Natural law vs the moral argument

Up until recently, I had thought that natural law theory was compatible with moral arguments formulated as follows:

  1. If God does not exist, then objective moral values and duties do not exist.
  2. Objective moral values and duties do exist.
  3. Therefore, God exists.

Moral arguments of this kind have been made popular by defenders such as CS Lewis and William Lane Craig, and this specific formulation comes from the latter. In a post from a few years ago I explained my position on the compatibility of this with natural law theory as follows:

I think technically we can still use [the argument] as [formulated above], but we must recognise that it is partly dependent upon something like the fifth way for its soundness. At the end of the day I think much moral debate can be had without reference to God, since it is based on what is knowable about our nature. But ultimately I think any viable ethics depends on God, including natural law. (section 4.1)

This is admittedly not giving much credit to the argument, but I have since realized that even this weak support for the moral argument is misplaced. It seems to me that once we clarify the above formulation, the first premise will be seen to be incompatible with natural law theory, or at least some increasingly popular versions of it.

To start on the more technical side of things, the first premise should be understood as a non-trivially true counterfactual with an impossible antecedent (see here for details):

1′. If God did not exist, then objective moral values and duties would not exist.

So far there is still no obvious incompatibility with natural law theory, but we can go further. Presumably, if we are running this argument, then we think that there is something special about moral values and duties that calls out for a theistic explanation. That is, we are not interested in the general fact that anything whatsoever exists, but particularly the fact that moral values and duties exist. If this were not the case, then wouldn’t really be running a moral argument at all, but would instead be running a cosmological argument.

The point of the first premise, then, is that we finite agents are not sufficient to account for objective moral standards, and so the presence of such standards would imply the existence of God. This suggests that another way of stating the first premise is as follows:

1*. If we were to exist without God, then objective moral values and duties would not exist.

(Those of us who are convinced that God is required to account for any existence should also read this as a non-trivially true counterfactual with an impossible antecedent.)

Apart from the reasoning that got us here, further confirmation that (1*) captures the intent of (1) comes from how the premise is often defended. Consider, for instance, the following quote from Craig:

If there is no God, then any ground for regarding the herd morality evolved by homo sapiens as objectively true seems to have been removed. After all, what is so special about human beings? They are just accidental by-products of nature which have evolved relatively recently on an infinitesimal speck of dust lost somewhere in a hostile and mindless universe and which are doomed to perish individually and collectively in a relatively short time. Some action, say, incest, may not be biologically or socially advantageous and so in the course of human evolution has become taboo; but there is on the atheistic view nothing really wrong about committing incest. If, as Kurtz states, “The moral principles that govern our behavior are rooted in habit and custom, feeling and fashion,” then the non-conformist who chooses to flout the herd morality is doing nothing more serious than acting unfashionably. (William Lane Craig, The Indispensability of Theological Meta-Ethical Foundations for Morality)

Notice that this line of argument envisions a world where we exist without God, and puzzles over where moral values and duties are supposed to come from in such a world.

Now, while natural law theory may not pose any obvious problem for (1) or (1′), once we recognize that these amount to (1*) the problem becomes clear. The whole burden of a natural law theory is to ground moral truths in the natures of things, and having the nature that we do is part of what it means for us to exist. In the world described by (1*), then, the fact that we still exist with natures means that we still have objective moral duties and values even though God is not in the picture — at least from the perspective of natural law.

Of course, the exact details of this will differ depending on the version of natural law theory we consider. On Platonism these natures will be unchanging Forms in some third realm, on Aristotelianism they are intrinsic teleologies in things, and the new natural lawyers focus more on the nature of practical reason than on the natures of things. And each of these has variants within it. Some versions of Platonism equate the Forms with divine ideas, so that taking God out of the picture will take out natures with him. But other versions have God completely separate, meaning that natures stay even after God is removed.

Thomistic natural law theory is of the Aristotelian variety and is the version I find most compelling. On the one hand, it agrees with Aristotle that morality is fundamentally grounded in the intrinsic teleology built into us by virtue of the natures we have. On the other hand, contrary to Aristotle, it says that this intrinsic teleology still depends on God. Mind you, not in a way that makes it distinct from our nature, as if our teleology could in any way be separated from what we are. Rather, it is by creating and sustaining us as the kinds of creatures we are that God upholds the intrinsic teleology that fundamentally grounds morality. Of course, the details of this are quite complicated, but the point is that on the Thomistic view our intrinsic teleology is not mutually exclusive with God being the cause of our nature.

