Immortality of the soul and the soul's proper operation

This is an attempt to make an argument for the natural immortality of the soul from the premise that the soul has a proper operation that is independent of the body. The argument is going to be rather odd, because it depends on my rather eccentric four-dimensionalist version of Aristotelian metaphysics.

Start with the thought of how substances typically grow in space. They do this by causing themselves to have accidents in new locations, and they come to exist where these new accidents are. Thus, if I eat and my stomach becomes distended, I now have an accident of stomachness in a location where previously I didn’t, and normally I come to be partly located where my accidents are.

It is plausible (at least to a four-dimensionalist) that spatiotemporal substances grow in time like they grow in space. Thus, they produce accidents in a new temporal location, a future one, and typically come to be located where the accidents are—maybe they come to be there by being active in and through the accidents. (There are exceptions: in transsubstantiation, the bread and wine don’t follow their accidents. But I am focusing on what naturally happens, not on miracles.)

Suppose now that the soul has a proper operation that is independent of the body. Given the fact that my intellectual function is temporal in nature, it is plausible that in this proper operation, my soul is producing a future accident of mine—say, a future accident of grasping some abstract fact—and does so regardless of how sorry and near-to-death a state my body has. But a substance normally stretches both spatially and temporally to become partly located where its accidents are. So by producing a future accident of mine the soul normally ensures that I will be there in that future to be active in and through that accident. Thus the soul, in exercising that future-directed proper activity, makes me exist in the future.

Now that I’ve written this down, I see a gap. The fact that the soul has a proper operation independent of the body does not imply that the soul always engages in that operation. If it does not always engage in that operation, then there is the danger that if my body should perish at a time when the operation is not engaged in, the soul would fail to extend my existence futureward, and I would perish entirely.

On this version of the proper function argument, we thus need a proper operation that the soul normally or naturally always engages in. We might worry, however, that the intellectual operations all cease when we are in dreamless sleep. However, we might suppose that the soul by its nature always carries forward in time some aspect of the understandings or abstractions that it has gained, and this carrying forward in time is indeed a proper operation that occurs even in dreamless sleep, since we do not lose our intellectual gains when we are asleep. (We should distinguish this carrying forward of an aspect of the intellectual gains from the aspects of memory that are mediated by the brain. The need to do this is a weakness of the argument.)

The above depends on my idiosyncratic picture of persistence over time: substances cause their future existence. Divine sustenance is divine cooperation with this causation. The argument has holes. But I feel I may be on to something.

The argument does not establish that we necessarily are immortal. We are only naturally immortal, in that normally we do not perish. It is possible, as far as the argument goes, that the proper operation should fail to succeed in extending us into the future, if only because God might choose to stop cooperating in the way that constitutes sustenance (but I trust he won’t).

Transsubstantiation and magnets

On Thomistic accounts of transsubstantiation, the accidents of bread and wine continue to exist even when the substance no longer does (having been turned into the substance of Christ’s body and blood). This seems problematic.

Here is an analogy that occurred to me. Consider a magnet. It’s not crazy to think of the magnet’s magnetic field as an accident of the magnet. But the magnetic field extends spatially beyond the magnet. Thus, it exists in places where the magnet does not.

Now, according to four-dimensionalism, time is rather like space. If so, then an accident existing when its substance does not is rather like an accident existing where its substance does not. Hence to the four-dimensionalist, the magnet analogy should be quite helpful.

Actually, if we throw relativity into the mix, then we can get an even closer analogy, assuming still that a magnet’s field is an accident of the magnet. Imagine that the magnet is annihilated. The magnetic field disappears, but gradually, starting near the magnet, because all effects propagate at most at the speed of light. Thus, even when the magnet is destroyed, for a short period its magnetic field still exists.

That said, I don’t know if the magnet’s field is an accident of it. (Rob Koons in conversation suggested it might be.) But it’s comprehensible to think of it as such, and hence the analogy makes Thomistic transsubtantiaton comprehensible, I think.

A Thomistic argument for the possibility of an afterlife for animals

1. Accidents are more intimately dependent on substance than substantial forms on matter.

2. If (1) is true and God can make accidents survive without the substance, then God can make forms survive without matter.

3. If God can make forms survive without matter, then God can ensure life after death for animals by making their forms survive and restoring their matter.

4. God can make accidents survive without the substance.

5. So, God can ensure life after death for animals.

The most controversial claim here is (4), but that follows from the Thomistic account of the transsubstantiation.

