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.

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.

Aquinas on drunkenness and sleep

Aquinas argues that

drunkenness is a mortal sin, because then a man willingly and knowingly deprives himself of the use of reason, whereby he performs virtuous deeds and avoids sin, and thus he sins mortally by running the risk of falling into sin.

On the other hand, Aquinas also argues that sleep suspends the use of reason:

What a man does while asleep, against the moral law, is not imputed to him as a sin; as Augustine says (Gen. ad lit. xii, 15). But this would not be the case if man, while asleep, had free use of his reason and intellect. Therefore the judgment of the intellect is hindered by suspension of the senses.

One might try to reconcile the two claims by saying that sleep is something that befalls us involuntarily, and that it would be wrong to willingly and knowingly go to sleep. But that would not fit with ordinary human practice, and would contradict Aquinas’ own rejection of the claim that it is “against virtue for a person to set himself to sleep”. Moreover, Aquinas notes without any moral warnings that sleep—like baths, contemplation of the truth and other apparently quite innocent things—assuages sorrow.

So what’s going on?

And to add a further complication, Proverbs 31:6 seems to recommend the use of alcohol as an analgesic.

I can think of three things one could say on behalf of Aquinas.

First, one might attempt a Double Effect justification. In sleep, the body rests. Aquinas certainly thinks so: the discussion of the suspension of reason during sleep presupposes that the primary effect of sleep is on the body. It is this bodily rest, rather than the suspension of reason, that is intended. One might worry that the suspension of reason is a means to rest. However, non-human animals, who lack reason in Aquinas’s sense of the word, also sleep. Presumably whatever benefits they derive from the sleep are available to us, and it seems not unlikely that many of these do not depend on the suspension of reason. Similarly, alcohol helps with pain in non-human animals, and so the mechanism by which it helps may not depend on the suspension of reason.

That said, I don’t think Aquinas would want to take this approach (though it may well work for me). For Aquinas thinks that it is stupid we cannot claim that an invariable or typical effect of something intended counts as unintended (Commentary on the Physics, Book II, Lecture 8, paragraph 214). But the suspension of reason is indeed an invariable or typical effect of sleep.

A second approach focuses on Aquinas’ response to the question of why the loss of rationality during the sexual act does not render the sexual act wrong, from which I already quoted the rejection of the claim that it’s vicious to set oneself to sleep:

it is not contrary to virtue, if the act of reason be sometimes interrupted for something that is done in accordance with reason … .

This approach does not seem to be based on Double Effect, but rather on some sort of principle that it is permissible to suspend a good for the sake of that same good. This principle applies neatly to sleep as well as to the biblical case of analgesic use of alcohol (given that reason opposes suffering the pain).

But this approach would also moderate Aquinas’s seemingly absolute rejection of drunkenness. For we can imagine cases where it seems that reason would recommend drunkenness, such as when a tyrant will kill you if you refuse to get drunk with them. And once one allows drunkenness in such extreme cases, what is to prevent allowing it in more moderate cases, such as getting drunk with one’s boss in the hope of getting a deserved promotion… or maybe just for fun? Aquinas can say that these cases are immoral and hence against reason, but that would beg the question.

A third approach would note that sleep, unlike drunken stupor, is a natural human state, and information processing in sleep is itself a part of our human rational processing. However, while this gives a neat explanation of why it’s permissible to set oneself to sleep, it doesn’t explain the permissibility of the analgesic use of alcohol or, more significantly in modern times, of the use of general anaesthesia during medical procedures.

A different approach for justifying sleep, the analgesic use of alcohol and general anaesthesia insists that temporary suspension of a good is different from willful opposition to the good. To eat in an hour rather than now does not oppose the good of food. The down side of this fourth approach is that it seems to destroy Aquinas’s argument against drunkenness as opposed to the good of reason. And it seems to let in too much: can’t one say that by torturing someone, one is merely suspending their painless state?

I think the best philosophical solution is the first, Double Effect. Aquinas alas can’t use it because his version of Double Effect is too narrow, given his view that typical effects of intended things count as intended.

The Fifth Way, remixed even more

In the previous two posts (here and here) I offered interpretations or remixes of Aquinas’s Fourth and Fifth ways read as ways of showing how a theistic Aristotelianism solves a pressing problem that the basic Aristotelian metaphysics cannot solve.

Here I want to do again for the Fifth Way, but now I will depart further from the text, and so while the previous two posts might have been interpretations, this one is much more of just a remix of the Fifth Way, with some ingredients from my version of the Fourth Way thrown in.