This brings us back to (1*). This premise asks us to consider the world where per impossible God does not exist and yet we still do. Because in such a world we still exist, we also still have natures and the intrinsic teleology which fundamentally grounds morality. This remains true even our natures arose through blind evolutionary processes since what’s important is the nature we have, not how we got it. So, in this world where we exist without God there is still the foundational morality that arises from the natural law: it is still wrong for us to lie, to murder, to steal, etc.; we still have categorical obligations, are held accountable, and have a basis for moral authorities (see section 2.4 here); we still have objective virtues and vices; actions are still objectively good and bad. Of course, there will be no duties arising from divine commands, but on natural law theories, these are in addition to the natural law, not instead of it.

So, then, for those of us who accept the Thomistic account of natural law, the moral argument we’re considering should be rejected as unsound. And I suspect the same would be true for some other versions of natural law theory, whether they be Platonic, Aristotelian, or from the new natural lawyers. It is certainly true for Aristotle’s own version, which doesn’t even construe God as the cause of our intrinsic teleology. On the other hand, there is also a lesson for those defenders of the argument who don’t accept any of these natural law accounts: a full defense of the first premise requires a thorough critique of these different natural law theories, which is no simple task. Certainly not as simple as the quote above appears. After all, natural law theories have a long pedigree in the history of Western thought.

While this objection doesn’t affect all moral arguments, it is noteworthy because the version it does affect is quite common. The argument might still have apologetic value insofar as it could convince someone who already rejects natural law, but such a rhetorical strategy makes me somewhat uneasy.

Self-perfective immanent activity

At the beginning of his Nicomachean Ethics, Aristotle distinguishes two ways an activity can be related to the end for which that activity is done: either the activity is distinct from its end, or they are the same. We call those activities that are distinct from their ends transient and those that are the same immanent.

Now, because an activity can be done for a variety of reasons, it’s possible that sometimes it is transient and other times that it is immanent. For example, a paradigmatic example of transient activity is the building of an object, like a chair or house. In the paradigmatic case, you perform the activity for the sake of having the object, and since the object itself is distinct from the activity that brings it into being it follows that the activity is transient. But in another instance, you may not necessarily build a chair for the sake of the chair, but simply because you enjoy the process itself — perhaps you’ll break the chair down again after you’re done, so that you can rebuild it again tomorrow. In this case, the same underlying activity is now immanent. The upshot of this is that while we speak of the activity being transient or immanent, it’s really the activity considered with respect to a particular end that is transient or immanent. If we keep the activity but change the end, then we might also change between transience and immanence.

Moreover, there is a sense in which the distinction between transience and immanence is really between two ends of a spectrum rather than a dichotomy. To see this, imagine building a chair for the sake of developing skill in carpentry. There’s a sense in which this is transient, since the skill exercised in an activity — and future activities of the same sort — is not the same as the activity itself. But even so, the skill of an activity surely has more in common with that activity than the completely separate object it produces. So, we might say that building something for the sake of developing skill is more transient than building something for the enjoyment of building while being more immanent than building something in order simply to have that thing.

Speaking paradigmatically, then, the building of an object is a good example of a transient activity. A good example of an immanent activity, on the other hand, is the musical performance by an orchestra. In this latter case, the orchestra doesn’t perform in order to produce something at the end of it all, but simply for its own sake.

Interestingly, there are other immanent activities which seem qualitatively different from the orchestra performance, and our aim here is to give an account of this difference. The first example that jumps to mind is the activity of life in a living thing — life is, after all, a continual activity that a living thing is engaged in until it dies, and is immanent insofar as it is concerned with developing and sustaining the living thing. Another simpler example is the activity of learning, insofar as learning some things now enables me to learn other things later.

The main difference between the immanent activities that we’ve mentioned so far is that living and learning both involve a feedback loop of sorts, where earlier actions in the activity can enable or hinder later ones. If I start with learning correct things then this sets me up to learn more correct things later, but if I am taught mistaken information then this will hinder with my ability to learn correct things later — or, as Aristotle and Aquinas said, a small error in the beginning will lead to a large error in the end.[1] Something similar could be said for life, although in this case there are many feedback loops that we could consider. To take a simple one, if I eat improperly then this can interfere with my ability to eat food that is good for me, which in severe cases can even lead to things like refeeding syndrome. Or, again, if I damage my legs to the point where I can’t use them anymore, then moving myself to food and drink becomes more difficult.

