Aquinas's embryology and the theory of relativity

Aquinas famously thinks that there is a succession of forms in utero, with first a vegetable form, then an animal form, and then a rational animal (human) form. No two of these forms are had simultaneously.

But if a three-dimensionally extended object that has form A comes to be a three-dimensionally extended object that has form B, with no other forms intervening, then, in every inertial reference frame except for at most one, there is a time at which some of the matter has form A and some of the matter has form B. So unless there is a privileged frame, Aquinas’s story doesn’t work.

In the following diagram, the slanted dashed line indicates a reference frame where some of the matter has form A (red) and some has B (blue).

Here is a variant that could work, but does not seem very plausible. We could imagine that when we have a transition from A to B, the matter of A, except at one point, passes to B through one or more other forms, indicated by the yellow portion of the diagram. These might be forms of mere particles, or they could be some special forms. In other words, A dies off into a point, with the dead matter acquiring transitional forms, and then B starts growing from the last point of A, incorporating the transitional forms. Where the A and B substances meet will be a point either of A or of B, but not of both. The narrowing of A and the growth of B happen at the speed or light or less.

On this variant, no inertial frame contains both A and B points. (If light moves at 45 degrees from horizontal in the diagram, then inertial frames correspond to lines like the dashed one making a less than 45 degree angle with the horizontal.)

But there is something rather weird going on here. Suppose that A is the vegetable form and B is the animal form (a similar argument will apply if A is the animal form and B the human form). Then close to the pointy meeting between A and B, the yellow stuff contains the vast majority of what biology would call “the embryo”, and a fairly well-developed one, since it’s on the cusp of becoming an animal. Yet the vast majority of that “embryo” is the yellow stuff—neither the vegetable nor the animal, but something else, maybe mere atoms. Indeed, once we get close enough to the meeting point, the yellow will materially function just like an embryo, since a tiny subatomic hole makes no difference to material functioning. This is very odd, and gives us reason to reject Aquinas’s story.

Of course, the main alternative to Aquinas’s story is that the gametes change into a human being. That faces some of the same difficulties. However, I think the difficulties are less if the gametes are not themselves a substance, but a plurality of substances, perhaps particle-substances. In the diagram below, the gamete-stuff is in yellow, and the blue indicates the human being. We still have the problem that early on most of what we have will need to be biologically very close to a functioning zygote, and yet it is in yellow, except for a small blue hole corresponding to where ensoulment is spreading out from a single point. But I think this is less problematic, because at this juncture the yellow stuff is something that is less obviously an organism. (Admittedly, the blue stuff is less obviously an organism when it is nearly a point. But what makes it an organism is that while its matter has little going for it, it’s got the right form.)

So, relativity makes it hard to hold on to Aquinas’s embryology. Which is a nice thing for pro-life Thomists who want to defend ensoulment at conception and hence deny Aquinas's embryology--or Catholic Thomists who find the doctrine of the Immaculate Conception incompatible with that embryology.

Maybe there is some way of getting out of this by using the considerations from yesterday’s post, though.

Pointy endpoints and internal space and time

In a series of recent posts, starting with this one, I argued that relativity theory gives us good reason to think that at the start and end of our lives we are pointlike in spatial extension. Crucial to these arguments was the idea that there is no privileged reference frame.

The conclusion is, of course, rather counterintuitive. While it is plausible that we start as a cell and that we shrink with old age, in neither case are we pointlike.

However, in some earlier posts, like this one, I explored the idea that substances may have internal space and internal time, in addition to the external spacetime of the universe.

Here is a suggestion that could save the intuition that we are not spartially pointlike at the beginning and end of life. We have internal space and time, and our internal space and time has an absolute simultaneity relation. With respect to internal time, at the first and last moments of our lives (I’m simplifying by assuming there are such moments), we have significant non-pointlike spatial extension. Of course, most external frames of reference do not agree with our internal simultaneity relation, and in most of them, we are pointlike at the beginning and end of our lives. But that’s fine: our intuition relates to our internal space and time.

The above suggestion is inspired by Rob Koons’ suggestion that our rest frame could be the privileged frame with respect to which we could have spatially non-pointlike endpoints of life. That suggestion doesn’t work for the technical reason, which Koons also noted, that there doesn’t seem to be a well-defined notion of a privileged frame of a squashy organism. (One might try to go with the rest frame of the center of mass. But an organism’s center of mass can move faster than light—e.g., in a fast amputation. And faster than light motion doesn’t define a reference frame.) But even if there isn’t a well-defined rest frame, there is a family of “approximate rest” frames that are intuitively close to what we would expect the rest frame to do. And then we could suppose that the internal simultaneity relation is pretty close to these approximate rest frames.

Note that we should not expect the internal simultaneity relations to align neatly between substances (except in the special case of substantial change where we might reasonably suppose that the old substances’s later internal simultaneity relations approximate the new substance’s earlier ones), and hence they do not define a global privileged simultaneity relation that would threaten relativity theory.

So now I think that my argument about spatially pointy endpoints of life gives us a choice between three options:

1. Accept spatially pointy endpoints.

2. Accept a global privileged reference frame.

3. Accept privileged reference frames specialized for individual substances.

In the last option, I think the best way is the way of internal space and time, but I suppose one could also think there are privileged external reference frames specialized for individual substances.

Accepting privileged reference frames specialized for individual substances could also help materialists deal with the problem of the unity of consciousness for a spatially extended brain.

