Non-local real presence of Christ

Aquinas’s account of location for material substance is as follows. Ordinary material substances have a special accident—one more fundamental than all other matter-related accidents—he calls “dimensive quantity”, but which I will just call “dimensions”. This accident makes the object have a specific shape and size. The substance is then in a place provided that its dimensions are “commensurate with” that place—namely, provided that the dimensions are fitted into the place.

We can now say that a substance x is present in a place z in virtue of the following two presentness facts:

1. x is present in its dimensions D

2. the dimensions D are present in place z.

Furthermore, in the ordinary case, we can have an account of what “present” means in (a) and (b). A substance’s being present in dimensions D is just the substance’s having the dimensions D as an accident. And the dimensions being present in a place z is just their being commensurate with z. (This last one would bear more analysis, but that’s not my interest here.) When we have (a) and (b) with “present” grounded in this way—by having and commensuration respectively—we have what St Thomas call “local presence” or what we might call “ordinary physical location”.

Now, in the Eucharist the following happens according to Thomas. The substance of the bread turns into the body of Christ. The accidents of the bread miraculously remain in existence, but are no longer the accidents of any existing substance (whether bread or Christ). In particular, the dimensions D of the bread remain (and are a subject for the other accidents). And Christ’s body is present on the altar (say) because of the following two presentness facts:

3. Christ’s body is present in the dimensions D which are formerly of the bread

4. the dimensions D are present on the altar.

The ground of (d) just like that of an ordinary case of (b): the dimensions are commensurate with the place. But since Aquinas insists that Christ does not take on the accidents of the bread, the ground of (c) must be different from the ground of the ordinary case of (a): Christ does not have D. (In particular, Christ is not round and thin when transsubstantiation happens in a western Catholic Church.) Instead, Thomas says about (c) that Christ is “substantially” in the “foreign” dimensions D, but is not a subject of these dimensions, i.e., does not have them. As a result, we have the same structure of presence as in the ordinary case—it is mediated by dimensions—but because the grounds of the substance’s presence in the dimensions are different, this is not ordinary physical location any more.

In my 2008 paper, I gave up on figuring out what is meant by “substantial presence”, and indeed suggested that the problem is insoluble, and we should go for a different solution, one on which Christ has ordinary physical location on the altar. That solution may well be right, but I want to try out a more Thomistic solution—though the full story does not fit with everything Thomas says.

Consider the relationship between Seabiscuit and his accident of swiftness. This relationship has two features which make for interdependence:

1. Seabiscuit’s swiftness ontologically depends on Seabiscuit, i.e., Seabiscuit ontologically sustains his swiftness

2. Seabiscuit is qualified by his swiftness.

In all ordinary cases, the relations of ontologically sustaining and being qualified by between a substance and an accident are coextensive. Seabiscuit sustains all his accidents and they all qualify him, and similarly for all substances. To have an accident is then for the accident to ontologically depend on one and for one to be qualified by it.

Expanded out this way, we have a richer story as to what grounds an ordinary substance being present in its dimensions: the substance ontologically sustains the dimensions and is qualified by them.

Now, Thomas’s denial that Christ is “subject to” the dimensions of the bread means one aspect of the ordinary relationship between a substance and its accident is absent here—Christ is not qualified by the dimensions. However, that still leaves the possibility that the other aspect of the relationship is present. In other words, we can suppose that miraculously Christ’s body ontologically sustains “foreign” accidents that this body is not qualified by. This ontological sustenance relationship makes Christ’s body be substantially in the accidents, including in the dimensions.

Thus, the expanded account is:

1. Christ’s body is present in the dimensions D formerly of the bread by ontologically sustaining these dimensions in the way that a substance sustains its accidents but without D qualifying Christ’s body and hence without D becoming its accident.

2. The dimensions D are commensurate with a place, just as in ordinary physical location.

The presence in (1) is a special case of a type of presence that Thomas recognizes in his account of divine omnipresence. Thomas says that God is present to all things “by his essence”, namely by directly being their cause. This causation is, of course, divine sustenance. Thus, Christ’s body’s being “substantially” in the dimensions by sustaining them ontologically is like God’s being “by essence” present to all things by sustaining them. This is a recognized and metaphysically serious mode of presence, and hence it plausibly counts as a real presence.

At this point, it may seem that I have solved the problem of what Aquinas means by the substantial presence of Christ’s body in the dimensions of (the former) bread. But there is one hitch. I think Aquinas disagrees with my account. When Aquinas discusses how the accidents of bread and wine can remain without their substances, his answer is not that the body of Christ sustains them, but that God sustains them, because anything that can be done by creaturely causes can be done by God. St Thomas’s phrasing very much sounds like he thinks the sustenance of the accidents is done directly by the power of God.

The account I am offering requires that God miraculously bestow on Christ’s body the power to sustain accidents foreign to it (without being qualified by them). I don’t see any good reason to think this can’t happen. We thus have an extension of Thomas’s account, but it is one that I think is compatible with other aspects of his metaphysics and theology.

I am still not completely convinced that I should abandon my account on which Christ’s body is present in the Eucharist by ordinary physical location. My account clearly makes Christ’s body by really present. The modified Thomistic account may do that, but it may not.

I want to end with a consideration in favor of the Thomistic view that Christ’s presence in the Eucharist is not ordinary physical location. Many Protestants think that Christ’s body is “spiritually present”, and historically the Reformed wing of the Protestant tradition has taken spiritual presence quite seriously—not just as symbol—while denying ordinary physical presence (I am grateful to one of my graduate students for pointing this out). An account of Christ’s real presence that makes Christ not be ordinary physically present thus has an advantage: it fits with the intuitions not only of many Catholic thinkers but also of many non-Catholic ones. Perhaps the modified Thomistic account just is what spiritual presence is, and hence we have a way of moving Catholics and some Protestants closer together through St Thomas.

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’.

Aquinas on Incarnation as a rock or animal

Aquinas thinks it would be unfitting for God to become incarnate as a non-rational creature. In Summa Theologiae III.4.1, his reasoning is that human nature had an appropriate dignity, as it “was apt to contain the Word Himself in some way through its operation, by knowing Him and loving Him”, but not so for the non-rational creatures. In Summa Contra Gentiles 4.55 we have a different and more philosophical argument:

We must also observe that the rational creature alone acts of itself, for irrational creatures are more driven by natural impetus than act of themselves [magis aguntur naturali impetu quam agant per seipsas]; thus they are to be regarded as instruments rather than principal agents. Now it was fitting that God should assume a creature capable of acting of itself as principal agent, because an instrumental agent acts through being moved to action, whereas the principal agent acts itself and of itself. Accordingly, if God were to do anything by means of an irrational creature, all that is required in accordance with that creature’s natural condition is that it be moved by God, and there is no need for it to be assumed into personal union so as to act itself, since its natural condition does not admit this, it being admitted solely by the condition of rational nature [quia hoc eius naturalis conditio non recepit, sed solum conditio rationalis naturae]. (Shapcote, with italicized phrases retranslated.)

In neither text does Thomas deny the metaphysical possibility of God being incarnate as a nonrational creature, such as a rock, plant or animal. While this is an argument from silence, I think it is a pretty strong one: if he thought it was impossible, we really would expect him to say so, rather than merely saying it was unfitting.