Of course, there is a great gap between the possibility of an afterlife for an animal and its actuality. And the above argument works just as well for plants and fungi.

A metaphysical argument for survivalism

Corruptionist Thomists think that after death and before the resurrection, our souls exist in a disembodied state and have mental states, but we do not exist. For we are not our souls. Survivalist Thomists think we continue to exist between death and the resurrection. They agree that we are not our souls, but tend to think that in the disembodied we have our souls as proper parts.

Here is a metaphysical argument against corruptionism and for survivalism.

1. An accident that has a subject is a part of that subject.

2. There are mental state accidents in the disembodied state.

3. All mental state accidents in the disembodied state have a subject.

4. The soul does not have accidents as parts.

5. Therefore, the mental state accidents in the disembodied state have something other than the soul as their subject.

6. The only two candidates for a subject of mental state accidents are the soul and the person.

7. Therefore, the mental state accidents in the disembodied state have the person as their subject.

8. Therefore, the person exists in the disembodied state.

(This argument is a way of turning Jeremy Skrzypek’s accident-based defense of survivalism into a positive argument for survivalism. Maybe Skrzypek has already done this, too.)

The argument is slightly complicated by the fact that Thomists accept the possibility of subjectless accidents existing miraculously (in the Eucharist). Nonetheless, I do not know of any Thomists who think the disembodied state is such a miracle. Given that Thomists generally think that the survival of the soul after death is not itself miraculous, they are unlikely to require the miracle of subjectless accidents in that case, and hence will accept premise 3.

Premise 2 is common ground between survivalists and corruptionists, as both agree that there is suffering in hell and purgatory and joy in heaven even in the disembodied state.

I think the controversial premises are 1 and 4. I myself am inclined to deny the conjunction of the two premises (even though I think survivalism is true for other reasons).

Premise 1 is a core assumption of compositional metaphysics, and compositional metaphysics is one of the main attractions of Thomism.

One reason to accept premise 4 is that the soul is the form of the human being, and one of the main tasks for forms in Aristotelian metaphysics is to unify complex objects. But if forms are themselves complex, then they are also in need of unification, and we are off on a regress. So forms should be simple, and in particular should not have accidents as parts.

Another reason to accept 4 is that if the soul or form has mental state accidents as parts, it becomes very mysterious what else the form is made of besides these accidents. Perhaps there is the esse or act of being. But it seems wrong to think of the form as made of accidents and esse. (I myself reject the idea that objects are “made of” their parts. But the intuition is a common one.)

Two attempts at deriving internal time from the causal order of modes

It would be nice to define the internal time of a substance in terms of the causal order of its accidents.

For each mode (i.e., accident or substantial form) α that a finite substance x has, there is the event c_α of α’s being caused. Causal priority provides a strict partial ordering on the events c_α.

Perhaps the simplest theory of the internal time of the substance x is that the moments of internal time just are the events c_α and their order just is the causal priority order.

This has the consequence that internal time need not be totally ordered, since one can have cases where α ≠ β but there is no priority relation between c_α and c_β. This consequence is welcome and unwelcome. It is welcome, as it allows one to give a nice account of bilocation involving the bifurcation of internal time. It is unwelcome, as intuitively time is linear. Let’s see if we can do something to reduce the unwelcome consequence.

Let’s suppose—as per causal finitism—that causal interactions are discrete. Then we can define a fundamental distance between the moments of internal time: d(c_α, c_β) is the length of the longest unidirectional causal priority chain between c_α and c_β. One might reasonably hypothesize that d(c_α, c_β) is something of the order of magnitude of the temporal distance between c_α and c_β in the rest frame of the substance in units of the order of Planck time. (Note that d is not a metric because of the unidirectionality constraint on the chains.)

This lets us have a second way of defining the internal time of a substance x. Let f be x’s substantial form. Then we can define “the start time” of a mode α as d(f, α): the length of the longest internal causal priority chain from c_f to c_α. Now likely some modes will have a simultaneous internal start time—they will have the same distance to c_f.

For this to define an intuitively plausible time sequence, we need the substance to have lots of interconnections between its accidents. Ordinary substances do seem to have that.

And perhaps some accidents won’t have an internal start time—if God turns me blue right now, my blueness won’t have an internal start time. But nonetheless that blueness can be “attached” to my internal temporal sequence by noting that it will be close according to d to some of my near-future accidents. For that miraculous blueness will interact with some of my other accidents to produce new accidents that are properly in my middle age. For instance, it will interact with my memories of observations of things not turning blue to generate the accident of surprise.