On Aristotelian metaphysics, each substance aims at its own good. The good of a substance is defined by the substance’s form, and the form points the substance at that good. But this good is just an internal good of the substance. Think of this internal good as akin to MacIntyre’s internal goods of a practice. The directedness at the internal goods is largely a matter of a priori metaphysical reasoning about substance. But now let’s go back to the things themselves—for, after all, the Five Ways are supposed to be empirical. If we do that, we come across two facts I want to stress.

First, the internal goods of substances tend to be intelligible to us as goods independently of the forms of these substances. Squirrels grow and reproduce. We understand growing and reproduction as valuable features. Imagine that squirrels instead characteristically scratched themselves to near-death. Even if their nature specified such self-scratching as their end, without a further more comprehensive story such self-scratching wouldn’t be intelligible to us as a good. Now, it is true that we tend to judge things by ourselves: it is also our human good to grow and to reproduce, and so it is easy for us to recognize that as good in squirrels. But I do not think we should say that when we judge squirrels’ growth and reproduction as a good thing independently of the form of the squirrel we are simply mistaken—and yet if we were just imposing merely human standards, we would be mistaken.

We might make the point as follows. It is good for a squirrel to fulfill its form by growing and reproducing. But it is also good, in a different sense of “good”, that the squirrel’s form includes growth and reproduction. This different sense of “good” is missing from basic Aristotelianism, a point central to my reading of the Fourth Way.

So we have something that calls for an explanation: Why is the squirrel’s form aimed at something that is actually good in this further sense?

And here is a related and but less abstract question. The teleology of a squirrel harmonizes to a significant extent with the goods of other species. We have an ecology. A “circle of life”.

The squirrel’s activity, thus, is not only directed at its internal good, and that internal good is intelligible as a good apart from its internal form, but the pursuit of that internal good harmonizes with the goods of other things in nature. This coordination between the ends of different species is something that basic Aristotelianism has a serious difficulty explaining.

There are thus two senses in which there are external goods found in nature: first, the internal goods are themselves typically intelligible as goods independently of the forms that define them; second, the end-directed activities of the organisms are good for the ecology at large. Both of these call for an explanation, and Aquinas’ suggested explanation seems excellent: “Therefore some intelligent being exists by whom all natural things are directed to their end.”

Note that the ecological dimensions might be explained evolutionarily, as long as we have an explanation of the coincidence between the normative and the statistical, a coincidence that forms the heart of my previous reading/remix of the Fifth Way.

The Fifth Way, also remixed

Thomas writes:

We see that things which lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God.

Central to Aristotle’s thought is the normative thesis that all substances have proper functions or ends defined by their immanent forms. Moreover, Aristotle makes the statistical claim that for the most part things things function correctly—they function to fulfill their ends.

The statistical claim is epistemologically important: that an activity or structure is usually exhibited by members of a kind is a central piece of evidence for that activity’s or structure’s correctness. But logically the statistical facts and the normative facts are independent: it is logically possible for all sheep to be three-legged, or for only a few pecan trees to produce pollen.

To see that we are committed to the connection between the normative and the statistical facts, consider the ridiculousness of the hypothesis that one of the ends of salmon is to prove theorems about high-dimensional topology. The utter unsuitability of the salmon brain to that end is conclusive evidence against the hypothesis. But this is only if we think there is a connection between the normative and the statistical facts—without such a connection, we could simply suppose that all salmon fall short of their topological researcher nature.

Note, too, just how massive the coincidence between the normative and statistical facts is: we see it across millions of species.

As Aquinas concedes, in intelligent substances we have some hope of an explanation of the coincidence: the intelligent substance consciously aims at its self-fulfillment. (Though leaning on this may be too much of a concession, because we still need to explain why this aiming isn’t futile, like a crank’s attempts to trisect angles.) But why do unintelligent substances’ activities in fact harmonize with their self-fulfillment, and do so massively, across all the millions of species we have? Why is it that we do not salmon-like fish with mathematical activity as their purpose, snake-like reptiles with flying as their end, and apes whose primary purpose is turning their bodies into gold by exposure to solar radiation?

A theistic explanation of the massive coincidence is compelling, and it provides another theistic solution to the shortcomings of a pure Aristotelian system.

The Fourth Way, remixed

I’m playing with a reading—or perhaps remix—of Aquinas’ Fourth and Fifth Ways as giving a theistic solution to a problem that non-theistic Aristotelianism has no solution to. In this post, I will discuss the Fourth Way, and in the next, the Fifth.

