began to exist, or x and y began at the same time with different matter.

There is another reason to prefer (2) to (1). We not only want an account of the distinction of substances within a world, but between possible worlds. But there are many possible worlds where I exist but where my current matter is different from the matter I now have in the actual world (namely, because my diet was different). Thus, (1) has no hope of being extended to an account of transworld distinction. But (2) has some hope of such an extension. At the very least, it gives a sufficient condition for distinctness in the transworld case, while (1) does not even do that.

But now here is an interesting thing. If (2) is the true story about the distinction between material substances of the same species, it follows that:

3. It is impossible for there to be two material substances of the same species that have no beginning in time.

But if Causal Finitism (the doctrine that one effect cannot have infinitely many causes) is false, it seems like it should be possible to have an organism that has lived for an infinite amount of time, and likewise possible to have two such organisms in one species. So (2) gives us a new reason to accept Causal Finitism.

However, personally, I don’t like the Aristotelian account of distinctions between substances.

A tweak to the Aristotelian account of individuation

The standard Aristotelian story about individuation of finite substances is two-fold:

1. What makes x and y distinct when x and y are members of different species is their difference in form

2. What makes x and y distinct when x and y are members of the same species is their difference in matter.

But I think a slight tweak is in order. Suppose Alice and Spot are both members of different species and have a difference of matter. By the standard story, what accounts for their distinction is just their having different form. But it seems right to say that their difference in matter is also sufficient to distinguish them. The distinction between Alice and Spot is overdetermined by a difference in species and a difference in matter.

If so, then intead of (1) and (2), we should have an inclusively disjunctive account:

3. What makes x and y distinct is that they have a difference in form or have a difference in matter or both.

To make this account work even better, I will stipulate that the difference between an immaterial substance (say, an angel) and a material substance (say, a human) also counts as a difference in matter. Thus, there are two sorts of differences of matter: two things having different matter, or one thing having matter and the other not.

Transsubstantiation and the conversion of bread into Christ's body

One of the philosophical challenges of Aquinas’ account of transsubstantiation is his insistence that the bread and wine are not merely annihilated and replaced by Christ’s body and blood, but that they are changed into Christ’s body and blood.

Now, it is easy to see how bread could be changed into a part of Christ’s body. That routinely happened when Christ ate bread in his earthly life. But Aquinas thinks that Christ is wholly present in the Eucharist, so that can’t be the account. But it is very puzzling what it would mean for an item B to be changed into an individual item C that already existed prior to the change. What would it mean, for instance, for the chair I am sitting on to change into the laptop I am typing this on? It is easy to imagine God moving the fundamental particles of the chair into positions such that they constitute a laptop. But that would be a case of the chair changing into a second laptop, not into the laptop that I am typing this on. Indeed, it seems like it’s impossible for something to change into something that already exists, simply because the thing already exists.

Aquinas is well aware of this objection, and has a fascinating response:

A form cannot be changed into another form, or one [designated] matter into another [designated] matter, by the power of a finite agent. However, such a conversion can be effected by the power of an infinite agent, which has an action on the whole entity. For the common nature of being belongs to each form and to each [designated] matter, and the author of being (auctor entis) is able to convert what there is of being in the one (id quod entitatis est una) into what there is of being in the other (id quod est entitatis in altera), by removing that by which it was distinguished from the latter.

Here is what I think is going on. Like many other philosophers before and after him, Aquinas thinks that individual objects need something whereby they are individuated—something that distinguishes them from other things. The project of figuring out what individuates things from other things is indeed a major part of Aristotelian metaphysics. Aquinas’ point seems to be this. God wields a very fine scalpel at the level of being, a scalpel so infinitely sharp that no finite being can wield it. That scalpel allows God to slice off an individual B that which distinguishes B from an individual C. When God slices that off, B literally loses its identity, and becomes C, as there is then nothing whereby B can be distinguished from C. (That God has such a fine scalpel is also indicated by the way that in the Eucharist he can slice a substance away from its accidents, and have the accidents remain without the substance.)