Both arguments seem to me to be based on the idea that if it’s fitting for God becomes incarnate as X, if there is to be much of a point to this incarnation, this X needs to be of a sort that can express the divine person in a special way. If the Logos were to become a piece of granite, the petrous behavior of the rock would not differ from that of any other piece of granite. But if the Logos becomes a human, the rational behavior of this human is able to distinctively express the Logos in a way that ordinary human persons do not. We see this in the Gospels: Jesus as a human being, in his free human choices, movingly expresses the personality of the Second Person of the Trinity. He is just as human as all of us, but all of us humans are different from one another in our operations in a way that is expressive of the person. Of course, all pieces of granite are different from another, but these differences are not due to the operations of the rock differently expressing the rock’s hypostasis (we shouldn’t say person!). Rather they are due to the differences in the matter the rock was formed from and the external forces. God can be expressed in granite.

Of course, every rock reflects God’s goodness, and some rocks especially so, say because they are formed into a beautiful statue or inscribed with a meaningful text. But the special expression of God’s goodness is just a function of the rock’s initial matter and external influences. If God wants a rock to particularly well express him, there is no advantage to God’s becoming the rock: “all that is required … is that it be moved by God”—and all rocks are ultimately moved by God. But it is different for a human, that is a self-originator of its behavior. For the self-originated agency to be fully an expression of God, the person who is human, from whom that behavior originates, needs to be a person who is God. There is thus something that the Logos can accomplish by taking on a rational nature that cannot be accomplished in any other way. We might say that all of creation is God’s self-expression by creatures, but in becoming a human, God can be self-expressed in a creature—something that could not happen if God were to become a non-rational creature. This highlights how it it is that the Incarnation is also an ultimate completion of the act of creation. God’s becoming a non-rational creature would be just God showing off, rather than God manifesting his love by living that love as a human.

TWo closing thoughts. First, I think Aquinas’ Contra Gentiles argument works best if non-rational creatures function deterministically. Given quantum mechanics, we have good reason to think they are indeterministic. But nonetheless the basic point remains: randomness is not really a self-expression, so even if the Logos were to control the quantum processes from the inside, it seems that as long as that control was fully in accordance with the nature of the non-rational creature, it wouldn’t be distinctively expressive of divinity.

Second, I am not sure that Aquinas’ Contra Gentiles argument fits well with Aquinas’ theological compatibilism, on which God can through primary causation make us freely behave a particular way. At least we can say that the argument works better if we have theological indeterminism. And thus theological indeterminism has a theological advantage: it gives us a deep reason for why the incarnation as a human is fitting.

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.

How has Aquinas not proved the Trinity?

St Thomas holds that we cannot know by natural reason that God is a Trinity. However, he also endorses a version of St Augustine’s account of the Trinity, on which God has a mental Word or concept of himself that he generates mentally, and then there is a Love that is responsive to that Word. Why is this not a proof by natural reason?

On this point, Thomas is sadly brief in the Summa Theologiae: “Again, the similarity with our intellect does not sufficiently prove anything about God, since the intellect is not found univocally in God and in us.”

But Aquinas thinks that we can literally talk about God, even if we do so by means of analogy. He has argued, by reason, that God exists and has all perfections. One of these perfections is knowledge of everything, and thus of himself. Does this not commit Aquinas to being able to say on the basis of natural reason that God generates his self-knowledge, a self-knowledge that, by divine simplicity, must then be God himself rather than a mere creature? And does not God love himself under the description that this knowledge provides?

I think Aquinas would (with perhaps minor cavils) endorse all the claims in my previous paragraph as knowable by natural reason. How is this not a proof of the Trinity? I think the answer is this. Focus on the generation of the Son—the case of the Holy Spirit will presumably be similar. We do not know by reason whether the relation of generating self-knowledge is a real relation in God. If it is a real relation it will individuate the knower from the knowledge, thereby ensuring that there are at least two persons in God. But it needs to be a real relation in God, rather than a merely conceptual one. And here Thomas’s brief remark about univocity seems apposite. Aquinas thinks that what makes our language about God analogical rather than univocal is that the grounding of claims about God is radically different from the grounding of similar claims about creatures. Thus, when we say Socrates is wise, this is grounded by the inherence in Socrates of an accident of wisdom, while when we say God is wise, this is grounded by the identity between God and his wisdom. Because of this, even if it turns out that in us the generation of self-knowledge is a real relation (but not one between persons, since we are not simple, and hence our self-knowledge does not need to be of one essence with us), since the grounding structure of claims about God is radically different, as far as unaided human reason goes, it may not be grounded in a real relation in God—though it might be. We need God’s revelation to know if it is a real relation or not. And indeed God has revealed that it is.

Does everything in time change?

Over the last two days, I’ve been thinking critically about Aquinas’ First Way. Central to my thinking, and especially yesterday’s post, was the idea that you could have an unmoved mover who is in time but isn’t pure act and who isn’t God. Such an unmoved mover constantly and unchangingly exercises—perhaps mentally—one and the same causal power to make something else move.

But I now wonder if this is possible. Suppose a demiurge that exists in time and has the power to make Bob rotate, and constantly exercises this power. Could this demiurge be unchanging? After all, at noon the demiurge is actively rotating Bob at noon, and at 1 pm the demiurge is actively rotating Bob at 1 pm. We can easily and coherently suppose that the demiurge engages in qualitatively the same activity at 1 pm as at noon. That was the intuition that was driving my thinking about this. But can we coherently add that it is the numerically same activity? For if it’s not numerically the same activity at 1 pm as at noon, then the demiurge has undergone a change, from engaging in activity a₁₂ to engaging in activity a₁₃, even if the two activities are exactly alike.

I am not sure, but I feel a pull to thinking that rotating Bob at 1 pm is a different thing from rotating Bob at noon, assuming that the agent is in time. I don’t just mean that it has different effects—which it does, since spinning-at-noon is a different effect from spinning-at-one—but that the activity of causing rotation is itself different. Maybe the pull comes from this thought. Perdurantists think that substances exist at different times by having different temporal parts at them. Perdurantism is likely false for substances. But whether or not it is true for substanes, it seems very plausible for events and activities. What made World War II exist on each day between September 1, 1939 and September 2, 1945 is that there were hostilities on each day, hostilities that are a part of World War II. Even if on two successive days the hostilities happened to be exactly alike, they would have been numerically different hostilities. If this is right in general, then the activity of rotating Bob at 1 pm is numerically different from that of rotating Bob at noon.

Furthermore, I think existence is a kind of activity. This is most obvious in the case of living things, given the Aristotelian idea that life is the existence of the living and life is an activity, but I think is true in general. Thus a thing that exists in time over a lifetime engages in a sequence of numerically different activities—existing at t₁, existing at t₂, and so on. And hence it changes. And intrinsically so. If so, then everything that exists in time must always change.

If the suggestion that there are no unchanging activities that last over time, then we can escape my worry yesterday that perhaps the sequence of moved movers in the First Way leads to a mover that is unchanging with respect to the activity of moving the next mover in the sequence but is still changing in some other coincidental respect. For the activity of moving the next mover in the sequence would have to change over time, and so the mover would be changing in respect of of its moving the next item in the sequence.

But perhaps not. For we might admit that in all the cases we are familiar with, activity only perdures over time, and there is always something numerically different happening at different times, but say that we could still imagine a being where the numerically same activity is temporally multilocated. And such a being could everlastingly rotate Bob with the activity of spinning Bob being genuinely unchanging.

I don’t know.

How do we get to an unmoved mover?

I just realized that there is a difficulty in Aquinas’ First Way that I think hasn’t been noted, which builds on the difficulty noted yesterday.

Put the First Way in the following simpleminded way, which I think captures the central ideas:

1. Causes of change are either passers-on of change or originators of change.

2. It can’t be that the causes of change are all passers-on of change.

3. So there must be an originator of change.

4. And this is an unmoved mover (or, more precisely, unchanged changer).

There is a fair amount of detail one can fill in to argue for (2), but that’s not what I want to focus on. I want to focus on the move from (3) to (4).

What licenses us in thinking that an originator of change is itself unchanging?