The Fourth Way starts with the principle that degreed predicates, predicates where it makes sense to talk of “more” and “less”, are predicated in comparison to a maximal case. Infamously, however, given modern science, Aquinas’ down-to-earth illustration of that principle, namely that heat is predicated in comparison to the maximal case—allegedly, fire—is not not an example of the principle, but is actually a counterexample to it. There just is no such thing as maximum heat.

But nevermind heat. Aquinas wants to apply the Fourth Way to goodness. Now, the Aristotelian system that he has adopted already has an account of the good: a thing is good to the extent that it fulfills its proper function, a proper function that is defined by the thing’s form. Note that this account, too, does not match Aquinas’ gradation principle: unlike in Plato, forms are not self-predicating, so rather than the Form of the Sheep being the most ovine thing possible, the Aristotelian form of the sheep is immanent in each sheep, directing each sheep to an ovine perfection that no object actually meets.

But the Aristotelian account of the good is incomplete. While it allows us to compare the goodness of things within a kind—the four-legged sheep better fulfills its form than a three-legged one—there are also meaningful value comparisons between kinds. When Jesus says that we are “worth more than many sparrows” (Mt. 10:31), what he is saying is entirely commonsense. The human has much more good than the sparrow. The sparrow has more good than the worm. And the worm has more good than a mushroom. There really is a something like a great chain of being in reality. These comparisons, however, are not simply grounded in the immanent forms of things. The form of the worm need make no reference to mushrooms, nor that of a mushroom to worms.

Note that these interspecies value comparisons not only cannot be read off from the immanent forms, but sometimes they are in a kind of tension with the immanent forms. An earthworm’s form limits the neural development of the worm. Were the worm to grow a brain as big as a dog’s, it wouldn’t be able to burrow as well. And a mushroom that walked around would fail to be properly rooted as a mushroom ought.

Interspecies value comparison is a genuine problem that Aristotelianism faces, though some Aristotelians are willing to bite the bullet and deny the meaningfulness of such comparisons. Platonism did not face this problem—it could just talk of varying degrees of participation in the Form fo the Good—but Platonism lacked a satisfactory solution to the problem of intraspecies comparisons (Platonism’s solution would be to posit a self-exemplified Form for each species, which would involve the absurd idea that there is a perfect Sheep, which somehow manages to be both a sheep and immaterial, and we have all sorts of silly questions about whether it is male or female, what color it is, whether it has an even or an odd number of hairs, etc.)

A theistic Aristotelianism, however, has a solution to the problem of interspecies value comparison, in addition to non-theistic Aristotelianism’s solution to the intraspecies’ problem. There is a great chain of being defined by the ways in which the various species participate in the being that has all perfections. The human exemplifies intellection, the sparrow approximates omnipresence through rapid movement and exemplifies a significant degree of intelligence, the worm approximates omnipresence less well and has a lower degree of intelligence, while the mushroom at least exemplifies life. What grounds the goodness of these qualities independently of the forms of the things they are found in, and what makes for their axiological directionality (more intelligence is better than less), is then comparison to the maximal case, namely God.

Note that while this gives something like a great chain of being, it need not exactly be a great chain of being. We should not seek after a strictly total ordering—a partial ordering matches intuition better.

I don’t have a knock-down argument that theistic Aristotelianism is the only good Aristotelian solution to the problem of interspecies comparison. But it is a very good solution, and so once we have accepted basic Aristotelianism, it gives us significant reason to adopt the theistic version.

An earlier, more compact, version of this argument is here.

Aquinas and Descartes on substance dualism

Roughly, Aquinas thinks of a substance as something that:

1. is existentially independent of other things, and

2. is complete in its nature.

There is a fair amount of work needed to spell out the details of 1 and 2, and that goes beyond my exegetical capacities. But my interest is in structural points. Things that satisfy (1), Aquinas calls “subsistent beings”. Thus, all substances are subsistent beings, but the converse is not true, because Aquinas thinks the rational soul is a subsistent being and not a substance.

Descartes, on the other hand, understands substance solely in terms of (1).

Now, historically, it seems to be Descartes and not Thomas who set the agenda for discussions of the view called “substance dualism”. Thus, it seems more accurate to think of substance dualists as holding to a duality of substance in Descartes’ sense of substance than in Aquinas’.

But if we translate this to Thomistic vocabulary, then it seems we get:

3. A “substance dualist” in the modern sense of the term is someone who thinks there are two subsistent beings in the human being.