Accidents and truthmakers

It is difficult to hold (a) Aquinas’ idea that in transubstantiation the accidents of bread and wine continue existing after the bread and wine have perished together with (b) the idea that accidents are truthmakers for predications.

For if the accident of the whiteness of the bread is a truthmaker for the proposition that the bread is white, then it is (absurdly) true to say that the bread is white even after transubstantiation, since when the truthmaker exists, the proposition it makes true is true.

So, if one wants to hold on to the logical possibility that accidents could outlast their substance, one has to modify the thesis that accidents are truthmakers for predications. Instead, perhaps, one could say that the truthmaker for the proposition that x is F is x’s Fness together with x. This solves the problem of the bread being white after transubstantiation, since after transubstantiation there is no bread, and so if the truthmaker is the accident of whiteness together with the bread, then after transubstantiation the bread part of the truthmaker doesn’t exist. So all is well.

But here is a further puzzle. Intuitively, if God can detach the bread’s accidents from the bread when the bread ceases to exist, why can’t God detach the bread’s accidents from the bread while the bread continues to exist? But if God could detach the bread’s accidents from the bread while the bread continued to exist, then God could detach, say, the whiteness W of a bread from a bread B, and then the bread could be dyed black. Were that possible, it couldn’t be true that W and B are a truthmaker for the proposition that the bread is white, since W and B could continue to exist without the bread being white any more.

So, holding that the substance and its accident is a truthmaker for the predication, while accepting the logical possibility of Aquinas-style transubstantiation, requires one to hold that God can only detach the bread’s accidents from the bread while annihilating the bread. That seems counterintuitive.

Another move is this. Posit an “attachment” trope. Thus, when x is F, there are three particular things: x, x’s accident of Fness, and an attachment trope between x and x’s accident of Fness. Further, posit that in transubstantiation the ordinary accidents continue to exist, but the attachment tropes perish. And now we can say that the truthmaker of “The bread is white” is B, W and the attachment trope between B and W. (There is no infinite regress, since we can suppose that the attachment trope cannot exist detached.) But God can make W exist without the attachment trope, and either with or without B.

But it is an unpleasant thing that the attachment trope is a metaphysical ingredient posited solely to save transubstantiation. Moreover, the attachment trope would be a counterexample to the Thomistic principle that God can supply whatever creatures do. For it is essential to the story that the attachment trope cannot possibly exist in the absence of bread.

Probably, the Thomist’s best move is to deny that accidents (whether with or without the underlying substance) provide truthmakers for predications. If we did that, then a nice bonus is that we can have accidents moving between substances, which would provide a nice metaphysical account of why it is that flamingos turn pink after eating pink stuff.

Internal time and God

1. The internal time of a substance is constituted by the causal order within its accidents.
2. But God is a substance that has no accidents.
3. So God has no internal time.

Pity that both premises are controversial.

Tropes of tropes

Suppose that x is F if and only if x has a trope of Fness as a part of it.

Here is a cute little problem. Suppose Jim is hurting and has a trope of pain, call it Pin. But Pin is an improper part of Pin. Thus, Pin has a trope of pain—namely itself—as a part of it, and hence Pin is hurting. Thus, wherever someone is hurting, there is something else hurting, too, namely their pain.

The standard move against “two many thinkers” moves is to say that one of them is thinking derivatively. But if we do that, then it looks like the fact that Jim is hurting is more likely to be derivative than the fact that Pin is hurting. For Jim hurts in virtue of having Pin as a part of it, while Pin hurts in virtue of having itself as a part of it, which seems a non-derivative way of hurting. But it seems wrong to say that Jim is hurting merely derivatively, so the real subject of the pain is Pin.

An easy solution is to say that x is F if and only if x has a trope of Fness as a proper part of it.

But this leads to an ugly regress. A trope is a trope, so it must have a trope of tropeness as a proper part of it. The trope of tropeness is also a trope, so it must then have another trope of tropeness as a proper part and so on. (This isn’t a problem if you allow improper parthood, as then you can arrest the regress: the trope of tropeness has itself as an improper part, and that’s it.)