Let’s explore this account. First note that it seems to commit Aquinas to a different account of the individuation of material objects from his usual one. Aristotelians normally think that material objects are distinguished either by having different forms or, when the form is the same, by having different matter. Now, the bread on the altar and the body of Christ do have different forms: one is bread and the other is a human body. So on the usual Aristotelian account of what makes the bread different from the body of Christ, it is the bread’s bready form. But slicing away the bready form does not turn the bread into the body of Christ, or indeed into any human body. It just turns the bread into a formless lump of matter.

Perhaps we should suppose, however, that there is more than just literal removal going on. Maybe what happens is that God removes the bready form and replaces it with the form of the human body. But great as that miracle would be, that would just turn bread into a human, not into this human, Jesus Christ.

What if we suppose that God removes the bready form and replaces it with the form of Jesus Christ (namely, the soul of Jesus Christ)? But now the bread is simply becoming a new part of the body of Christ (in a miraculous verison of the way that the bread you may have for lunch may become new cells in you), and so only a part of Christ is present in the Eucharist.

But perhaps what I have described doesn’t slice away enough. Suppose the following happens. God slices the bready form away from the bread. That still leaves the bread’s matter. And the matter of the bread is distinct from the matter of Christ’s body. God continues removing the grounds of distinctness. He wields his infinitely sharp scalpel and carefully removes that in the matter of the bread which makes it be distinct from the matter of Christ’s body. The result is that that now the matter of the bread is not distinct from the matter of Christ’s body. Indeed, the matter of the bread literally converts into the matter of Christ’s body, not merely a new part of Christ’s body.

A major problem with this interpretation is that the form of bread is annihilated, whereas Thomas thinks the form of bread is also converted into the form of Christ’s body (admittedly with a qualification; see ST III.75.A6repl2 for details).

But perhaps we should make another move. Suppose that we have a non-Aristotelian account of individuation that works as follows: for any two created things, B and C, there is a relation that B has to C that individuates B from C and a relation that C has to B that individuates C from B. We can imagine each created thing having a vast number of labels. Somehow Alice has written into her being “I am not Bob” and “I am not Seabiscuit” and “I am not Oak Tree #18289”, and Bob has written into his being “I am not Alice” and “I am not Seabiscuit” and “I am not Oak Tree #18289”. This relational account of individuation does not require form or matter. It is not very Aristotelian. But it has a great theological merit: it makes the individuation of creatures be an image of the individuation of persons in the Trinity, which also proceeds (according to Western Christians) by opposed relations. Now imagine that God slices off of Alice the label “I am not Seabiscuit.” Instantly, Alice is converted into Seabiscuit. (Of course, it’s not right to say that Alice is Seabiscuit now. In this respect, it’s like when Bucephalus turned into a cadaver: Bucephalus and the horse-shaped cadaver are distinct entities.)

The exegetical problem with this interpretation is that it forces one to reject the standard Aristotelian story about individuation across species being by form and within a species being by matter. Instead, individuation is always by “individuating relations”. I am happy with this, because I never liked the standard Aristotelian story. But it makes it unlikely that the story is what Thomas has in mind.

But suppose one wants this to be more Aristotelian. Here is a way to do this. Take the orthodox Aristotelian account that across species individuation is by form and within species by matter. This account leaves unanswered the question of what makes a human form and a horse form different, as well as the question of what makes Peter’s matter different from Paul’s matter. Suppose we answer these questions by the relational account, thereby combining the Aristotelian account with the relational. Thus, a human form has (perhaps primitive) distinctness relations to all other kinds of forms, and Peter’s matter has a (perhaps primitive) distinctness relation to all other chunks of matter.

We can now imagine the following happening. There is bread on the altar. At the moment of consecration, God (a) removes from the bready form that which distinguishes it from a human form and (b) removes from the bread’s matter that which distinguishes it from Christ’s matter. Step (a) ensures that now the bread has human form, while step (b) ensures that the human form is that of Christ, since within a species the numerical distinction of forms is due to matter.