And now it looks like Aquinas himself is a substance dualist in this sense. For Aquinas thinks that there are two subsistent beings in Socrates: one of them is Socrates (who is a substance in the Thomistic sense of the word) and the other is Socrates’ soul (which is a merely subsistent being). To make it sound even more like substance dualism, note that Thomas thinks that Socrates is an animal and animals are bodies (as I have learned from Christopher Tomaszewski, there are two senses of body: one is for the material substance as a whole and the other is for the matter; it is body in the sense of the material substance that Socrates is, not body in the sense of matter). Thus, one of these subsistent beings or substances-in-the-Cartesian-sense is a body and the other is a soul, just as on standard Cartesian substance dualism.

But of course there are glaring difference between Aquinas’ dualism and typical modern substance dualisms. First, and most glaringly, one of the two subsistent beings or Cartesian substances on Aquinas’s view is a part of the other: the soul is a part of the human substance. On all the modern substance dualisms I know of, neither substance is a part of the other. Second, of the two subsistent beings or Cartesian substances, it is the body (i.e., the material substance) that Aquinas identifies Socrates with. Aquinas is explicit that we are not souls. Third, for Aquinas the body depends for its existence on the soul—when the soul departs from the body, the body (as body, though perhaps not as matter) perishes (while on the other hand, the soul depends on the matter for its identity).

Now, let’s move to Descartes. Descartes’ substance dualism is widely criticized by Thomists. But when Thomists criticize Descartes for holding to a duality of substances, there is a danger that they are understanding substance in the Thomistic sense. For, as we saw, if we understand substance in the Cartesian sense, then Aquinas himself believes in a duality of substances (but with important structural differences). Does Descartes think there is a duality of substances in the Thomistic sense? That is not clear to me, and may depend on fine details of exactly how the completeness in nature (condition (2) above) is understood. It seems at least in principle open to Descartes to think that the soul is incomplete in its nature without the body or that the body is incomplete in its nature without the soul (the pineal gland absent the soul sure sounds incomplete) or that each is incomplete without the other.

So, here is where we are at this point: When discussing Aquinas, Descartes and substance dualism we need to be very careful whether we understand substance in the Thomistic or the Cartesian sense. If we take the Cartesian sense, both thinkers are substance dualists. If we take the Thomistic sense, Aquinas clearly is not, but it is also not clear that Descartes is. There are really important and obvious structural differences between Thomas and Descartes here, but they should not be seen as differences in the number of substances.

And here is a final exegetical remark about Aquinas. Aquinas’ account of the human soul seems carefully engineered to make the soul be the sort of thing—namely, a subsistent being—that can non-miraculously survive in the absence of the substance—the human being—that it is normally a part of. This makes it exegetically probable that Aquinas believed that the soul does in fact survive in the absence of the human being after death. And thus we have some indirect evidence that, in contemporary terminology, Aquinas is a corruptionist: that he thinks we do not survive death though our souls do (but we come back into existence at the resurrection). For if he weren’t a corruptionist, his ontology of the soul would be needlessly complex, since the soul would not need to survive without a human being if the human being survived death.

And indeed, I think Aquinas’s ontology is needlessly complex. It is simpler to have the soul not be a subsistent being. This makes the soul incapable of surviving death in the absence of the human being. And that makes for a better view of the afterlife—the human being survives the loss of the matter, and the soul survives but only as part of the human being.

More on the privation theory of evil

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

1. every evil is a privation

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

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

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

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

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

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

Why the Five Ways don't prove the existence of five (or more!) deities

Here is a potential problem for Aquinas’ Five Ways. Each of them proves the existence of a very special being. But do they each prove the existence of the same being?

After giving the Five Ways in Summa Theologica I, Aquinas goes on to argue that the being he proved the existence of has the attributes that are needed for it to be the God of Western monotheism. But the problem now is this: What if the attributes are not all the attributes of the same being? What if, say, the being proved with the Fourth Way is good but not simple, while the being proved with the First Way is simple but not good?

I now think I see how Aquinas avoids the multiplicity problem. He does this by not relying on Ways 3–5 in his arguments for the attributes of God, even when doing so would make the argument much simpler. An excellent example is Question 6, Article 1, “Whether God is good?” Since the conclusion of the Fourth Way is that there is a maximally good being, it would have been trivial for Aquinas to just give a back-reference to the Fourth Way. But instead Thomas gives a compressed but complex argument that “the first effective cause of all things” must be desirable and hence good. In doing so, Aquinas is working not with the Fourth Way, but the Second Way, the argument from efficient causes.

Admittedly, at other times, as in his arguments for simplicity, St. Thomas relies on God not having any potentiality, something that comes directly from the First Way’s prime mover argument.