One can, of course, solve the problem by saying that the trope theory only applies to substances: a substance x is F if and only if x has a trope of Fness as a proper part of it, while on the other hand, tropes can have attributes without these attributes being connected with the tropes having tropes. But that seems ad hoc.

As a believer in Aristotelian accidents and forms, which are both basically tropes, I need to face the problem, too. I have two ways out. First, maybe all tropes are causal powers. Then we can say that if “is F” predicates a power, then x is F if and only if x has a trope of Fness as a proper part. But for attribution of non-powers, we have a different story.

Second, maybe the relation between objects and their tropes is not parthood, but some other primitive relation. Some things stand in that relation to themselves (maybe, a trope of tropeness stands in that relation to itself) and others do not (Pin is not so related to itself). This multiplies primitive relations, but only if the relation of parthood is a primitive relation in the system.

The usefulness of having two kinds of quantifiers

A central Aristotelian insight is that substances exist in a primary way and other things—say, accidents—in a derivative way. This insight implies that use of a single existential quantifier ∃x for both substances and forms does not cut nature at the joints as well as it can be cut.

Here are two pieces of terminology that together not only capture the above insight about existence, but do a lot of other (but closely related) ontological work:

1. a fundamental quantifier ∃u over substances.

2. for any y, a quantifier ∃_yx over all the (immediate) modes (tropes) of y.

We can now define:

• a is a substance iff ∃u(u = a)

• b is a (immediate) mode of a iff ∃_ax(x = b)

• f is a substantial form of a substance a iff a is a substance and ∃_ax(x = f): substantial forms are immediate modes of substances

• b is a (first-level) accident of a substance a iff u is a substance ∃_ax∃_xy(y = b & y ≠ x): first-level accidents are immediate modes of substantial forms, distinct from these forms (this qualifier is needed so that God wouldn’t coount as having any accidents

• f is a substantial form iff ∃u∃_ux(x = f)

• b is a (first-level) accident iff ∃u∃_ux∃_xy(y = b).

This is a close variant on the suggestion here.

Grounding accidents in substances

Consider this plausible principle:

1. x partially grounds y if and only if there are cs that fully ground y and x is one of the cs.

But now consider this plausible-sounding Aristotelian claim:

2. The substance (or its form or its essence—the details won’t matter) partially grounds each of its accidents.

Note that the grounding here is not full. For if my substance fully grounded my accident of sleepiness, then my substance would be metaphysically sufficient for my sleepiness, and I would be always sleepy, which is fortunately not the case.

So, by 2, my sleepiness is partly grounded by my substance (i.e., me?), and merely partly. By 1, then, it follows there are other things, beside my substance, such that my sleepiness is fully grounded by my substance and those other things. What are those other things? Is it other accidents of me? If so, then the problem repeats for them. Or is it something beyond my substance or accidents? But what would that be?

I am inclined to think that the solution to this problem is to reject 1. Somehow, 1 is reminiscent to me of the false view that:

3. x indeterministically causes y only if there are cs that deterministically cause y and x is one of the cs.

A Catholic argument against presentism

1. If Catholic teaching on the Eucharist is true, then there is a time t such that an accident of bread exists-at-t and no substance of which it is an accident exists-at-t.
2. It is metaphysically impossible that an accident exists and no substance of which it is an accident exists.
3. If presentism is true and x exists-at-t, then it is true at t that x exists.
4. Catholic teaching on the Eucharist is true.
5. If presentism is true and Catholic teaching on the Eucharist is true, then it is true at some time t that an accident of bread exists and no substance of which it is an accident exists. (By 1 and 3)
6. There is no time t such at that time it is true that an accident of bread exists and no substance of which it is an accident exists. (By 2)
7. So at least one of presentism and Catholic teaching on the Eucharist is false. (By 5 and 6)
8. So presentism is false. (By 4 and 7)

Traditionally, Catholic philosophers have denied (2). But (2) is very plausible, so we have a good argument against presentism.

Aristotelian perdurance

The perdurantist thinks that we are four-dimensional beings made up of three-dimensional slices, temporal parts, from which we inherit our changing properties such as thinking. One good reason to deny perdurance is that implies that our thinking is derivative from another entity's thinking, namely from the part's thinking, pace Andrew Bailey's very plausible thesis that our thinking does not derive from another entity's thinking. Another issue is that perdurance has at most a 50% chance of being true for me: since the slice thinks the same thoughts as the four-dimensional being, I have at least a 50% chance of turning out to be the slice--contrary to perdurance.