Relativistic Aristotelian beginnings

From purely geometrical facts, it follows that every spatially extended entity is arbitrarily small at its beginning and at its end in almost every reference frame.

A stronger result is possible in the special case of the beginnings of substances in simple Aristotelian substantial change. In simple Aristotelian substantial change, substance A wholly changes into a new substance B by having all of the terminal matter of A be the proximate matter of B without any temporal gap. I claim that then substance B comes into existence at a single point in every reference frame (i.e., the temporal bottom of B fits into a light cone).

For suppose that in some frame F, substance B comes into existence at two F-simultaneous and distinct spacetime points z₁ and z₂ (these could be points at which there is still A but arbitrarily close to points of B or these could be points at which there is B but that are arbitrarily close to points of A). Then there is another frame F′ at which z₁ is earlier than z₂. Let t′_i be the time of z_i in F′. Because of how the terminal matter of A is the proximate matter of B, there is matter of A arbitrarily close to z₂. Hence, arbitrarily close to time t′₂, we will have A still existing. However, arbitrarily close to time t′₁ we will have B already existing. Since t′₁ < t′₂, it follows that according to F, we will have A still existing after B has already come to exist. So the cause is partly later than the effect, which is absurd.

Maybe there is a way around this in more complex cases where multiple substances result in one new substance. I am not sure.

But here is another way to see the pointiness of the beginnings of substances if one accepts the Aristotelian idea that substances are individuated by their initial matter and we take matter to be infinitely subdivisible. Suppose in frame F, substance B begins at distinct and simultaneous points z₁ and z₂. Let F′ as before be a frame where z₁ is earlier than z₂. Then according to frame F, substance B already exists before its matter close to z₂ exists (I am assuming matter is infinitely subdivisible, and in this case a relevant division happened). So its matter close to z₂ cannot be essential to its individuation. And there is a third frame, F″, where z₁ is later than z₂, and so the matter close to z₁ cannot be essential to B’s individuation. It follows that none of the matter can be essential to the individuation of the substance if the substance starts at two or more places at once. Thus, a substance must start at a single point.

What happens in substantial change then? It seems that if we are to preserve relativity, we have to say that the new substance comes into existence at a single point z out of one or more preceding substances. If matter individuates (which I am dubious of), then the matter immediately around z is what does the individuating. The substance’s form then spreads out from z, perhaps incorporating more and more of the stuff around z, at the speed of light or less.

Of course, all these problems disappear if we allow for faster-than-light causation in substantial change. But that should be a last resort.

Substantial change and simultaneous causation

Some philosophers hold that all fundamental instances of causal relations are simultaneous. Many of these philosophers are Aristotelians, though presentism provides a plausible route to this simultaneity doctrine independently of (other) Aristotelian considerations. I think the phenomenon of substantial change shows that this simultaneity doctrine is false.

When a horse changes into a carcass (or an electron-positron pair changes into a pair of photons) we have substantial change. Clearly, in such a case, the horse is the cause of the carcass.

Notice, however, that there is never a time at which both the horse and the carcass exists. This means that substantial change involves properly diachronic rather than simultaneous causation. And while there is a way of building a diachronic causal explanation out of simultaneous causation and persistence, I don’t see any way of doing that here. The trick in that way was to use the persistence of one or both of the relata of simultaneous causation to extend the relationship temporally. But here adding the earlier persistence of the horse or the later persistence of the carcass does not help, because it is still not the case that the horse and carcass have any moment of co-existence.

I think that this is where an Aristotelian will try to bring in matter. The horse has matter. When the horse perishes, its matter persists and comes to make up a carcass. We have a simultaneous relation between the horse and its matter, and then we have a simultaneous relation between the matter and the carcass.

But this doesn’t solve the problem. For the horse doesn’t just cause a heap of matter—it causes a carcass of a particular sort, made up of substances other than the substance of the horse. What persists in substantial change, on a classic Aristotelian view, is at most the prime matter. And the prime matter does not explain the form had by the carcass (or the parts of the carcass, if the carcass counts as a heap of substances).

We can even see the problem at the level of the accidents. Take the horse’s shape S_h and the carcass’s very similar shape S_c. Then, clearly, S_h causes S_c. One can see this empirically: if one rearranges the legs of the dying horse, the carcass’s shape changes correspondingly. But the only relevant thing that on the Aristotelian story persists across the change from horse to carcass is the matter: S_h does not persist, nor does anything that grounds S_h.

On reflection, the last line of thought shows that there could be a problem even for accidental change. For it seems likely to the case that a substance has an accident A which partially causes itself to be replaced by an accident B incompatible with itself. For instance, consider my current shape S₁. In a moment, my body will shift into a new shape S₂. The shape S₁ partially causes the shape S₂. Yet there is never a moment where I have both shapes. Indeed, at any time where I have shape S₁, that’s the only shape I have. So, the shape S₁ cannot cause any different future shape of me, assuming causation is always simultaneous.

This problem may be less serious than for substantial change, however, because one might say that S₁ does not cause S₂, but there is some deeper persisting accident that first causes me to have S₁ and then causes me to have S₂, so that there is no more a causal relationship between S₁ and S₂ than between a shadow of a moving person first appearing in one place and then in another. I think it is implausible to think that all cases where an accident A partially causes its immediate replacement by an accident B can be accounted by positing A and B to be mere epiphenomena, but I am not sure I have as good an argument against this as I do against the substantial change case.

I conclude from all this that while simultaneous causation is possible, it is not the case that all diachronic causation reduces to simultaneous causation.