This reduces the specter of the attributes being scattered between five beings, corresponding to the Five Ways, to a worry about the attributes being scattered between two beings, corresponding to the First and Second Ways. But the First and Second Ways are probably too closely logically connected for the latter to be a serious worry. The First Way shows that there is a being that is first in the order of the actualizing of the potentiality for change, an unchanged changer, a prime mover. The Second Way shows that there is a being that is first in the order of efficient causation. But to actualize the potentiality for change is a form of efficient causation. Thus, the first being in the order of efficient causation will also be a prime mover. So there is a simple—so simple that I don’t recall Aquinas stating it in the Summa Theologica—argument from the conclusion of the Second Way to the same being satisfying the conclusion of the First Way.

Consequently, in the arguments for the attributes of God, Aquinas needs to only work with the conclusion of the Second Way, and all the attributes he establishes, he establishes as present in any being of the sort the Second Way talks about.

That still leaves a multiplicity problem within the scope of a single Way. What if there are multiple first efficient causes (one for earth, one for the moon, and so on, say)? Here Thomas has three solutions: any first being has to be utterly simple, and only one being can be that on metaphysical grounds; any being that is pure actuality has to be perfect, and only one being can be that; and the world has a unity and harmony that requires a unified first cause rather than a plurality of first causes.

Finally, when all the attributes of God have been established, we can—though Aquinas apparently does not, perhaps because he thinks it’s too easy?—come back to Ways Three through Five and ask whether the being established by these ways is that same one God? The ultimate orderers of the world in the Fifth Way are surely to be identified with the first cause of the Second Way once that first cause is shown to be one, perfect, intelligent, and cause of all other than himself. Plausibly, the maximally good being of the Fourth Way has to be perfect, and Aquinas has given us an argument that there is only one perfect being. Finally, the being in the conclusion of the Third Way is also a first cause, and hence all that has been said about the conclusion of the Second Way applies there. So, Aquinas has the resources to solve the multiplicity problem.

All this leaves an interesting question. As I read the text, the Second Way is central, and Aquinas’ subsequent natural theology in the Summa Theologica tries to show that every being that can satisfy the conclusion of the Second Way has the standard attributes of God and there is only one such being. But could Aquinas have started with the Third Way, or the Fourth, or the Fifth, instead of the First and Second, in the arguments for the divine attributes? Would doing so be easier or harder?

Substances do not have substantial proper parts

It's an old maxim of Aristotelian metaphysics that substances do not have substantial proper parts. Here's an argument for it, in the case of material substances. Suppose a material substance A has a substance B as a proper part. Now, arguably A is wholly composed of two parts: the matter M and the form F.

Now the form G of B cannot overlap M, as then the form would be partly material. So G must be a part of F. But forms of substances are simples. So G must be all of F. But then we have two substances with the numerically same form, and that seems absurd.

A central assumption in the argument is that forms are simples. There may be a way of making an argument without that assumption. Suppose we say that G, the form of B, is a proper part of F, the form of A. Now if any proper part of a substance is a substance, then my heart is a substance--it's nicely delineated, and one of the best candidates. But I can survive the destruction of my heart (I would just need a machine to circulate the blood). And surely if my heart is destroyed, its form is destroyed as well. But my form doesn't seem to be intrinsically changed by the destruction of my heart. Yet if the form of the heart were a part of my form, then my form would be intrinsically changed by the destruction of the heart.

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.

My favorite Aquinas quote

Hence we must say that the distinction and multitude of things come from the intention of the first agent, who is God. For He brought things into being in order that His goodness might be communicated to creatures, and be represented by them; and because His goodness could not be adequately represented by one creature alone, He produced many and diverse creatures, that what was wanting to one in the representation of the divine goodness might be supplied by another. For goodness, which in God is simple and uniform, in creatures is manifold and divided and hence the whole universe together participates the divine goodness more perfectly, and represents it better than any single creature whatever. (S.Th. I.47.1)

Two thoughts on theologians who say "God does not exist"

Some theologians like to say that God does not exist. They say this to mark the radical difference between God and creatures.

1. If one is going to say such things, a more helpful way to speak would be: "God exists but we don't." For that would still get across the radical difference between God and creatures, but get right the fact that God is the one who is the more real. Compared to God's reality, we are but shadows. It is said that God said to St Catherine of Siena: "I am who I am, and you are she who is not." This poetically conveys a deep truth. We are but shadows, and "shadow" is often an overstatement.