Now, orchestra performances do not involve feedback loops of the kind we see in living and learning. Certainly what happens earlier in the performance will influence what should happen later in the performance, as the orchestra reacts to tempo changes or unplanned off-keys. In fact, such influence will occur even if everything is going exactly as planned, since the performance itself depends on the proper ordering of the actions within it. The difference here, though, is that earlier actions in the performance will not enable or hinder any musician’s ability to act later in the performance: the cellist playing a certain set of notes will not affect the violinist’s ability to play the violin.

In order to give an account of this difference between immanent activities, we must start with an account of activities in general which is expressive enough for us to point out where the difference lies. And indeed, we can give such an account: an activity is the measured exercise of powers for the sake of some end, where the end for which the activity is done determines the appropriate measure. A thing’s powers are what determine what it can and can’t do, and whenever that thing engages in an activity it does so by exercising its powers. The end for which the activity is done determines how and when those powers are to be used, which is what we refer to as their measured exercise. Thus, we can distinguish between three things: the activity, its end, and its powers.

We’ve already said that the difference between immanent and transient activities lies in the unity of the activity with its end: they are the same in immanent activities but distinct in transient activities. Going a step further, we can see that the difference between the two kinds of immanent activities that we’ve been discussing lies in the unity of the activity with its powers: either the activity influences its own powers, for better or worse, or it doesn’t. The orchestra performance does not affect the powers by which it exists, but the activities of living and learning include within themselves the development and sustenance of their powers.

Now, if the activity consists in the exercise of its powers, then what is happening when it influences its powers like this? To answer this we borrow a series of distinctions from Kenny: a power can be distinguished from its possessor, its vehicle, and its exercise.[2] The possessor is the thing (or things) that has the power, and the exercise is the manifestation of the power in a particular context.[3] The vehicle of the power is that feature (or features) of the possessor which grounds the power by providing the components used in its exercise. To give an example, I am the possessor of the power to walk, which I exercise whenever I use my legs to move, and the vehicle of which includes the bone and muscle structures in my leg together with the relevant parts of my nervous system. And the vehicle of a musician’s power to play an instrument includes their skill in playing that instrument, the relevant body parts, and the instrument itself. Influencing the vehicle of a power will influence the possessor’s ability to exercise that power, for better or worse, which is precisely what happens when an activity influences its own powers. When I stub my toe while walking, for instance, I hinder my power to walk by damaging a part of the vehicle of that power. And when I do physical exercise, I enable my power to walk by developing the strength of that vehicle.

All of this helps us see more clearly the difference between the immanent activities we’ve been considering. The orchestra performance does not affect the vehicles of the powers of the musicians to play their instruments, but what we choose to do in our life can and does affect the vehicles of the powers we exercise when living, causing our muscles to strengthen or weaken, our blood pressure to raise or lower, and so on.

Oderberg has called the latter class of immanent activity self-perfective, where the sense of perfection is that of completedness or wholeness or actualization rather than of moral perfection.[4] Self-perfective immanent activities are immanent activities which are unified with the powers that underlie them so that part of the activity is the further enablement of those powers. We might wonder, could there be an immanent activity which is done for the sake of hindering its powers rather than enabling them? Reflecting on what we’ve already said we can see that there could not: an immanent activity is done for its own sake and consists in the exercise of its powers. Thus, the hindrance of those powers would go contrary to that activity, and so if it were done for the sake of this hindrance the activity would both be done for its own sake and against its own sake, which is absurd.

Of course, this is not to say that a self-perfective immanent activity always succeeds in enabling its powers, for any number of things could cause it to fail to one degree or another. But in order to fail, you are nevertheless still aiming at the goal you failed to achieve, which is the point. Moreover, what it means for an activity to enable its own powers cannot be divorced from the appropriate measure of those powers. For example, part of human development is an increase in height, but it’s not as if increasing your height is always better for your life as a human. At some point, increasing your height will hinder your ability to live well.

Notes

  1. Paraphrased from the opening of Aquinas’s On Being and Essence, himself citing Aristotle’s On the Heavens and the Earth.
  2. I got this from Feser’s Scholastic Metaphysics (p. 45), who was citing Kenny’s The Metaphysics of Mind (pp. 73-74).
  3. For a detailed discussion of this, see Oderberg’s Finality Revived: Powers and Intentionality.
  4. See Oderberg’s Teleology: Inorganic and Organic.