The idea seems to be that if a cause of change is itself changing, then it is merely a passer-on of change. But this need not be. In my previous post, I imagined an unchanging and timeless demiurge endowed by God with the power to originate change, and noted that in that scenario the demiurge is an unmoved mover but isn’t God.

But now let’s build up and modify my demiurge story. First, let’s be concrete about what motion the demiurge causes. The demiurge has been gifted by God with the power to directly will Bob to rotate around a fixed axis, and the demiurge changelessly exercises this power. (Maybe Bob is one of the Aristotelian heavenly spheres). Second, let’s specify that the demiurge, albeit unchanging, is in time and has an unchanging body in addition to a mind and will. If we can’t have a changeless thing in space and time, don’t worry about it. The third step will fix that. The third step is this. The demiurge itself is caused by God to slowly orbit the sun in a way that the demiurge does not notice.

Thus, we have a demiurge with a mental power to make Bob rotate, and the demiurge exercises this mental power changelessly. At the same time, and completelessly coincidentally to the demiurge’s exercise of the mental power to make Bob rotate, the demiurge orbits the sun.

The demiurge is thus a moved mover. But it is also an originator rather than passer-on of change. In Aristotelian terminology, the demiurge is a moved mover per accidens: its own movement around the sun is coincidental to its origination of Bob’s axial rotation.

We cannot, thus, assume from the existence of an originator of change that there is an unmoved mover.

Does Aquinas have the resources to fill in the gap? Of course, if the (accidentally) moved originator of change coming out of step (3) of the argument is itself changing, that change has to have a cause, and we can then run the argument again. If we can rule out an ungrounded infinite sequence of accidentally moved originators of change—ones that like our demiurge happen to be moving in one respect but produce change by a coincidental exercise of power—then we can get to a genuinely unmoved mover.

But Aquinas’ main tool for avoiding regresses in cosmological arguments is the idea that there cannot be an infinite regress in a per se causal sequence. And while there are complications in the notion of a per se causal sequence, I think it is pretty clear that the sequence I am imagining is not a per se causal sequence. The demiurge’s moving of Bob is coincidental to the demiurge’s own motion. Suppose that a demiurge makes Bob spin by an unchanging exercise of a mental power, and a tetartourge by an unchanging exercise of a mental power makes the demiurge coincidentally slowly orbit the sun while the tetartourge coincidentally orbits the moon. Then the tetartourge is not a cause of Bob’s motion. But in a per se causal sequence we have transitivity: the earlier items are always causes of the later ones. So this is not a per se causal sequence.

Of course, we might ask what explains the demiurge’s (and tetartourge’s) possession and exercise of the mental power to make something else move. But now we are deviating from the First Way: we are asking for explanations of something other than change. I think one can fill this in, by an argument about causation and regresses rather than change and motion. But if we do that, then the stuff about change and motion that is at the heart of the First Way can simply drop out.

I titled my previous post “An easily patched hole in the First Way”. But I think I was too glib there, too. In that context, too, I think one needs to go beyond the resources of the First Way to patch the hole.

An easily patched hole in the First Way

In his First Way, Aquinas argues that as we trace back the sequence of movers from effect to cause, we get to a first unmoved mover, and this is God.

But need the unmoved mover thus reached in the sequence of movers be God? Imagine this scenario. God creates some material beings, as well as an unchanging, timeless and immaterial demiurge that has the power to make the material beings move—and indeed exercises that power. Then if we were to trace back the sequence of movers, the unmoved mover we would get to would be the demiurge, not God. This demiurge would have potentiality, but not a temporal potentiality, so it would not be itself in motion, and hence it would be an unmoved mover.

This doesn’t deeply affect the argument, since Aquinas could do the same thing as he does in the Third Way, where he traces contingent beings to a necessary being, and then considers the possibility of necessary beings that get their necessity from other beings, and traces it back to an absolutely necessary being, namely God. Similarly, God could say that any unmoved mover that has some potentiality or contingency depends on a prior being and so on, and in the end we would get to God anyway.

Indeed, even in this scenario with a demiurge, we might want to say that it is God and not the demiurge who is the first unmoved mover. For God would still be a mover, albeit working through the demiurge who is a secondary cause, and God would be unmoved, and God would be first. So Aquinas would still be correct that the “first mover” is God—it’s just that the scenario suggests that Aquinas does skip a step.

Per se and per accidens multiplication of causes

Can there be an infinite sequence of efficient causes? Famously, Aquinas says both “No” and “Yes”, and makes a distinction between a per se ordering (“No”) and an accidental ordering (“Yes”). But it is difficult to reconstruct how the distinction goes, and whether there is good reason to maintain given modern physics.

Here is the central passage from Summa Theologiae I.46.2 reply 7, in Freddoso’s translation:

It is impossible to proceed to infinity per se among efficient causes, i.e., it is impossible for causes that are required per se for a given effect to be multiplied to infinity—as, for instance, if a rock were being moved with a stick, and the stick were being moved by a hand, and so on ad infinitum.

By contrast, it is not impossible to proceed to infinity per accidens among agent causes, i.e., it is not impossible if all the causes that are multiplied to infinity belong to a single order (ordinem) of causes and if their multiplication is incidental (per accidens)—as, for instance, if a craftsman were to use many hammers incidentally, because one after another kept breaking. In such a case, it is incidental to any given hammer that it acts after the action of a given one of the other hammers. In the same way, it is incidental to this man, insofar as he generates, that he himself was generated by another. For he generates insofar as he is a man and not insofar as he is the son of some other man, since all the men who generate belong to the same order (gradum) of efficient causality, viz., the order of a particular generating cause. In this sense, it is not impossible for man to be generated by man ad infinitum.

However, it would indeed be impossible for the generation of this man to depend upon that man, and upon an elemental body [a corpore elementari], and upon the sun, and so on ad infinitum.

What’s going on here? Re-reading the text (and double-checking against the Latin) I notice that per se and per accidens are introduced not as modifying the causal relations, but the infinite multiplication of causes. No indication is given initially that the causation functions differently in the two cases. Further, it is striking that both of the examples of per accidens multiplication of causes involve causes of the same type: hammers and humans (Freddoso’s “man” translates homo throughout the text).

To a first approximation, it seems then that what is forbidden is a regress of infinitely many types of causes, whereas a regress of infinitely many tokens is permitted. But that is too simple. After all, if an infinite causal sequence of humans generating humans were possible, it would surely also be possible for each of these humans to be qualitatively different from the others—say, in exact shade of eye color—and hence for there to be infinitely many types among them. In other words, not just any type will do.

Let’s focus in on two other ingredients in the text, the observation that the humans all “belong to the same order of efficient causality”, and the sun–elementary body–human example. Both of these rang a bell to me, because I had recently been writing on the Principle of Proportionate Causality. At Summa Theologiae I.4.2, St Thomas makes a different distinction that distinguishes between the human–human and the sun–body–human cases:

whatever perfection exists in an effect must be found in the effective cause: either in the same formality, if it is a univocal agent—as when man reproduces man; or in a more eminent degree [eminentiori modo], if it is an equivocal agent—thus in the sun is the likeness of whatever is generated by the sun’s power.

Here is a suggestion. In distinguishing per se and per accidens infinite multiplication of causes, Aquinas is indeed distinguishing counting types and tokens. But the types he is counting are what one might call “causal types” or “perfections”. The idea is that we have the same causal type when we have univocal agency, “as when man reproduces man”, and different causal type when we have equivocal agency, as when the sun generates something, since on Aquinas’ astronomical theory the sun is sui generis and hence when the sun generates, the sun is quite different from what it generates. In other words, I am tentatively suggesting that we identify the gradus of efficient causality of I.46.2 with the modus of perfection of I.4.2.