2. There are many metaphysicians who like to say that complex artifacts like tables, chairs and blowguns don't exist. But many of them say this only in philosophical contexts and not in "ordinary" contexts, or they qualify the "don't exist" with a "really". They may or may not be misguided in the form of their odd denial, but what they (we!) are getting at is plausible: There is a deep difference between the kind of being that a table, chair or blowgun has, and the kind of being that a horse or a photon have (some of these philosophers will class the horse with the chair; that's mistaken, but the basic point I am making isn't affected). The ordinary language sentences "The pig exists" and "The car exists" have very different (nonpropositional) grounds: the former is grounded in a single thing while the latter is grounded in the arrangement of many things. Well, these theologians, like these metaphysicians, are also impressed by a deep ontological difference (a deeper one, perhaps). But like the metaphysician who is willing to speak with nonphilosophers in ordinary ways, these theologians should be willing to say "God exists" in contexts of ordinary worship. Or like the metaphysician who says that computers don't really exist, she could simply make a qualification: "God doesn't exist in the shadowy way." Or, more perspicuously?, she could say: "We don't really exist, but God does." (Though I think that if one does that, one should also distinguish us from artifacts. Perhaps the distinction could be marked with "really" and "really really"!)

Why did God become man?

One way to put the question of the theory of the atonement might seem be to ask with Anselm: "Why did God become man?"

I do not think that that is the right way, though. For God is omnirational. This means that whenever he acts, he is moved by all the unexcluded good reasons for the action. But almost any good that is achieved by a morally permissible action will provide God with an unexcluded good reason for that action. Very high up among the goods achieved by God through the Incarnation is ensuring that we can be forgiven with justice. But there are many other goods achieved by the Incarnation: Aquinas lists nine other great goods. And besides the great goods, there are far lesser but nonetheless genuine goods, such as cooperating with Joseph in the making of tables. Plausibly, there are many goods in between the really great ones and the far lesser ones, such as providing Israel with a king, bringing the nations to Israel in worship, and healing certain lepers through a face-to-face interaction.

One might try to run some kind of a distinction between the goods wrought in the Incarnation, so as to delineate the goods that are the proper subject of a theory of the atonement or the proper answers to "Why did God become man?" Let's try a few such distinctions.

First, there is a distinction between those goods that could be achieved without God becoming man and those goods that can only be achieved by God becoming man. But this won't draw the distinguishing line in the right place. First, pace Anselm, it is far from clear that we couldn't be forgiven with justice simply by divine fiat. Certainly, Aquinas thought we could. It would be fitting for the penalty to be paid by Christ on our behalf, but it would not be unjust for God simply to release us. Second, some of the goods lower down on the list require the Incarnation. Thus, the good of God's cooperating with Joseph in carpentry (this cooperation makes me think of Enoch walking with God, but in the case of Joseph there is a greater literalness) requires an Incarnation. (God can, by his omnipotent power, create tables ex nihilo, but such creation is not carpentry.) Likewise, there is a value to God healing the lepers through a face-to-face interaction of a sort that can only be had by means of the Incarnation.

Second, perhaps we could distinguish between reasons that are such that if they were present on their own, God would still have decided on the Incarnation, and reasons that were only contributory. Thus, while omnirationality implies that God became man in part in order to work with Joseph, surely if no other goods were realized by the Incarnation than God's engaging in carpentry with Joseph, then there would be no Incarnation. But why think that? God could have done it. Maybe it would be an unlikely scenario, but surely a possible one. Why accept the counterfactual of free will that had God had working with Joseph as the only reason to be Incarnate then he wouldn't have done it? Such a counterfactual seems meaningless (or trivially false) to me, and even Molinists need not extend their view to counterfactuals of divine freedom.

Third, perhaps we can distinguish reasons such that were they absent, the Incarnation would not have occurred. But again we get into dubious counterfactuals about divine decisions. Take one of the "big" reasons for the Incarnation. I see no reason to accept the counterfactual that had that reason been absent, there would have been no Incarnation. God might still have become incarnate for the other reasons.

There is, of course, a distinction as to the weight of the reasons. The "big" reasons are much better reasons. But this distinction is one of degree.

So it seems to me that the answer to the question of why God became man is simply a list. Aquinas gives ten items to put on the list. There are many more. We can prioritize the items on the list, of course. But each of the items on the list will be a reason that God was acting in the light of, since God acts in the light of all the unexcluded good reasons in favor of his action.

This does not imply that there is no such thing as a theory of the atonement, just that the question "Why did God become man?" doesn't delineate the theory precisely enough.

Grounding inhomogeneity and analogy

I ought to respect innocent human life. So I ought not feed cyanide to the innocent. I ought to respect the legitimate intellectual autonomy of others. So I ought not force my students to believe all my metaphysical views.