 

Dialogue on God’s interaction with the universe

Bob: How can an immaterial God interact with a material universe?

Alice: The question itself needs to be questioned before we can answer it.

Bob: How so? It seems like a fairly straightforward question.

Alice: Well, consider the word “interact.” God does not interact with anything. To interact requires action going in both directions, and since God is pure actuality this is impossible. Rather God acts on and through creatures without them acting on him.

Bob: Ok, so we’ll change the question to how an immaterial God can act on or through a material creature.

Alice: It’s better but still has problems. When you ask “how” God can act, what type of answer are you expecting?

Bob: I’m not sure I lay out exactly the type of answering I’m looking for, but I can give you illustrative examples. Fire heats by inducing mean molecular motion, I pick up things with my hands, and one stone acts on another by knocking into it. In each of these cases, I can point to the means or process by which some action is performed by one thing on another.

Alice: But on that account, the question is loaded! In each case, you could give some organ, part, or some material property by which one thing causes something in another thing. None of these kinds of answers apply to God since he has no organs, parts, or material properties. And to assume this in the question at hand is to preclude the possibility of giving an answer.

Bob: I grant your point but how, then, am I to proceed? Surely there’s a legitimate question to be asked here? And if we can’t use physical categories to have the conversation, then what can we use? After all, surely all our knowledge comes from our experiences of physical things?

Alice: It is true that all human cognition starts with sense data. But through abstraction and other intellective acts, we can move beyond these data, so that while our knowledge starts with our experiences it needn’t end with them. We do this, for example, when studying infinities in mathematics or when picking out idealized models in physics. Even in imagining things that don’t really exist, like fictional characters and stories, we are moving beyond what we have experienced. I agree that there is a legitimate question to be asked, but my point is that it should not be understood as a physical question but as a meta-physical one.

Bob: Ok, granted that the question — and therefore answer — is metaphysical, how would you answer?

Alice: One of the broadest distinctions we have in metaphysics is that between act and potency. Just as we’ve been saying, we come to understand this distinction through everyday phenomena like change and multiplicity. And once we understand act and potency, we can then move beyond these phenomena to talk about things beyond our everyday experience, like God. It is with categories such as these that we need to approach the question.

Bob: I understand the distinction between act and potency, and I understand that God is conceived of as a being of pure actuality. But how does this distinction answer the question?

Alice: It doesn’t by itself answer the question. But it is the first step in showing that the question is, in a way, misplaced.

Bob: I don’t see how it could be misplaced. After all, it seems quite natural to ask how a thing without arms or legs could act on material things.

Alice: Let me explain. Once we arrive at the distinction between act and potency we can draw out various corollaries, two of which interest us here. First, things act only insofar as they are in act. The basic idea behind this is that acting on something involves actualizing potentials in that thing, and since potency cannot actualize anything this can only happen insofar as the thing acting is in act. Second, potency limits act. When an act is understood as the actualization of this or that potency, it becomes qualified (or limited) by that potency. For example, the act of mean molecular motion is of itself not limited to a time or place or speed, but when it comes to actualize the potencies in something being heated then it will be limited in these ways.

Bob: I don’t see how all of this relates to the question. How do either of these help us find the metaphysical hand by which God acts on a material thing?

Alice: The point is that he doesn’t need such a hand in the first place! As material beings, we exist through the actualization of potencies in our matter. As such, our actions are limited in various ways, which is why we cause by means of organs, parts, tools, contact, etc. A particular fire can’t heat something across the world because it’s limited by its matter to a specific place and time. A particular stone can’t simply make another move whenever, but has to collide with it, because its causal influence is limited to where and when it is.

Bob: And what about God?

Alice: As we’ve said, God is pure actuality, which is to say that there is no potency in him that limits his action. He simply brings about his effects immediately, without any need for the various means we need as material beings. This is why I said the question is misplaced. If anything is surprising it’s that we limited beings can interact with each other, not that the unlimited God can act on us.

Bob: That may be evident upon later metaphysical reflection, but I think the question arises quite naturally from our everyday experience of how things interact with one another. After seeing that things typically interact by various means that depend on their materiality, we quite reasonably ask how it is that an immaterial God could do something similar.