The picture of efficient causation that arises from I.4.2 is that in a finite or infinite causal regress we have two types of moves between effect and cause: a lateral move to a cause with the same perfection as the effect and an ascending vertical move to a cause that has the perfection more eminently.

The lateral moves only accidentally multiply the explanations, because the lateral moves do not really explain the perfection. If I got my humanity from another human, there is a sense in which this is not really an explanation of where my humanity comes from. The human I got my humanity from was just passing that humanity on. I need to move upwards, attributing my humanity to a higher cause. On this reading, Aquinas is claiming that there can only be finitely many upwards moves in a causal regress. Why? Maybe because infinite passing-on of more to less eminent perfections is just as unexplanatory as finite passing on of the same perfection. We need an ultimate origin of the perfections, a highest cause.

I like this approach, but it fits better with the sun–elemenatary body–human example than the hand–stick–rock example. It seems, after all, that in the hand–stick–rock example we have the same relevant perfection in all three items—locomotion, which is passed from hand to stick and then from stick to rock. This would thus seem like a per accidens multiplication rather than a per se one. If so, then it is tempting to say that Aquinas’ hand–stick–rock example is inapt. But perhaps we can say this. Hand-motion is probably meant to be a voluntary human activity. Plausibly, this is different in causal type from stick-motion: going from stick to hand is indeed an explanatory ascent. But it’s harder to see the progression from rock to stick as an explanatory ascent. After all, a rock can move a stick just as much as a stick can move a rock. But perhaps we can still think we have an ascent from rock-moving to stick-moved-by-hand, since a stick-moved-by-hand maybe has more of the perfection of the voluntary hand motion to it? That sounds iffy, but it’s the best I can do.

I wish Aquinas discussed a case of stick–stick–stick, where each stick moves the next? Would he make this be a per se multiplication of causes like the hand–stick–rock case? If so, that’s a count against my reading. Or would he say that it’s an accidental multiplication? If so, then my tentative reading might be right.

It’s also possible that Aquinas’ examples of hand–stick–rock and sun–elementary body–human are in fact more unlike than he noticed, and that it is the latter that is a better example of per se multiplication of causes.

Per se and per accidens ordered series

I’ve never been quite clear on Aquinas’ famous distinction between per se and per accidens ordered series, though I really like the clarity of Ed Feser’s explanation. Abridging greatly:

An instrumental cause is one that derives whatever causal power it has from something else. … [A]ll the causes in [a per se] series other than the first are instrumental [and thus] are said to be ordered per se or “essentially,” for their being causes at all depends essentially on the activity of that which uses them as instruments. By contrast, causes ordered per accidens or “accidentally” do not essentially depend for their efficacy on the activity of earlier causes in the series. To use Aquinas’s example, a father possesses the power to generate sons independently of the activity of his own father … .

The problem here is that it’s really hard to think of any examples of purely instrumental causes in this sense. Take Aquinas’s example of a per se series where the hand moves a stick which moves the stone. That may work in his physics, but not in ours. Every stick is basically a stiff spring—there are no rigid bodies. So, for ease of visualization, let’s imagine a hand that pushes one end of a spring, and the other end of the spring pushes the stone. When you push your end of the spring, the spring compresses a little. A compression wave travels down the spring and the tension in the spring equalizes. The spring is now “charged” with elastic potential energy. And it then pushes on both the hand and the stone by means of the elastic potential energy. There is an unavoidable delay between your pushing your end of the spring and the other end pushing the stone (unavoidable, because physical causation doesn’t exceed the speed of light).

Now, once the spring is compressed, its pushing on the stone is its own causal activity. We can see this as follows. Suppose God annihilated your hand. For a very short while, the other end of the spring wouldn’t notice. It would still be pushing against the stone, and the stone would still be moving. Then the spring would decompress in the direction where the hand used to be, and the stone’s movement would stop. But a very short while is still something—it’s enough to show that the spring is acting on its own. The point isn’t that the stone would gradually slow down. The point, rather, is that it takes a while for the stone’s movement to be at all affected, because otherwise we could have faster-than-light communication between the hand and the spring.

What goes for springs goes for sticks. And I don’t know any better examples. Take Feser’s example in his Five Ways book of a cup held up by a desk which is held up by a floor. Feser says the desk “has no power on its own to hold the cup there. The desk too would fall to the earth unless the floor held it aloft”. Yes, it would—but not instantly. If the floor were to disappear, the tension in the desk’s legs—which, again, are just stiff springs—would continue to press upward on the desktop, which would press upward on the cup, counteracting gravity. But then because the bottoms of the legs are unsupported, the tension in the legs would relax, the legs would imperceptibly lengthen, and the whole thing would start to fall. Still, for a short while the top of the desk would have been utterly unaffected by the disappearance of the floor. It would only start accelerating downward once the tension in the legs dissipatated. It takes a time of at least L/c, where L is the length of the legs and c is the speed of light, for that to happen. Again, the legs of the table are charged-up springs whose internal tension is holding up the desktop.

If this is right, then we don’t have any clear examples of the kind of purely instrumental causality that Feser—and, fairly likely, Aquinas—is talking about. Now, it may be that the deep metaphysics of causation is indeed such that indeed all creaturely causation is indeed of this instrumental sort, being the instrument of the first cause. But since Aquinas is using the idea of per se causal series to establish the existence of the first cause, we need an argument here that does not depend on the existence of the first cause.

Towards a solution to the "God as author of evil" problem for the Thomistic model of meticulous providence

On the Thomistic primary/secondary causation model of meticulous divine providence, when we act wrongly, God fully determines the positive aspects of the action with primary causation, and we in parallel cause the action with secondary causation.

Like many people, I worry that this makes God the author of sin in an objectionable way.

Alice and Bob are studying together for a calculus exam that will be graded on a curve. In order that she may do terribly on the exam, and thus that he might do better, and hence be more likely to get into his dream PhD program in ethics, Bob lies to Alice, who has missed three weeks of class, that the derivative of the logarithm is the exponential.

What does God cause in Bob’s action on the Thomistic model? It seems that all of the following are positive aspects:

1. The physical movements in Bob’s mouth, throat, and lungs.

2. The sounds in the air.

So far we don’t have a serious theological problem. For (1) and (2) are not intrinsically bad, since Bob could virtuously utter the same sounds while playacting on stage. But let’s add some more aspects:

3. Bob’s intention that the speech constitute an assertion of the proposition that the derivative of the logarithm is the exponential.

4. Bob’s intention that the asserted proposition be a falsehood that Alice comes to believe and that leads to her doing terribly on the exam.

Perhaps one can argue that falsity a negative thing—a lack of conformity with reality. However, intending falsity seems to be a positive thing, a positive (but wicked) act of the will. Thus it seems that (3) and (4) are positive things. But once we put together all of (1)–(4), or even just (3) and (4), then it’s hard to deny that what we have is something wicked, and so if God is intending all of (1)–(4), it’s hard to avoid the idea that this makes God responsible for the sin in a highly problematic way.

There may be a way out, however. In both written and spoken language, meaning is normally not constituted just by the positive aspects of reality but also by negative ones. In spoken language, we can think of the positive aspects as the peaks of the soundwaves (considered as pressure waves in the air). But if you remove the troughs from the soundwaves, you lose the communication. In print, on the other hand, the meaning depends not just on the ink that’s there, but on the ink that’s not there. A page wholly covered with ink means nothing. We only have meaningful letters because the inked regions are surrounded by non-inked regions.