So, some ought claims are grounded, in part or whole, in other ought claims, and sometimes in further non-normative claims (such as that cyanide kills). This is familiar in many other cases. Thus, it's a standard libertarian view about freedom that some exercises of freedom are only derivately free: they are free insofar as they flow from a character that was formed by other free actions.

It would generate a vicious regress to suppose that all free actions are derivatively free. (In this case, the impossibility of the regress is obvious from the fact that we've only performed finitely many actions in our history.) Likewise, it would be a vicious regress to suppose all ought claims are grounded in further ought claims.

So there are some thing that are derivatively obligatory and some that are non-derivatively obligatory. (The two categories might overlap. For if I promise to fulfill a non-derivative obligation, then that obligation is both non-derivatively obligatory and obligatory by derivation from the duty to keep promises.) Likewise for freedom and many other properties. The non-derivative cases may be brute and ungrounded, or they may be grounded in a different kind of fact (e.g., maybe non-derivative freedom is grounded in alternate possibilities or non-derivative ought is grounded in divine commands—I am not advocating either option as it stands).

Here is a maxim I find plausible: Properties that exhibit this kind of grounding inhomogeneity—sometimes being grounded in one kind of fact and sometimes either ungrounded or grounded in a different kind of fact—are in fact non-fundamental.

This may lead one to say that properties that exhibit this kind of inhomogeneity are really disjunctive. That (or the related suggestion that they are existentially quantified) may be true, but I think it isn't the whole truth. Maybe freedom just is the disjunction of non-derivative and derivative freedom. But it's not a mere disjunction, in the way that being red or cubical is. It's a disjunction between related properties. In the cases of freedom and obligation, the relationship here seems to me to be precisely that of Aristotelian analogy: there is a focal sense of freedom and obligation—the non-derivative case—and there is a non-focal sense as well.

Conjecture: When we are dealing with a somewhat natural property that exhibits grounding inhomogeneity, we are precisely dealing with a disjunction (or quantificational combination) between analogous more fundamental properties.

Aquinas' thinking on divine names fits well here. St Thomas thinks that when we predicate wisdom of God and Socrates, we do so analogically, because God's wisdom is God and Socrates' wisdom is accidental to him. But this difference is precisely a grounding inhomogeneity in the property wisdom, with God being the focal case.

The unavoidability of sin

Aquinas says that without grace we can avoid each individual mortal sin but not all mortal sin, at least not for a significant length of time.

On its face, this seems contradictory. After all, I can avoid the first mortal sin. If I avoid it, then I should be able to avoid the next one. And so on. And hence I should be able to avoid all mortal sin.

But this argument mistakenly agglomerates what one can do. For instance, suppose that there is a mine field with a thousand mines. I know how to defuse a mine, but I have an independent probability of 10% of slipping and detonating the mine. It's correct to say that each mine can be defused by me—being able to do this with 90% reliability is sufficient for this—but it is incorrect to say that I can defuse the whole minefield. It is appropriate to look at the minefield that one is to defuse and think: "This is an impossible task without help."

The person without grace is unable to presently control her future actions in favor of the good. Each individual action is in her power, but she cannot control them all at once. Hence she can rightly look with trepidation at her future moral life and say: "This is an impossible task without help."

But a virtuous person can control future actions in favor of the good en masse, by growing in virtue and resolving to do good.

How can I knowingly and freely do wrong?

I accept the following two claims:

1. Every free action is done for a reason.
2. If an action is obligatory, then I have on balance reason to do it.

Consider cases where I know that an action is obligatory, but I don't do it. How could that be? Well, one option is that I don't realize that obligatory actions are ones I have on balance reason to do. Put that case aside: I do know it sometimes when I do wrong. So I know that I have on balance reason to do an action, but I refrain from it. But then how could I have a reason for my refraining? And without a reason, my action wouldn't be free.

It strikes me that this version of the problem of akrasia may not be particularly difficult. There is no deep puzzle about how someone might choose a game of chess over a jog for a reason. A jog is healthier but a game of chess is more intellectually challenging, and one might choose the game of chess because it is more intellectually challenging. In other words, there is a respect in which the game of chess is better than the jog, and when one freely chooses the game of chess, one does so on the basis of some such respect. The jog, of course, also has something going for it: it is healthier, and one can freely choose it because it is better in respect of health.