Alice: That’s a fair point. The answer, then, is that an immaterial God does not do something similar. He does not interact, but rather he acts. And he does not act by means of something, but rather he acts immediately. His action is similar to ours in that it arises from him being in act, but it is different from ours in that his being in act is not limited by any potencies within himself.

Bob: I see. In a way, it is almost an inevitable consequence of his being the creator of everything. If he needed a means by which to act, then this means could not have been created by him.

McTaggart and meta-time

There is what I take to be an error common among my fellow Thomists regarding change and certain theories of time. Put tersely, this error says that the B-theory of time is committed to the Parmenidian denial of change. I had decided to write something about it, but after doing a bit of research, it occurred to me that a form of this error goes all the way back to the start of the contemporary debate about the nature of time. That is to say, a variant of this error is present in John McTaggart’s paper The Unreality of Time. Before I can write about the error of my fellow Thomists, then, it seems appropriate to first say something about McTaggart’s mistake. And that is the aim of this post.

As the name suggests, McTaggart’s paper puts forward an argument that time is unreal. In the course of doing this he introduces a distinction that is now commonplace in philosophy of time, namely the distinction between the A-series and B-series:

For the sake of brevity I shall speak of the series of positions running from the far past through the near past to the present, and then from the present to the near future and the far future, as the A series. The series of positions which runs from earlier to later I shall call the B series. The contents of a position in time are called events. The contents of a single position are admitted to be properly called a plurality of events. (I believe, however, that they can as truly, though not moretruly, be called a single event. This view is not universally accepted, and it is not necessary for my argument.) A position in time is called a moment.

The A-series is indexed by tensed terms like past, present, and future. The B-series, by contrast, is indexed by tenseless terms like earlier than, and later than. Both of these series index the same time into a time series (or timeline), but they do so differently: in an A-series there is a privileged moment we call “present,” and other moments are called past or present through reference to this moment. In a B-series, by contrast, there is no such privilege and all moments are, in a sense, on an equal footing.

McTaggart divides the time series into “moments” and calls the things at these moments “events.” Now, we need to clarify something here, because it’s key to understanding McTaggart’s mistake. We typically think of events as existing in reality and persisting across moments, as when I wave my hand for a few seconds. And at least initially McTaggart seems to talk in terms of change of reality, which aligns well with this typical way of thinking. However, he quickly switches to talking about change of the time series itself, which is what leads him into all manner of strange places. What do I mean by this? Let’s say I waved my hand from 12 to 12:05 and then stopped. Did the event of my waving go out of existence? Surely it did once 12:05 came along. But what if I asked whether the event happening at 12:02 went out of existence? On a typical reading — in which reality is the thing that changes — the answer would be the same, since I’ve just reworded the same question. But if we read it in terms of the time series rather than reality, then the question becomes whether me-waving-at-12:02 went out of existence. Do you see the difference? We are no longer asking about the event that spanned 12:02 (together with some other moments), but rather the particular slice of the event at 12:02 (rather than the slices at other moments).

As I said, in the course of his discussion McTaggart switches from talking about the event to talking about slices of the event. The confusing thing is that he refers to the latter as the event too. This is something important to keep in mind as we proceed.

With this in hand, we can formulate McTaggart’s argument as follows:

  1. Change is essential to time.
  2. Change is impossible if the moments of time are ordered only by the B-series.
  3. Therefore, the moments of time are at least ordered by the A-series.
  4. Being ordered by the A-series involves a contradiction.
  5. Therefore, the reality of time involves a contradiction.
  6. Therefore, there is no reality of time.

The relevant points here are (2) and (4). In defending both of these points, McTaggart makes unmotivated (and strange) assumptions about the nature of change and the interpretation of his distinction between the A- and B-series.

In discussing (2), he starts off well enough but quickly makes the switch that was discussed above:

If, then, a B series without an A series can constitute time, change must be possible without an A series. Let us suppose that the distinction of past, present and future does not apply to reality. Can change apply to reality? What is it that changes?

Could we say that, in a time which formed a B series but not an A series, the change consisted in the fact that an event ceased to be an event, while another event began to be an event? If this were the case, we should certainly have got a change.

But this is impossible. An event can never cease to be an event. It can never get out of any time series in which it once is. If N is ever earlier than O and later than M, it will always be, and has always been, earlier than O and later than M, since the relations of earlier and later are permanent.