It could well turn out that the language of the mind in discursively thinking beings like us is like that as well, so that a thought or intention is constituted not only by ontologically positive but also by ontologically negative aspects. Now you could be responsible for the ink within the print inscription

5. The derivative of the logarithm is the exponential

without being responsible for the inscription. For instance, you and a friend might have had a plan to draw a black rectangle and you divided up the labor as follows: you inked the region of rectangle covered by the letters of “The derivative of the logarithm is the exponential” and then your friend would ink the rest of the containing rectangle—i.e., everything outside the letters. But your friend didn’t do the job. Similarly, then, if intentions are constituted by both positive and negative features, God could intend the positive features of an intention without being responsible for the intention as such.

This does place constraints on the language of the mind, i.e., on the actual mental accidents that constitutes our thoughts, and specifically our intentions. Note, though, that we don’t need that all intentions have a negative constituent. Only intentions to produce negative things, like falsehood, need to have a negative constituent for us to avert the problem of God willing intentional sin. We could imagine a written language where positive phrases are written in two colors of ink, one for the letters and the other for the surrounding rectangle, and their negations are written by omitting the ink for the letters. In such a language, statements involving positive phrases are purely positive, while those involving negative phrases are partly negative.

I am not very happy with this solution. I still worry that being responsible for the ink in (5) makes one responsible for (5) when one chooses not to have the rest of the rectangle filled in.

An argument against the Thomistic primary/secondary causation account of strong providence

Most people agree that one cannot have circularity in the order of explanation when one keeps the type of explanation fixed. Some like me think one cannot have circularity in the order of explanation at all. I argued for this thesis in my previous post today. Now I want to draw an interesting application.

On one influential (and I think exegetically correct, pace Eleonore Stump) reading of Aquinas, God decides what our free choices will be. Our free choices cannot be determined by created causes, but they are determined by God. This is because God’s causation is primary causation which is of a different sort from the secondary causation which is creaturely causation. God can primarily cause you to freely secondarily cause something, and this is how providence and free will interact. Often the analogy between an author and a character is given: the author decides what the character will freely do and this does not infringe on the character’s freedom.

But now observe this (which was brought home to me by a paper of one of our grad students). On this picture, God will presumably sometimes providentially make earlier actions happen because of later ones. Thus, God may want you to perform some heroic self-sacrifice in ten years. So, right now God prepares you for this by having you freely engage in small self-sacrifices now. In the “because” corresponding to the explanatory order of providence and primary causation, we thus have:

1. You engage in small self-sacrifices because you will engage in a great self-sacrifice.

However, divine primary causation does not undercut secondary causation, and we have the standard Aristotelian story of habituation at the level of secondary causation in light of which we have:

2. You will engage in a great self-sacrifice because you are engaging in small self-sacrifices.

These explanations form a heterotypic explanatory loop (i.e., we have explanations of two different sorts in opposite directions). But if I am right that no explanatory loop is possible, the above story is not possible. However, there is nothing to rule out the above story if the above Thomistic account of primary and secondary causation’s role in providence is correct. Hence, I think we should reject that account.

Two decreases in tension between faith and science

Over the past two hundred years or so, one new tension point arose for the relationship between Christianity and science due to scientific progress—namely, evolution. At the same time, several tension points disappeared due two other instances of scientific progress.

The first instance of this scientific progress was the general abandonment of the Aristotelian eternal world model of the universe with Big Bang cosmology. In the middle ages, Jewish, Islamic and Christian thinkers struggled with the tension between the science/philosophy of the day strongly tending towards a universe that always existed and the theological commitment to a creation a finite amount of time ago. That problem is gone.

The second instance is our scientific understanding of the continuity of organic development from zygote to embryo to infant to adult, which has made quite implausible the old view of discontinuous transition in utero from vegetable to animal to human. This old view was the dominant scientific view of human origins until fairly recently, and it had serious tensions with Christian theology.

The first of these embryological tensions was with Christian moral views about abortion. While traditionally Christians opposed both contraception and abortion, abortion was morally seen as a form of homicide. But on the discontinuous transition view, abortion prior to human ensoulment would only be contraception.

The second embryological tension was a technical problem in Christology. Suppose that in the Incarnation we have the vegetable, mere animal and rational animal sequence. Then Aquinas observes there are two possibilities, neither of which is theologically appealing.

First, it could be that God becomes incarnate as a vegetable or a mere animal. But this seems, as Aquinas says, “unbecoming”. And he seem to be right. The Incarnation reveals to us the person of the Logos, and it would be unbecoming that the Logos become a non-personal being.

Second, it could be that the Incarnation happens only at the beginning of the third stage of development, namely once everything is ready for a rational animal. But then Aquinas says “the whole conception could not be attributed to the Son of God”. Indeed, don’t we even have a tension with the Apostles’ Creed line that Christ “was conceived by the Holy Spirit”? For on this option, Christ was not conceived at all. What was conceived was a vegetable, not Christ. (Indeed, none of us were conceived on this view.) Moreover, one might worry that then there would be a sense in which the flesh of Christ would pre-exist the Incarnation. And that makes it difficult to say that the Word became flesh—for the flesh that Scripture says he “became” would already in a sense have been there, and one can’t become this flesh, since this flesh already has its own identity. (Granted, there may well be some Aristotelian metaphysics one can do to lessen this last worry.)

Aquinas solves the problem by supposing that Christ is conceived fully formed in Mary’s womb, and hence has the rational soul from the first moment of his existence. But this solution is itself problematic. Absent gradual development from a zygote, is this conception at all? If God were to create an adult human either ex nihilo or out of some pre-existing matter, we would not consider that a conception. But neither should we then consider it a conception if God creates a fully-formed fetus, even if he does that out of the pre-existing matter of Mary. So we still have a problem with the Apostles’ creed’s “was conceived by the Holy Spirit”. Moreover, it seems that this deprives Mary of a significant chunk of her motherhood.

But the problem entirely disappears once we think that the human beings begin their existence at conception. Christ is conceived by the Holy Spirit, presumably in that Mary’s ovum is transformed into a zygote by the infinite power of the Holy Spirit, which zygote is the Christ who then grows in utero like we all do.

(Catholics also note that the new scientific understanding of human embryonic development also helps with the doctrine of Mary’s immaculate conception—for only a rational being can be immaculately conceived, since original sin or freedom from it can only apply to a rational being.)

A Thomistic argument for the Principle of Proportional Causality

The Principle of Proportionate Causality (PPC) defended by Aquinas and other scholastics says that a perfection P can only be caused by something that has P either formally or eminently. To have P formally is to have P. Roughly, to have P eminently is to have a perfection greater than P.

(Some add: “has P virtually” to the list of options. But to have P virtually is just to have the power to produce P, and as our student Colin Causey has noted, this trivializes PPC.)

There are obvious apparent counterexamples to PPC:

• Two parents who are bad at mathematics can have a mathematical genius as a child.

• Ugly monkeys typing at random can produce a beautiful poem.

• A robot putting together parts at random can make a stronger and smarter robot.

It’s tempting to throw PPC out. But there are also cases where one feels a pull towards PPC:

• How can things that represent come from non-representing stuff?

• How can the conscious come from the non-conscious?

• How can something with dignity come from something without any?

• How can the active come from the inactive?

• How can an “ought” come from a mere “is”, i.e., something with normativity from something without any?

Many contemporary philosophers think there is no impossibility even in these cases, but I think most will agree that there is something puzzling about these kinds of causation—that we have some sort of an intuition towards PPC in these cases, of a sort we do not have in the cases of the “obvious apparent counterexamples”. What is the difference between the cases?

Well, in the counterexamples, the differences between the cause and the effect are, arguably, a matter of degree. The two parents have a much lower degree of mathematical ability. The monkeys have a certain beauty to them—being productive of beauty is a kind of beauty—albeit perhaps a lesser one than their lucky output. The robot’s output is just a more sophisticated bunch of moving parts than the robot itself.