But there is an interesting Aristotelian version of perdurance. I am a four-dimensional being, but I have a sequence of special accidents D_t corresponding to the times t at which I exist. Then all my changing features are grounded in features of these accidents. For instance, I am thinking at t provided that D_t is thinking*, where thinking* is whatever feature of an accident D_t that makes the possessor of D_t be thinking. For categorial reasons, thinking* isn't thinking: only substances think, but non-divine substances think in virtue of having an accident that in turn is thinking*.

What are the D_t accidents? One option is that they are the accident of existing at t. But perhaps there is a more Thomistic option: perhaps in the case of material substances they can be identified with something like Thomas's accidents of dimensive quantity. Thomas thought that material substances had a special accident, a dimensive quantity, and all their other accidents were in turn accidents of its dimensive quantity. This is a very similar role to that played by D_t. Or, perhaps, we could take D_t to be an accident of occupying such-and-such a three-dimensional region of four-dimensional space. There is room for further research here (and if anybody wants to work more out and co-author, they are very welcome).

There is a major difference in outlook between this and typical perdurance pictures. On typical perdurance views, the slices are prior to the four-dimensional whole. On this Aristotelian perdurantism, the D_t accidents are, like all accidents, posterior to the substance, which is four-dimensional. Apart from this, the view might not be that distant from standard perdurantism. I have proposed in another post that an Aristotelian could identify parts with certain kinds of accidents. On that identification, the D_t accidents could turn out to be parts. But the difference in outlook remains: the parts really are just accidents of the whole. And the parts don't have the same features as the whole does. They have features for which we have no names, features we can only identify as that feature of the accident that grounds the substance as being F.

This post is really just a combination of this and this.

Colors and transsubstantiation

This is going to be very speculative, and I doubt it yields an orthodox account of transsubstantiation, but since there is some chance that it does yield such an account (and if it doesn't, we might get a deeper picture of transsubstantiation by thinking about why it fails), it's worth thinking about.

Let's say, as a first approximation, that an object is white at a spacetime region U provided that the object has a direct causal power of reflecting light incident on U diffusely and approximately uniformly across the visible spectrum. Observe that in this definition nothing was said about U being a region that is occupied by the object. It is logically possible for an object to have a causal power of action at a spatial and/or temporal distance, thereby diffusely and approximately uniformly reflecting light incident on a region unoccupied by the object. Now suppose that a white piece of bread is going to be destroyed, but just before it is destroyed the causal power of whiteness that it has is enhanced to work at a temporal distance, thereby diffusely and approximately uniformly reflecting light incident on a spatial region shaped like a piece of bread in the future after the destruction of the piece of bread. Then there is a sense in which the whiteness of the piece of bread persists after the destruction of the piece of bread.

It seems there are two senses in which we can say that the whiteness of an ordinary object is at a location V. One sense is that the relevant causal power is located at V and the other sense is that the object is directly causing light to be reflected whitely at V. The location of the accident of whiteness can be identified either with the location of the causal ground of the reflection or with the location of the immediate effect of that causal ground (the second matches how Aquinas understands the locations of angels: they are deemed present where they act). Normally, the two locations coincide or are very close together. So there is a a sense in which, in the scenario where the bread has the power of causing white reflections after its destruction, the accident of whiteness exists at the location where the reflection occurs, and hence continues to exist after the destruction of the bread.

Accidents outliving their substances

Thomas Aquinas's take on transsubstantiation supposes that the accidents of bread and wine can continue existing even after the bread and wine have perished, something that was heavily criticized by people like Jan Hus.

But here is an argument for the possibility of an accident outliving its substance. Consider a very long rattlesnake, stretching out to maybe ten million kilometers in length. The rattlesnake is rattling for one second. The rattling of the tail is an accident of the rattlesnake, call this accident R. Then the snake is near-instantaneously destroyed, e.g., by a series of synchronized explosive charges.

Well, near-instantaneously in one reference frame! This snake is long enough that there will be another reference frame in which the front half is destroyed 15 seconds before the back half is. In this reference frame, there will be a time when the rattling of the tail occurs even though the front half of the snake doesn't exist. But a snake whose front half has been destroyed is no longer existing. So in this reference frame the accident R exists even though the snake no longer does.

Granted, in the case of the snake it is only true in some reference frames that the snake doesn't exist while R does, while in the Eucharist the persistence of the accidents past the demise of the bread and wine takes place in all reference frames. But once we have seen that the principle that accidents must be contemporaneous with their substance is not generally true, I think some wind is taken out of the objector's sails.