The question in the first paragraph is about the application of change to reality. But by the time we get to the second paragraph he’s switched to talking about events as slices of real events. He correctly notes that if the slice of the event ceased to exist or came into existence, then “we should certainly have got a change.” But he incorrectly assumes that this change would be of the reality he was talking about in the previous paragraph. That he’s thinking in terms of slices becomes very clear in the third paragraph, when he evaluates the suggestion in the second. He says, for instance, that “An event can never cease to be an event. It can never get out of any time series in which it once is.” Now for a normal event to go out of existence, all that is required is for it not to exist at a later time. As soon as we start talking about getting out of the time series, then we’ve moved to talking about slices of events rather than real events. And once we start talking about that, then we’ve moved away from talking about change in reality toward talking about change of the time series.[1]

So we have that McTaggart intends to account for change in reality by reference to change in the time series. But now we have a problem, for this account seems to really only push the question of change up a level: from reality to the time series. What, then, accounts for the change in the time series? If we were to apply McTaggart’s account again, then we would have to posit a meta-time series which tracks the change of the time series. Changes in the time series would be accounted for by reference to changes in this meta-time series. But now we have the same problem again, for which we’d need to posit a meta-meta-time. And so on. Eventually we’d need be led to an infinitely nested collection of times and meta-times, and we wouldn’t have gotten any closer to accounting for the change we started with. In other words, McTaggart’s account of change leads to a vicious infinite regress.

This conclusion comes up in the paper a number of times in different forms, but it’s not clear to me whether McTaggart realizes that they’re all instances of the same problem. In the present section he rejects the possibility of the time series changing in this way (“the relations of earlier and later are permanent”), and thereby rejects the adequacy of the B-series given his account of change. Indeed, the same conviction continues through his entire rejection of the B-series being able to account for change. Consider, for instance, the paragraphs that follow:

Or shall we say that one event M merges itself into another event N, while preserving a certain identity by means of an unchanged element, so that we can say, not merely that M has ceased and N begun, but that it is M which has become N? Still, the same difficulty recurs. M and N may have a common element, but they are not the same event, or there would be no change. If therefore M changes into N at a certain moment, then, at that moment, M has ceased to be M, and N has begun to be N. But we have seen that no event can cease to be, or begin to be, itself, since it never ceases to have a place as itself in the B series. Thus, one event cannot change into another.

Neither can the change be looked for in the numerically different moments of absolute time, supposing such moments to exist. For the same arguments will apply here. Each such moment would have its own place in the B series, since each would be earlier or later than each of the others. And as the B series indicate permanent relations, no moment could ever cease to be, nor could it become another moment.

This entire discussion is predicated on the confusion between the change of reality and the change of the time series. Needless to say I think his criticism of the adequacy of the B-series to track change misses the mark, and this becomes fairly clear once we fix up this confusion. All one needs for change is that things can have different properties at different times, and nothing about this requires that we talk about these times in terms of past, present, and future (that is, the A-series). If time t1 is earlier than time t2, and I have different properties at these times, then I have changed. The B-series, then, is more than capable to track change.

McTaggart continues with his confusion when moving to discuss the A-series:

Since, therefore, what occurs in time [event-slices] never begins or ceases to be, or to be itself, and since, again, if there is to be change it must be change of what occurs in time (for the timeless never changes), I submit that only one alternative remains. Changes must happen to the events of such a nature that the occurrence of these changes does not hinder the events from being events, and the same events, both before and after the change.

Now what characteristics of an event are there which can change and yet leave the event the same event? (I use the word characteristic as a general term to include both the qualities which the event possesses, and the relations of which it is a term — or rather the fact that the event is a term of these relations.) It seems to me that there is only one class of such characteristics — namely, the determination of the event in question by the terms of the A series.

Here he envisages what we might call a “spotlight” theory of time. The ordered events permanently exist in the time series, and the present moment has a temporal spotlight shining on it. This enables us to track the progression of time by following the progression of this spotlight. Dropping the metaphor, this means that each of the event slices has one of three properties: it is past, it is present, or it is future. Only one such event slice is present, everything earlier than it is past, and everything later than it is future. McTaggart is forced into this because (1) he assumes change of reality involves change of the time series, and (2) he is convinced from preceding argumentation that this change cannot consist in the creation or destruction of event slices in the time series. Thus, his proposal: moments remain permanent without being created or destroyed, and the march of time consists in them merely changing their properties.