But in the examples where one feels pulled to PPC, the differences appear to be differences in kind. Indeed, I think we can all agree that the most plausible way to resist the implied claim in the “How can…?” questions that the thing is impossible is to show how to reduce the seemingly more perfect thing to something of the same sort as the alleged cause.

But “differences in kind” doesn’t seem quite sharp enough. After all, pretty much everyone (even, I assume, young earth creationists) will agree that dogs can come from wolves.

I’ve been puzzled by how one might understand and argue for PPC for a long time, without much progress. This morning I had an inspiration from Nicholas Rescher’s article on Aquinas’ “Principle of Epistemic Disparity”, that lesser minds cannot comprehend the ways of greater ones.

Suppose we order the types of good by a comprehensibility relation ≤ where G ≤ H means that it is possible to understand G by understanding H. Then ≤ is a partial preorder, i.e., a reflexive and transitive relation. It generates a strict partial preorder < where G < H provided that G ≤ H but not H ≤ G.

Next, say that good types G₁ and G₂ are cases of the same perfection provided that G₁ ≤ G₂ and G₂ ≤ G₁, i.e., that each can be understood by the other. Basically, we are taking perfections to be equivalence classes of types of good, under the relation ∼ such that G₁ ∼ G₂ if and only if G₁ ≤ G₂ and G₂ ≤ G₁. The relation ≤ extends in a natural way to the perfections: P ≤ Q if and only if whenever G is a case of P and H is a case of Q then G ≤ H. Note that ≤ is a partial order on the perfections. In particular, it is antisymmetric: if we have P ≤ Q and Q ≤ P, then we have P ≠ Q. Write P < Q provided that P ≤ Q and P ≠ Q.

Now on to a Thomistic argument for the PPC.

Being, truth and goodness are transcendentals. The cognitively more impressive perfection Q is thus also axiologically more impressive. Thus:

Axiological Thesis: If P < Q for perfections P and Q, then Q is a better kind of perfection than P.

The following is plausible on the kind of Aristotelian intrinsic notion of causation that Thomas works with:

Causal Thesis: By understanding the cause one understands the effect.

Thomistic ideas about transcendentals also yield:

Understandability Lemma: To understand a thing one only needs to understand the goods instantiated by the thing.

Finally, let’s add this technical assumption:

Conjunction Lemma: The conjunction of co-instantiable goods is a good.

And now on to the PPC. Suppose x causes y to have a good G and y has a type of good G that is a case of a perfection P. By the Causal Thesis, we understand G by understanding x. By the Conjunction Lemma, let H be the conjunction of all the good of x. By the Understandability Lemma, we understand x by understanding H. Thus, G ≤ H. Let Q be the perfection that H is a case of. Then P ≤ Q and x has Q. Then either P = Q or P < Q. In the former case, the cause has P formally. In the latter case, by the Axiological Thesis, the cause has P eminently.

Of course, the Axiological and Causal Theses, together with the Understandability Lemma, all depend on large and controversial parts of Aquinas’ system. But I think we are making some progress.

I am also toying with an interesting concept. Say that a perfection Q is irreducible provided that it cannot be understood by understanding any conjunction of perfections P such that P < Q. It’s not obvious that there are irreducible perfections, but I think it is plausible that there are. If so, one might have a weaker PPC restricted to irreducible perfections. I have yet to think through the pluses and minuses here.

Proportionate causality

Let’s assume for the sake of argument:

Aquinas’ Principle of Proportionate Causality: Anything that causes something to have a perfection F must either have F or some more perfect perfection G.

And let’s think about what follows.

The Compatibility Thesis: If F is a perfection, then F is compatible with every perfection.

Argument: If F is incompatible with a perfection G, then having F rules out having perfection G. And that’s limitive rather than perfect. Perhaps the case where G = F needs to be argued separately. But we can do that. If F is incompatible with F, then F rules out all other perfections as well, and as long as there is more than one perfection (as is plausible) that violates the first part of the argument.

The Entailment Thesis: If F and G are perfections, and G is more perfect than F, then G entails F.

Argument: If F and G are perfections, and it is both possible to have F without having G and to have F while having G, it is better to have both F and G than to have just G. But if it is better to have both F and G than to have just G, then F contributes something good that G does not, and hence we cannot say that G is more perfect than F—rather, in one respect F is more perfect and in another G is more perfect.

From the Entailment Thesis and Aquinas’ Principle of Proportionate Causality, we get:

The Strong Principle of Proportionate Causality: Anything that causes something to have a perfection F must have F.

Interesting.

Aquinas' argument for the immortality of the soul

Aquinas argues that because the human soul has a proper operation—abstract thought—that does not depend on the body, the soul would survive the destruction of the body.

I’ve never quite understood this argument. It seems to show that there could be a point to the soul surviving the destruction of the body, but that doesn’t show that it will.

It seems that by the same token one could say that because my fingers have an operation independent of my toes, my fingers would survive the destruction of the toes. But that need not be true. I could simultaneously have my toes and fingers crushed, and the fingers’ having an operation independent of the toes would do nothing to save them. In fact, in most cases, fingers perish at the same time as toes do. For in most, though not all, human lives, fingers perish when a person dies, and the toes do so as well. So the argument can’t be that strong.

Still, on reflection, there may be something we can learn from the fingers and toes analogy. We shouldn’t expect the fingers to perish simply as a metaphysical consequence of my toes perishing. By analogy, then, we shouldn’t expect the soul to perish simply as a metaphysical consequence of the body perishing. That’s not the immortality of the soul, but it’s some progress in that direction. After all, the main reason for thinking the soul to perish at death is precisely because one thinks this is a metaphysical consequence of the body perishing.

And I am not denying that there are good arguments for the immortality of the human soul. I think there may be an argument from proper operation that makes even more progress towards immortality, but I’ll leave that for another occasion. Moreover, I think the immortality of the human soul follows from the existence of God and the structure of human flourishing.

From theism to causal finitism

Causal Finitism—the thesis that nothing can have an infinite causal history—implies that there is a first cause, and our best hypothesis for what a first cause would be is God. Thus:

1. If Causal Finitism is true, God exists.

But I think one can also argue in the other direction:

2. If God exists, Causal Finitism is true.

Aquinas wouldn’t like this since he thought that God could create a per accidens ordered backwards-infinite causal series.

In this post, I want to sketch an argument for (2). The form of the argument is this.

3. God cannot create a sequence of beings ..., A₋₃, A₋₂, A₋₁, A₀ where each being causes the next one.

4. If God cannot create such a sequence, such a sequence is impossible.

5. The best explanation of the impossibility of such a sequence is Causal Finitism.

Claim (4) comes from omnipotence. Claim (5) is I think the weakest part of the argument. Causal Finitism follows logically from the conjunction of two theses, one ruling out backwards-infinite causal chains and the other ruling out infinite causal cooperation (a precise statement and a proof is given in Chapter 2 of my Infinity book). But I am now coming to think that there is a not crazy view where one accepts the anti-chain part of Causal Finitism but not the anti-cooperation part. However, (a) the main cost of Causal Finitism come from the anti-chain part (the anti-chain part is what forces either a discrete time or a discrete causal reinterpretation of physics), (b) there are significant anti-paradox benefits to maintaining the anti-cooperation part, and (c) the theory may seem more unified in having both parts.

Now let’s move on to (3). Here is an argument. Say that an instance of causation is chancy provided that the outcome has a probability less than one.

6. If God can create a backwards-infinite causal sequence of beings, he can create a backwards-infinite chancy causal sequence of beings as the only thing in creation.