This last account is quite Aristotelian, and only requires that we go one step further than Aristotle by supposing an answer to the question of what makes different kinds of forms different and distinct chunks of matter distinct. It’s too Aristotelian for my taste—I don’t want matter to play that much of a metaphysical role. But it is a cool account, I think. And it could be Aquinas’.

An Aristotelian argument for presentism

Here is a valid argument:

1. Matter survives substantial change.

2. It is not possible that there exist two substances of the same species with the very same matter.

3. If matter survives substantial change, it is possible to have two substances of the same species existing at different times with the very same matter.

4. So, it is possible to have two substances of the same species existing at different times with the very same matter. (1,3)

5. If presentism is not true, and it is possible to have two substances at different times existing with the very same matter, it is possible to have two substances of the same species existing with the very same matter.

6. So, if presentism is not true, it is possible to have two substances of the same species existing with the very same matter.

7. So, presentism is true. (2, 5)

Let’s think about the premises. I think Aristotle is committed to (1)—it’s essential to his solution to the alleged problem of change. Claim (2) is a famous Aristotelian commitment. Claim (3) is very, very plausible—surely matter moves around in the world, and it is possible to set things up so that I have the same atoms that Henry VIII had at some point in his life. Claim (5) follows when we note that the only two plausible alternatives to presentism are eternalism and growing block, and on both views if two substances of the same species exist at different times with the very same matter, then at the later time it is true that they both exist simpliciter.

However, given that there is excellent Aristotelian reason to deny presentism, the above argument gives some reason for Aristotelians to deny (1) or (2). Or to be more radical, and just deny that there is any such thing as the “matter” of traditional Aristotelianism.

Individuating substances by their matter

According to traditional Aristotelianism, what makes you and me be distinct entities is that although we are of the same species, we’re made of distinct chunks of matter.

Here is a quick initial problem with this. The matter in us changes. It is quite possible that someone has different matter at age 1 and at age 20, and so by the Aristotelian individuation criterion, they are a different entity of the same species at ages 1 and 20, which is false.

One way out of this is to embrace presentism. But presentism is incompatible with the Aristotelian conviction that truth supervenes on being.

Another move is to narrow down the individuation criterion to say that:

1. Conspecifics x and y are made distinct by their being simultaneously made of different chunks of matter.

There are two problems with this move.

First, time travel. If at age 20, with different matter, you enter a time machine and travel back to meet yourself back when you were 1, then 20-year-old you and 1-year-old you are made of different chunks of matter at the same time. And while many problems about time travel are solved by moving from external to internal time, that doesn’t work here. For one cannot say that matter individuates x and y at the same internal time, since internal time is a concept that only makes sense when you are dealing with a single substance.

Second, relativity theory and teleportation (which is also kind of like time travel). Suppose that by age 20 you have different matter from what you had at age 1. Then God teleports 20-year-old you 100 light-years away instantly or nearly instantly (with respect to some reference frame). Then there will be a reference frame with respect to which it is true that the teleported 20-year-old you is simultaneous with 1-year-old you. So either simultaneity with respect to that reference frame doesn’t count—and that leads us to a privileged reference frame, contrary at least to the spirit of relativity—or else you are not yourself, which is absurd.

While one can swallow the idea that time travel is impossible, spacelike teleportation seems clearly possible.

Here is another move: we replace (1) with:

2. Conspecifics x and y are made distinct by their originating in distinct chunks of matter.

And 20-year-old you, no matter how they travel in space and/or time, has originated in the same chunk of matter as 1-year-old you.

This move has a cost: it requires that we be somewhat non-realist about substantial change. Full-blown realism about substantial change requires the matter to stay in existence while the substance changes. But if matter can stay in existence when its substance perishes, then that matter could be re-formed into another substance of the same species, which would violate the origination-restricted indviduation criterion. On (2), we have to accept the theory that the matter of a thing perishes when the substance does. This removes one of the major motivations behind positing matter: namely, that matter is supposed to explain why a corpse looks like the living body (viz., because it is allegedly made of the same matter).