But this A-series proposal, just like the B-series proposal above, requires that there be some kind of meta-time. What, after all, would track the changes of the time series represented by the spotlight moving along it? Or, without metaphor, what would track the changes of the time series that occur when the event slices change their properties?

After much discussion about this McTaggart realizes that the way he’s construed things entails that there will be an infinite regress of times and meta-times. We might summarize the process as follows: we sought to give an account of change, and so we proposed the spotlight account. But this requires that we postulate a meta-time to track the change of the spotlight. If our original proposal was correct, then in order to account for this meta-time we need to propose a meta-spotlight. But this will in turn require a meta-meta-time. And so on. So we have a vicious infinite regress on our hands.

As far as it goes this is a valid conclusion, and one McTaggart could have raised when discussing the B-series earlier had he seen the implicit dependence upon meta-time there. As we’ve already said, however, instead of taking this as a reason to reject his account of change (in terms of the change of the time series), he takes it to mean that neither the A-series nor the B-series can be real. And since these are exhaustive options for time, he concludes that time cannot be real.

In fact, the problem isn’t with either the A-series or the B-series. As we did earlier, we can frame the infinite regress argument directly against McTaggart’s account of change without ever mentioning either series.

To summarize, then, McTaggart’s mistake was in confusing change to reality with change to time. Once this error is corrected, neither the A-series nor the B-series precludes the possibility of change, since both can track things having different properties at different times. And neither series necessarily leads one into an infinite regress.

Notes

  1. Initially McTaggart raises it as a hypothetical (“Could we say that…?”), and so long as it remains option that might admit of alternatives there is no problem in his argument. The only caveat would be that he cannot conclude to the unreality of time if he limits himself to only one option among others. The problem is that this is exactly what he does conclude.

We don’t do God

In a dialogue with the late Christopher Hitchens, John Haldane outlines why he thinks religion is crucial as a foundational political principle in societies made up of diverse cultures, religions, etc. Very roughly his position is (1) that the governing of such a society must be built around certain core notions like the respect for others’ rights or the pursuit of their well-being, and (2) that religion gives us the best (indeed, he thinks the only) grounds for motivating such respect or such a pursuit.

Backing up slightly it would be helpful to give some account of what we mean by “religion” and therefore, by contrast, “secularism.” The way I’ve come to understand it — and the way I think Haldane understands it too — is as follows: religion involves adding an extra layer to a worldview that admits of some form of transcendent reality, such that we can act justly or unjustly toward this reality. Religious living, then, is acting justly towards this reality. I deliberately phrase this in general terms because not all religions think this reality is one, or personal, or omniscient, or eternal, or any of the other attributes of the God of classical theism. Nevertheless they all have some notion of just activity toward this reality, even if perhaps they wouldn’t phrase it in exactly those terms. Secularism, by contrast, denies either (a) that there is a reality transcendent of us or (b) that we can act justly or unjustly toward it. For the purposes of living, then, the secularist has no interest in such a reality, even if they intellectually accept that it exists.

With this in hand, return to points (1) and (2) I mentioned above. I won’t say much regarding (1), but I appreciate that Haldane draws attention to the fact that “neutral” governance is an unachievable pipe dream. The point has been made in various ways before, but essentially it boils down to the fact that any governing system is committed (implicitly or explicitly) to a conception of the good that guides the decisions and trade-offs they make in governing.

With regards to (2) Haldane’s proposal for a religious grounding is that humans are created as image-bearers of God, and so our respect of other’s or our pursuit for their well-being would flow from our honouring God as part of our proper religious activity toward him. To phrase this in somewhat Thomistic terms, our respect for others is a participation in our respect for God. Of course, while this proposal doesn’t require the religion of a theistic sort, it does require a transcendent reality of which we can coherently be called image-bearers of as well as that justice toward this reality involve some form of honour. So while this proposal is certainly broader than the Abrahamic religions, it doesn’t extend to all religions.

At this point two clarifications can be made. First, contrary to what Hitchens assumes, Haldane’s proposal is not inconsistent with evolution, since the notion of creation he’s interested in is much broader than some seven-day account of creation. While it doesn’t even seem essential to Haldane’s proposal that we be created (since the key is that we’re image-bearers), even if we assume it is the creation could equally have occurred through evolution. This is an unfortunately common conflation found in the New Atheists, and is completely besides the point.