Accidents outlasting their substance

At least as traditionally philosophically understood, the Catholic understanding of transsubstantiation insists on the persistence of (at least some) of the accidents of bread and wine after the bread and wine have ceased to exist. But how can accidents exist without their substance?

Well, imagine a very long rattlesnake—say, a billion kilometers long—all stretched out in space. Suppose that the snake rattles its rattle at noon for a second, and one second after the end of the rattling a prearranged array of blasters simultaneously annihilates the whole snake.

Let R be the accident of the snake's rattling. A simple relativistic calculation shows that there is an inertial reference frame in which the rattling occurs after the vast majority of the snake—including all of the snake's vital organs (which I assume are placed much as in a normal snake)—has been annihilated. But an animal is dead, and hence non-existent (barring afterlife for animals; let's stipulate there is none), after all its vital organs have been annihilated. Thus, there is a reference frame in which the accident R exists after the substance S of the snake has been annihilated.

So special relativity gives us good reason to think that accidents can survive the destruction of the substance, at least in some inertial reference frames. But all inertial reference frames are supposed to be on par.

I suppose an opponent of transsubstantiation could insist that while an accident can survive the destruction of a substance in some reference frames, it cannot survive the destruction of the substance in all reference frames (as it would have to in the case of the Eucharist). But that requirement sounds a little ad hoc.

So, relativity theory gives us good reason to reject one of the most famous objections to transsubstantiation.

Eternalism and accidents without a subject

A classic objection to transubstatiation, famously pressed by Wycliffe, is that according to the Catholic understanding of the doctrine, the accidents of bread and wine persist even though the substance of bread and wine no longer exists. But in Aristotelian metaphysics, accidents are essentially dependent on their substance.

Eternalism—the view that past and future and present things all exist—provides a neat way for the Catholic to respond to Wycliffe. One can, if one so wishes, hold on to the idea that it is metaphysically necessary that a subject exists if an accident exists. But one denies that it is metaphysically necessary that the subject exists at the same time as the accident. The eternalist then holds that even if the bread and wine have perished at a time t₁ after transubstantation, nonetheless it is true at t₁ that the bread and wine exist, where the "exist" is tenseless. On this view, every accident has a subject in the same world but not always at the same time.

Are parts modes?

There are two variations on Aristotelian ontology. On the sparser version there are substances and their modes (accidents and essences). On the more bloated version there are substances, modes and (proper) parts. I want to argue that the more bloated version should be reduced to the sparser one.

Parts in an Aristotelian ontology are unlike the parts of typical contemporary ontologies. They are not substances, but rather they are objects that depend on the substance they are parts of. At least normally when a part, say a finger, comes to be detached from the substance it is a part of, it ceases to exist—a detached finger is a finger in name only, as Aristotle insists.

This makes the parts of Aristotelian ontology mode-like in their dependence on the whole. Ockham's razor then suggests that rather than supposing three fundamental categories—substances, mode and parts—we will do better to posit that a part is just a kind of mode. Thus, I really do have a heart, but my heart is just much a mode or accident of me—my cardiacality—as my knowing English is. Both my heart and my knowledge of English confer on me certain causal powers and causal liabilities (knowing English makes me liable to having my feelings hurt by uncomplimentary assertions in English!)

This is not an elimination of parts. Some of my accidents are parts and others are not. Which ones? I do not know. Maybe those accidents that occupy space are parts and those accidents that do not are not. My knowing English doesn't occupy space, while my cardiacality is somewhat vaguely but really located located in space.

Perhaps we need a finer distinction, though. Consider the strength of my arm. This isn't a part of me, but it seems to be located in my arm. I suggest that we distinguish between three ways that a mode can get a location. It can (a) inherit a location from a subject, or (b) it can inherit a location from its own modes, or (c) it can be located in its own right. I suggest that a mode is a part if and only if it has a location of type (b) or (c). The strength of my arm inherits its location from its subject—my arm—and hence is not a part. (It's important to the full development of this ontology that modes can nest. Thus, my arm is a mode of me, and the strength of that arm is a mode of this mode. Both I and my arm are subjects of the strength of the arm.)

I think the distinction between type (b) and type (c) parts is worth thinking about. Maybe matter, that mysterious ingredient in Aristotelian ontology, can be identified with type (c) parts?