7. Necessarily, if God creates a backwards-infinite chancy causal sequence of beings as the only thing in creation, then there is no creature x such that God determines x to exist.

8. Necessarily, if God creates, he acts in a way that determines that something other than God exists.

9. Necessarily, if God determines that something other than God exists then there is a creature x that God determines x to exist.

10. Necessarily, if God creates a backwards-infinite chancy causal sequence of beings, then there is a creature x such that God determines x to exist. (8,9)

11. Hence, God cannot create a backwards-infinite chancy causal sequence of beings. (7,10)

12. Hence, God cannot create a backwards-infinite causal sequence of beings. (6,11)

The thought behind (6) is an intuition about modal uniformity. I think (6) is probably the most vulnerable part of the argument, but I don’t think it’s the one Aquinas would attack. What I think Aquinas would attack would most likely be (7). I will get to that shortly.

But first a few words about (8). In theory, it is possible to determine that something exists without determining any particular thing to exist. One can imagine a being with a chancy causal power such that if it waves a wand necessarily either a bunny or a pigeon is caused to exist, with the probability of the bunny being 1/2 and the probability of the pigeon being 1/2. But God is not like that. God’s will is essentially efficacious and not chancy. God can play dice with the universe, but only by creating dice. Thus, if God wanted to ensure there is a bunny or a pigeon without ensuring which specific one exists, he would have to create a random system that has chancy propensities for a bunny and for a pigeon and that must exercise one of the two propensities.

In fact, I think divine simplicity may imply this. For by divine simplicity, any two possible worlds that differ must differ in something outside God. Now consider a world w₁ where God determines a bunny to exist, and a world w₂ where God merely determines that a bunny or a pigeon exists and in fact a bunny is what comes about. There seems to be no difference outside God between these two worlds (one might wonder about the relation of being-created: could there be an relation of being-created-chancily and being-created-non-chancily? this seems fishy to me, and suggests a regress—how are the two relations differently related to God? and do we want to multiply such relations, saying there is such a thing as being-created-chancily-with-probability-0.7?). If both worlds are possible, by divine simplicity they must be the same, which is absurd. So at least one must be impsosible. And w₂ is a better candidate for that than w₁.

That still doesn’t establish (8). For I admitted that God can play dice if he creates dice. Thus, it seems that God could determine that something exists without determining where it’s A or B or C (say) by determining there to be dice that decide whether A or B or C are produced. But on this story, God still determines there to be dice, so there is an x—a die—that God determines to exist. I think a bit more could be said here, but as I said, I don’t think this is the main thing Aquinas would object to.

Back to (7). Why can’t God create a chancy backwards-infinite causal sequence while determining some item A_n in it to exist? Well, the sequence is chancy, so the probability that A_n − 1 causes A_n given that A_n − 1 exists is some p < 1. But, necessarily, if one creature causes another, it does so with divine cooperation (Aquinas will not disagree), and conversely if God cooperates with one creature to cause another, the one creature does cause the other. That the probability that God cooperates with A_n − 1 to cause A_n is equal to the probability that A_n − 1 causes A_n, because necessarily one thing happens if and only if the other does. Thus, the probability that God cooperates with A_n − 1 to cause A_n, given that A_n − 1 exists, is p. But p < 1, so it sure doesn’t look like a case of God determining A_n to exist!

But perhaps there is something like overdetermination, but between determination and chanciness (so not exactly over-determination). Perhaps God both determines A_n to exist and chancily cooperates with A_n − 1 to produce A_n. One problem with this hypothesis is with divine simplicity: it does not seem that there is any difference outside God between a world where God does both and God merely cooperates or concurs. But Aquinas may respond: “Yes, exactly. Necessarily, when one creature chancily causes another, God’s primary causation determines which specific outcome results. Thus there is no world where God merely cooperates.” So now the view is that whenever we have chancy causation, necessarily God determines the outcome. But suppose I chancily toss a coin, and it has chance 1/2 of heads and chance 1/2 of tails. Then on this view, I get heads if and only if God determines that I get heads. Hence the chance that God determines I get heads is 1/2. But it seems plausible that God’s determinations are not measured by numerical probabilities, and in any case that they are not measured by numerical probabilities coming from our world’s physics!

Change and matter

Aristotle’s positing matter is driven by trying to respond to the Parmenidean idea that things can’t come from nothing, and hence we must posit something that persists in change, and that is matter.

But there two senses of “x comes from nothing”:

1. x is uncaused

2. x is not made out of pre-existing materials.

If “x comes from nothing” in the argument means (1), the argument for matter fails. All we need is a pre-existing efficient cause, which need not be the matter of x.

Thus, for the argument to work, “x comes from nothing” must mean (2). But now here is a curious thing. From the middle ages to our time, many Aristotelians are theists, and yet still seem to be pulled by Aristotle’s argument for matter. But if “x comes from nothing” means (2), then theism implies that it is quite possible for something to come from nothing: God can create it ex nihilo.

There are at least two possible responses from a theistic Aristotelian who likes the argument for matter. The first response is that only God can make things come from nothing in sense (2), and hence things caused to exist by finite causes (even if with God’s cooperation) cannot come from nothing in sense (2). But there plainly are such things all around us. So there is matter.

Now, at least one theistic Aristotelian, Aquinas, does explicitly argue that only God can create ex nihilo. But the argument is pretty controversial and depends on heavy-duty metaphysics, about finite and infinite causes. It is not just the assertion of a seemingly obvious Parmenidean “nothing comes from nothing” principle. Thus at least on this response, the argument for matter becomes a lot more controversial. (And, to be honest, I am not convinced by it.)

The second and simpler response is to say that it’s just an empirical fact that there are things in the world that don’t come from nothing in sense (2): oak trees, for example. Thus there in fact is matter. This response is pretty plausible, but can be questioned: one might say that we have continuity of causal powers rather than any matter that survives the generation.

Finally, it’s worth noting that I suspect Aristotle misunderstands the Parmenidean argument, which is actually a very simple reductio ad absurdum:

3. x came into existence.
4. If x came into existence, then x did not exist.
5. So, x did not exist.
6. But non-existence is absurd.

The crucial step here is (6): the Parmenidean thinks the very concept of something not existing is absurd (presumably because of the Parmenidean’s acceptance of a strong truthmaker principle). The argument is very simple: becoming presupposes the truth of some past-tensed non-existence statements, while non-existence statements are always false. Aristotle’s positing matter does nothing to refute this Parmenidean argument. Even if we grant that x’s matter pre-existed, it’s still true that x did not exist, and that’s all Parmenides needs. Likewise, Aristotle’s famous actuality/potentiality distinction doesn’t solve the problem. Even if x was pre-existed by a potentiality for existence, it’s still true that x wasn’t pre-existed by x—that would be a contradiction.

To solve Parmenides’ problem, however, we do not need to posit matter or potentiality or anything like that. We just need to reject the idea that negative existential statements are nonsensical. And Aristotle expressly does reject this idea: he says that a statement is true provided it says of what is that it is or of what is not that it is not. Having done that, Aristotle should take himself as done with Parmenides’ problem of change.

Aquinas on per se and accidentally ordered causal series

Famously, Aquinas thinks that an accidentally ordered infinite causes is possible, but a per se ordered one is not. The difference is that in a per se ordered series ..., A₋₂, A₋₁, A₀, item A_n − 1 (for n <  − 1) is not only the cause of A_n, but is the cause of A_n’s causing of A_n + 1. But in an accidentally ordered series, A_n − 1 is not the cause of A_n’s causing of A_n + 1. Aquinas illustrates the distinction with a sequence of an infinite sequence of fathers and sons, since a grandfather is not the cause of the father’s conceiving of a son.