Now, suppose that the choice is between playing a game of chess and keeping one's promise to visit a sick friend. Suppose the game of chess is more pleasant and intellectually challenging than visiting the sick friend. One can freely choose the game of chess because there are respects in which it is better than visiting the friend. There are, of course, respects in which the game of chess is worse: it is a breaking of a promise and a neglecting of a sick friend. But that there are respects in which visiting the sick friend is better does not make there be no reason to play chess instead, since there are respects in which the chess game is better.

But isn't visiting the sick friend on balance better? Certainly! But being on balance better is just another respect in which visiting the sick friend is better. It is still in some other respects better to play the game of chess. If one freely chooses to play the game of chess, then one chooses to do so on account of those other respects. That one option is on balance better is compatible with the other option being in some respects better. It is no more mysterious how one can act despite the knowledge that another option is on balance better than how one can act despite the knowledge that another option is more pleasant. The difference is that when one chooses against an action that one takes to be on balance better, one may incur a culpability that one does not incur when one chooses against an action that is merely more pleasant, but the incurring of that culpability is just another reason not to do the action.

But isn't it decisive if an action is on balance better? Isn't it irrational to go against such a decisive reading? Well, one can understand a decisive reason in three ways: (a) a reason that in fact decides one; (b) a reason that cannot but decide one; and (c) a reason that rationality requires one to go with. That an action is on balance better need not be what decides you, even if in fact you do the on balance better action. Now, granted, rationality requires one to go with an on balance better action. But that rationality requires something does not imply you will do it.

But if you don't, aren't you irrational, and hence not responsible? Well, if by irrational one means lack of responsiveness to reasons, then that would indeed imply lack of responsibility, but that is not one's state when one chooses to do the wrong thing for a reason. It need not even be true that one is not responsive to what is on balance better. For to be responsive to a reason does not require that one act on that reason. The person who chooses the chess game over the jog is likely quite responsive to reasons of health. If she were not responsive to reasons of health, it might not be a choice but a shoo-in. Likewise, the person who chooses against what is on balance better is responsive to what is on balance better, but goes against it.

Now, of course, the person who knowingly does what she knows she on balance has reason not to do, does not respond to the reason in the way that she should. In that sense, she is irrational. But that sense of irrationality is quite compatible with responsibility.

Choice, rationality and contrastivity

Suppose I choose A over B. For me to have chosen over B, B must have been a relevant alternative. For instance, I am choosing to write this post over doing dishes, but I am not choosing to write this post over plugging in a soldering iron and grabbing its hot tip. Why? Well, I was impressed by some reasons in favor of doing dishes but not impressed by any reasons in favor of holding the tip of a hot soldering iron.

To choose A over B, I not only needed to have a reason to choose A, but also a reason to choose B. Moreover, plausibly, choices are contrastive and so are the reasons for them. If so, then the reason to choose B would have to have been a contrastive reason, a reason for choosing B over A. If this is right, then to choose A over B, I need a reason for A over B and a reason for B over A. Now when A rationally dominates B for me in the sense that any of my reasons for B is at least as much a reason for A, then I have no reason for B over A. But lacking a reason for B over A, I cannot choose A over B, paradoxical as that sounds. I may have reason to do A rather than B, but this isn't a matter of choice, because B is not a relevant alternative to A, since in the context of a choice between A and B, there are no reasons for B, i.e., no reasons for B over A.

We now have several principles:

• Rationality of Choice: one can only choose between options for which there are reasons in the context of choice
• Contrastivity of Reasons: reasons in the context of choice are always reasons for an option over the alternatives
• Domination Principle: choice between A and B is impossible when every reason for B is at least as much a reason for A
• Incommensurability Principle: choice between A and B is only possible when there is a reason for each of these that isn't, or isn't as much, a reason for the other.

The Domination and Incommensurability Principles are equivalent, and are basically endorsed by Aquinas. The argument at the beginning of the post shows that Rationality of Choice plus Contrastivity of Reasons implies the Domination and Incommensurability Principles.

An interesting consequence of the Incommensurability Principle is that one's moral psychology had better not endorse both of the following theses:

• Total Ordering of Strengths: for any two desires d₁ and d₂, either they are equal in strength, or one is stronger than the other
• Desires are Reasons: the reasons on the basis of which one chooses are desires and their strengths are the strengths of reasons.

For Total Ordering of Strengths, Desires are Reasons and Incommensurability together implies that there are no choices.

Humean compatibilists are committed to Desires are Reasons. Humean determinists are committed to Total Ordering of Strengths given how on Humean grounds we can test the strength of desire by seeing what the agent is determined by her psychological state to choose. If this is right then if Rationality and Contrastivity are true, Humeanism needs to be rejected.