Note, too, that (2) has a serious ambiguity once we have insisted that matter does not survive substantial change. By the chunk of matter that a substance originates in, do we mean the last chunk of matter before the substance’s existence or the first chunk of matter in the substance?

If we mean the last chunk of matter before the substance’s existence, there are two problems. First, it seems ad hoc to single out one aspect of the causes of the substance—the earlier matter—as doing the individuating. It seems better to individuate by means of the causes, applying the converse of the essentiality of origins. Second, it seems possible for an object to come into existence without prior matter. (If God exists, this is clear, since God creates ex nihilo. If God doesn’t exist, then very likely the world came into existence ex nihilo.) But then it seems quite possible for two objects of the same species to come into existence without prior matter. (Though if one wants to dispute this, one might point to the fact that a literal reading of the biblical creation account has God making the first two humans out of chunks of preexisting matter—soil and rib respectively. Maybe there is a deep metaphysical reason why this has to be so, and perhaps the initial ex nihilo created things had to be all of different species. But I just don’t find the latter requirement that plausible.)

So perhaps in (2) we mean the first chunk of matter in the substance. But if matter does not survive substantial change, then it seems plausible that the identity of the substance is prior to the identity of its initial matter, and hence the identity of the substance cannot come from its initial matter. This isn’t a very strong argument. Maybe the initial matter is prior to the substance, and has an identity of its own, while later matter is posterior to the substance.

So, our best version of the Aristotelian individuation account is this:

3. Conspecifics x and y are made distinct by their each having a different first chunk of matter.

Finally, it is interesting to note that (2) and (3) are only plausible if it is impossible for a material substance to have no beginning. But our best account for why a material substance cannot have a beginning is causal finitism. So those who like the Aristotelian account of individuation—I am not one of them—have another reason to accept causal finitism.

Why did Alice make this lectern?

Converse essentiality of qualitative origins holds that if possible objects x and y have the same qualitative causal history—i.e., their initial state is qualitatively the same and the causes of that are qualitatively the same, etc.—then x = y. Kripke’s lectern argument basically makes it plausible to think that if converse essentiality of qualitative origins holds, so does essentiality of origins—the thesis that an object couldn’t have had a different qualitative causal history than it did.

If we reject converse essentiality of origins, then we have a thorny explanatory problem: When Alice took piece of wood W and shaped it into a lectern with shape S, what explains why lectern L₁ rather than, say, lectern L₂ resulted?

One way out of this explanatory problem is a partial occasionalism: Whenever an object comes into existence, while creatures may decide what the qualities of the object are, God causes the specific haecceity.

Another way out is to replace converse essentiality of qualitative origins with a converse essentiality of full origins thesis: if possible objects have the qualitatively and numerically (apart possibly from their own identity) causal history, then they are the same. Then when Alice takes W and shapes it into a lectern with shape S, only L₁ (say) can result. But if Alice’s identical twin Barbara did it, it would have been (say) L₂.

We thus seem to have three options as to the explanation of why Alice produced L₁ rather than L₂.

1. converse essentiality of qualitative origins

2. converse essentiality of full origins

3. partially occasionalistic haecceitism.

Maybe there are other good ones.

Distinguishing between properties

Some philosophers worry about “principles of individuation” that make two things of one kind be different from another. Suppose we share that worry. Then we should be worried about Platonism. For it is very hard to say what make two fundamental Platonic entities of the same sort different, say being positively charged from being negatively charged, or saltiness from sweetness.

However, the light-weight Platonist, who denies that predication is to be grounded in possession of universals, has a nice story to tell about the above kinds of cases. For here is a qualitative difference between saltiness and sweetness:

• saltiness is necessarily had by all and only salty things, but

• sweetness is not necessarily had by all and only salty things.

But for the heavy-weight Platonist to tell this story would involve circularity, for what it is for a thing to be salty will be to exemplify saltiness.

Of course, this story only works for properties that aren’t necessarily coextensive. But it’s some progress.

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.