Now suppose we replace the people in Aquinas’s example with self-reproducing robots (von Neumann machines), each programmed by its predecessor to reproduce. Then we have a per se ordered series.

The following seems to me to be very plausible:

1. If a backwards infinite reproductive series of humans is possible, a backwards infinite reproductive series of robots is also possible.

Yet this seems to be something that Aquinas is committed to by his example of the accidentally ordered series.

Suppose one bites the bullet and denies (1). What is the relevant difference between the humans and the robots? It is presumably the determinism in the robots. Very well, then let’s suppose that each of the robots has a little hidden switch whose position is permanently set at the time of manufacturing. When the switch is in the D position, the robot is determined to reproduce at specific points in its life; when it is in the N position, at those points in its life, the robot performs an internal indeterministic quantum coin flip, reproducing on heads but not on tails.

It seems absurd to suppose that one could have a backwards infinite reproductive series of robots with the switches in the N position, but not in the D position. Yet that implausible conclusion seems to be what Aquinas’s position commits him to.

Here a suggestion for what Aquinas could do.

Aquinas thinks there is a very good metaphysical argument for rejecting backwards infinite per se ordered series. Suppose that argument is sound. Then Aquinas could say that this argument does not apply to the accidentally ordered case. But nonetheless there is a good argument based on a rearrangement principle or a principle of modal uniformity that:

2. If a backwards infinite series of robots with the switch in the N position is possible, so is a backwards infinite series of robots with the switch in the D position.

3. If a backwards infinite series of humans is possible, a backwards infinite series of robots with the switch in the N position is possible.

Given the impossibiliy of the series with the switch in the D position, it follows that the the backwards infinite sequence of humans is impossible. Aquinas can then simply say that he was wrong about his example (something that he is willing to concede anyway, due to an argument from al Ghazali specifically against an backwards infinite sequence of humans). But nothing in Aquinas’s theory commits him to the claim that every describable accidentally ordered backwards infinite sequence is possible. (An accidentally ordered backwards infinite sequence of square circles is not possible.)

At this point, Aquinas can do one of three things. First, he can say that while the backwards infinite sequence of humans or N-robots is impossible, we should remain agnostic whethere there are some backwards infinite accidentally ordered sequences are possible.

Second, he can give a plausibilistic argument that if the backwards infinite sequence of N-robots is impossible, probably all accidentally ordered backwards infinite sequences are impossible as well. (One might think this would require Aquinas to reject the possibility of an infinite past. This is not clear. He might still hold that an infinite past is possible as long as it doesn’t generate a backwards infinite causal sequence—imagine that every day in the past God creates a rock so far apart from all the other rocks that the rocks never interact).

Third, Aquinas could try to construct a new example of a backwards infinite accidentally ordered series that is possible. My intuition is that the best bet for trying to do this would be to construct a backwards infinite sequence where each item gets only a very slight causal contribution from its predecessor, and most of the explanation of the item’s existence involves God or some other single timeless being.

I myself like the second option.

Taking, not stealing

Aquinas says that when a starving person takes food needed for survival from someone who has too much, the act is a case of taking but not stealing. Aquinas’ reasoning is that property rights subserve survival, and in case of conflict the property rights cease, and the food ceases to be the property of the one who has too much, and so it is not theft for the poor to take it.

I think what is going on may be a bit more subtle than that. Suppose Alice and Bob both have too much and Carl is starving. Both Alice and Bob refuse their surplus to feed Carl. According to Aquinas’ analysis, both Alice and Bob lose their ownership.

But I think things may be a bit more subtle than that. Suppose that shortly after Alice and Bob’s wrongful refusal, Carl suddenly wins the lottery. It does not seem right to say that Carl can now take Alice and Bob’s surplus. Yet if Alice and Bob lost their ownership upon refusal to feed Carl, then either the surplus now belongs to Carl or it belongs to nobody, and in either case it wouldn’t be stealing from Alice and Bob for Carl to take it. Similarly, if after Carl’s lottery win, Alice were to take Bob’s surplus food, Alice would be stealing from Bob.

We could say that Alice and Bob regain their property when Carl wins the lottery, but it is strange to think that something that belongs to nobody or to Carl suddenly becomes Alice’s, despite Alice having no deep need of it, just because Carl won the lottery.

Here is a different kind of case that I think may shed some light on the matter. As before, suppose Alice has a surplus. Suppose Eva the mobster has informed David that if David doesn’t take Alice’s surplus, then Eva will murder Alice. Any reasonable person in Alice’s place would agree to having her surplus taken by David, but Alice is not a reasonable person. David nonetheless takes Alice’s surplus, thereby saving her life.

I think David acts rightly, precisely because as Aquinas thinks one needs to resolve a conflict between property and life in favor of life. But I don’t think we can analyze using Aquinas’ loss of ownership account. For if David takes Alice’s stuff, then Eva who made David do it is a thief (by proxy). But if under the circumstances Alice loses her ownership, then Eva is not a thief. I think the right thing to say is that Alice retains her ownership, but it is not wrong for David to take her stuff in order to save her life.

What should we say, then? Is David a thief, but a rightly acting thief? That is indeed one option. But I prefer this one. When you own something, that gives you a set of rights over it and against others. I suggest that these rights do not include an unconditional right not to be deprived of the use of the item. Specifically, there is no right not to be deprived of the use of the item when deprivation of use is the only way for someone’s life to be saved. This applies both in Aquinas’s case of starvation and in my mobster case. It is not an infringement on Alice’s ownership over her surplus when Carl takes her stuff to survive or when David takes her stuff in order to save Alice’s life. But when Carl’s need terminates, he does not get to then take Alice’s stuff, as if Alice had lost ownership, and the mastermind behind David’s taking the stuff, who unlike David isn’t acting to save Alice’s life, is a thief.

In fact, if we think about it, it becomes obvious that there is no unconditional right not to be deprived of the use of an owned item. Suppose I have my car on a plot of land that I own, and I foolishly sell you all the land surrounding the small rectangle that the car is physically on top of. By buying the land, you deprive me of the use of my car, barring your good will—I cannot drive the car off the rectangle without trespass. But you don’t steal my car by thus depriving me of its use.

Thus, neither Carl (when in need) nor David is stealing, even though both take something owned by someone else.

Aquinas quotes St. Ambrose with approval: “It is the hungry man’s bread that you withhold, the naked man’s cloak that you store away, the money that you bury in the earth is the price of the poor man’s ransom and freedom.” While St. Ambrose’s sentiment is very plausibly correct, on my account above it is not correct to take it literally. When Alice wrongfully withholds her surplus from starving Carl, the surplus is not literally owned by Carl. It is still owned by Alice, who has a duty to pass ownership to Carl, and Carl in turn is permitted to use Alice’s surplus—but it remains Alice’s, even if wrongfully so.

Indeed, here is an argument against the hypothesis that ownership literally passes to the needy. Suppose Carl is starving, and Alice and Bob refuse their surplus. Now, shortly after Carl coming to be starving, so does Fred. On an account on which ownership literally passes to the needy, Alice’s and Bob’s surplus belongs to Carl, and if Carl comes to claim it and at the same times so does Fred, Carl gets to defend that surplus, violently if necessary, from Fred, as long as that surplus is all needed for Carl’s survival. But it seems plausible that as long as Carl’s and Fred’s need is now equal, they have equal rights, even if Carl came to be needy slightly earlier. Furthermore, suppose Alice has ten loaves of bread and Carl needs one to survive. Which loaf of bread becomes Carl’s possession? Surely not all of them, and surely no specific one. It seems better to say: while Carl is in dire need, Alice has no right to withhold surplus from her. As soon as Carl and any other needy person has taken enough not to be in dire need, Alice may defend the rest of her surplus.