A theory of time

This isn't meant to be a very good theory, but it's a start. The primitive notion I want to explicate is this notion of temporal priority between events: A is at least in part earlier than the start of B. I will abbreviate this to "A is earlier than B". And then we say that A is earlier than B if and only if there is a chain of at least partial causation starting at A and ending at B.

A consequence of this theory is that it is not possible to have simultaneous causation: if A causes B, then A is earlier than B. That's a count against it, but perhaps not a fatal one.

Another consequence of this theory is that it gives no account of simultaneity between events. That may not be such a bad thing.

A limitation is that we have no notion of a time, just of temporal ordering of events. That may be fine. But the costs are adding up.

I am more troubled by the fact that this rules out time travel and, more generally, temporally backwards causal influences. This makes me want to reject the theory.

But I can reprise the theory, not as a theory of the temporal priority between events, but of the temporal priority between accidents (or maybe just modes?) of a single substance. Just say that an accident A of a substance S is earlier than an accident B of S if and only if there is a chain of at least partial causation between accidents of S starting at A and ending at B.

We still have to rule the possibility of temporally backwards causation within the life of a single substance. But that's less costly, I think, than ruling out temporally backwards causation between events in general.

We still have the problem of not having simultaneous causation or any account of simultaneity for that matter. And no notion of times.

We can introduce times as follows. In some worlds, it will happen that there are nomic relationships between the accidents of a substance that are simply parametrized in terms of some parameter t such that accident A is earlier than accident B (in the above causal sense) if and only if t(A)<t(B). In such a case, we can call values of this parameter times. In worlds where there is no such neat parametrization, there may be temporal priority, but no times.

We get divine internal atemporality now as a corollary of the claim that God has no accidents.

But there are still a lot of costs. For one, the lack of a notion of simultaneity makes it hard to make sense of the transcendental unity of apperception. Maybe that's just too bad for that unity?

The incarnation and adverbial ontology

Christ is God and Christ is a human. God is unchanging and humans are changing. God is omnipresent and humans are spatiotemporally delimited. God is all powerful and the power of humans is limited. All praise be to Christ on this Christmas day!

Yet such theological claims appear to lead to contradiction: is Christ unchanging or change? is he limited or unlimited? Since we have excellent reason to think the claims are all true, we have excellent reason to think the claims are not contradictory. A traditional way to resolve the apparent contradiction is to introduce a qua or as qualifier:

1. Christ is unchanging, omnipresent and omnipotent as God, but as human he changes, and is limited in presence and power.

Such answers do work logically speaking, but it would be good to have a little bit more to say about what the "as" does.

I want to suggest something that may not be original[note 1] but that I found enlightening. Start with the observation that there is no contradiction at all in this sentence:

2. Sam is quick as a reader and slow as a runner.

And there is an obvious and easy way to understand (2) that removes all appearance of contradiction:

3. Sam reads quickly and runs slowly.

No contradiction results from contradictory adverbs being attached to different predicates. From Sam reading quickly we can deduce that Sam does something quickly, but that does not contradict his doing something else slowly.

Now we can make the same move in regard to (1). We will need two base predicates which are then adverbially modified. The ones that come to mind are "is God" and "is human". Then (1) becomes:

4. Christ is God unchangingly, omnipresently and omnipotently, but he is human changingly and limitedly in presence and power.

So far that's just words. But now make it into ontology. The ontology takes a cue from Spinoza's nesting of modes. (Other philosophers have nested modes, but I think it is only in Spinoza that the nesting is really central.) When Sam reads quickly, there is Sam, who reads, and Sam's reading, which is quick. If Sam reads excessively quickly, there is Sam, who reads, and Sam's reading, which is quick, and the quickness of Sam's reading, which is excessive. All of these, other than Sam himself, are modes (Spinoza wrongly thinks Sam is a mode, too). We can now talk of a mode being directly or indirectly a mode of something. Thus, the quickness of Sam's reading is directly a mode of Sam's reading and indirectly a mode of Sam. The excessiveness of Sam's quickness of reading is directly a mode of Sam's quickness of reading and indirectly a mode of Sam's reading as well as of Sam.

Next theorize that a mode m is an essence of an individual x if and only if m is directly a mode of x. This could simply be a necessary "if and only if" or, more ambitiously, it could be an account of what it is to be an essence, essences being nothing but direct modes. Observe that this is a non-modal account of essence—here we are talking of essence in the ancient and medieval sense, not in the modern modal sense (such a distinction was pointed out by Fine, but the best account in print is by Michael Gorman).

Thus all our accidental modes are indirectly modes of us, through our essence. My present typing of this post is a mode of my humanity: I am human typingly. And Christ, unlike us, has (at least[note 2]) two essences: humanity and divinity. Thus any mode of his is one of his essences or is a mode of one of his essences. (Sometimes our words will be ambiguous. Thus when we say that "Christ is wise", that is ambiguous whether he is divine in a wise manner or is human in a wise manner or both.)

This account makes it plausible that analogy will be a central concept. Adverbs apply analogically across predicates. The "quickly" in "Sarah runs quickly" and "Sarah thinks quickly" is to be understood analogically. In general, I suspect cross-essence predications are to be understood analogically. That is a Thomistic aspect in the theory.

Another Aristotelian aspect is that we can make sense of "necessary accidents". Thus, Aristotle thinks it is an accident of a human that the human have a capacity for laughter, but he also thinks this is a necessary accident—every human necessarily has a capacity for laughter. It is insufficient for a mode to be an essence that the mode is necessary: it must be directly a mode of the individual. But just as it is indirectly a mode of me that I be laughing—I am human laughingly when I laugh (which differs from, say, being an alien or angel laughingly)—it indirectly but necessarily a mode of me that I have a capacity for laughter—I am a human with a capacity for laughter ("with..." is one of the many ways of indicating adverbial modifiers).

There is a serious theological difficulty. Does not the account contradict divine simplicity? After all, does not (4) posit a mode of God, namely divinity, and modes of a mode of God, namely omnipresence of divinity, omnipotence of divinity and unchangingness of divinity? Yes, but that only contradicts divine simplicity if these modes are all distinct. But they aren't distinct. Divinity, omnipresence of divinity and all the others are all just God. Thus God is his own mode in this technical vocabulary. But since predication of God is analogical, what this means it that God is related to himself in a way analogical to our relationship to our modes. (Compare: the person who loves herself is related to herself in a way analogical to the way someone who loves another is related to that other.) It's important not to take "mode" to mean "accident", but that was already something necessary from the fact that essences are modes.

Of course, this is not a complete account of divine simplicity yet. Something needs to be said about apparently contingent modes of God, such as creating Adam. (I think claims like "God creates Adam" should not be taken as predicating a mode of God. Why not, with the medievals, take the claim as predicating a mode of Adam? Or as predicating being creator of all contingent beings of God and contigency of Adam?)

This reconciliation with divine simplicity does, however, mean that I cannot simply define a substance as something that isn't a mode. For God on this reconciliation is a substance and a mode. (And that is Thomistic, too, though the vocabulary of "mode" is not. God is both substance and that substance's pure act.) We might define a substance as something that isn't a mode of anything else. Or we might say that x is a substance if and only if the proposition that x exists has a truthmaker which is x and has no other truthmaker.

Finally, I leave it as an exercise to the reader to extend my "metaphysically Aristotelian quantification" to this context. At the same time, some of my cross-level uses of "is" in this post will need some charitable analogical reading.

Eifelheim

I recently read, and very much enjoyed, Eifelheim (can be bought from amazon, or downloaded for free in pdf format from the author's literary agency), Michael Flynn's novel of aliens landing outside a Black Forest village in the 14th century. The best parts--from my point of view--of the novel were the interactions between the village's pastor, a man of formidable Parisian education (yes, this might seem unlikely, but there is a story there) and a friend of Ockham, and the aliens. Flynn captures cutting-edge 14th century scientific and philosophical thinking with great sympathy and surprising fidelity, and shows how a smart 14th century scholastic with Ockhamist tendencies would interact with 21st (or later) century science. We see the flexibility of scholastic categories, a flexibility that is going to be of interest to those of us still interested in a reconciliation between contemporary science and scholastic metaphysics.

I did not expect to read a novel that alludes to an Ockhamist argument against the possibility of nested accidents. (This is in support of an argument that the pastor gives against light having a velocity. The idea is that light is an accident of fire, so if light had a velocity, that velocity would be an accident of an accident, which is impossible.)

The medieval and alien characters are well-drawn and develop over the course of the novel. I was somewhat less happy with the portions set in the 21st century, but they were relatively briefer (and they may have been written first). All in all, quite an excellent piece of science fiction.