Second, and more importantly, Haldane is not proposing some form of divine command theory as his grounds. This point actually comes up explicitly in the discussion itself, but I thought it worth bringing attention to. His point is not that we respect each other our of duty imposed upon us by a God found in the revelation of a specific religion. Rather it is that grounding the motivation for following principles we can all agree to — such as the golden rule, or the respect of inviolable rights — requires a religious basis, and probably something like the particular basis he proposes.

Given these clarifications, what are we to make of Haldane’s position? The structure of the discussion unfortunately did not enable him to develop it to any great length or nuance, but we can comment on the gist of it that he managed to outline. As I’ve said already, I think point (1) is spot on. Regarding point (2), however, I’m inclined to think that it’s possible to develop an account of common goods that enables us to give the secular grounds of which Haldane is so skeptical. I’ve discussed this in one form or another on this blog for nearly two years, now that I look back. So to some extent I disagree with Haldane, but this disagreement is not as severe as might first appear, as can be seen in three points.

First, while I think such a secular grounds can be given, these ground are built on top of the nuanced Aristotelian teleological account of the good which Aquinas ably showed entails the existence of a supreme intelligence.[1] The grounds are secular in that they can be understood apart from religious considerations, even if they entail religious conclusions.[2]

Second, it must be admitted that the secular account doesn’t preclude the religious account given by Haldane. The two act together, enriching each other in ways sometimes inaccessible to the other. For instance, there is an existential impact of seeing all humans as images of a beloved Father that is out of reach for a purely secular account.

Third, while I think secular grounds can be given I have no illusions about how difficult such grounds would be to comprehend, let alone actually motivate someone to follow through on them. The difficulty of giving such an account has been a recurring theme since the time of Plato.[3] And once we have developed an account of goods and virtues, the particular kind commonness relevant to the project, powers and how they extend to common powers, the relation of common to private goods, rational duties, authority, justice, and so on, it’s difficult to be struck by anything other than the complexity and abstractness of it all, even if it appears to us satisfactory as a piece of systematic philosophy. And realistically, how many people will have the interest or capability to inform themselves of such an account? A further existential point is that such a dry account is far less motivating than the affection and honour found in the religious life. Overall then, I think a secular ground can be given, but that it is far too distant and disconnected from everyday life for it to be socially valuable. Haldane’s religious proposal is much better suited to this job.

In closing I want to clarify that neither the discussion between Hitchens and Haldane nor this post, are meant as an argument for religion. Rather, they’re discussions about the social value of religion in a diverse society.

Notes

  1. I am referring, of course, to Aquinas’s Fifth Way. Perhaps one of the clearest expositions of this is Edward Feser’s Between Aristotle and William Paley: Aquinas’s Fifth Way in Nova et Vetera Vol. 11, No. 3. See also Haldane’s own defense in his contribution to Atheism and Theism.
  2. This is not unlike what is true of many arguments for God’s existence, which run from things like change, existence, contingency, grades of perfection, and so on.
  3. As Rob Koons and Matthew O’Brien say in their article on poltical animals, “In attending to social nature, the ethically minded metaphysician must avoid both the Scylla of atomistic individualism and the Charybdis of organic collectivism. The attempt to navigate successfully the narrow strait between them has been a recurring theme in Western metaphysics, from the time of Plato to the present.”

The real distinction

Whenever we have two concepts, A and B, we can ask to what extent the things they pick out in reality are distinct. If they pick out distinct realities, then we say that there is a real distinction between them. If they pick out the same reality, however, then we say that there is a real identity between them. Even if two concepts are really identical with one another we can still meaningfully talk about a distinction between them, and Thomists say this can happen in two ways.

A conceptual (or merely logical) distinction is when the two concepts pick out the same reality in every way, and the only distinction to be had is in the way we’re considering that reality. For instance, Superman and Clark Kent are conceptually distinct from one another. There’s nothing true of Superman that is not also true of Clark Kent, and vice versa. Another example is a particular incline that is understood as either a downhill or an uphill. These are the same thing considered from different perspectives.

A virtual distinction arises when the two concepts pick out the same reality, but where this reality is understood with respect to two other really distinct things. In other words, we say that A is virtually distinct from B when (1) both A and B pick out some reality Z, (2) A is Z understood with respect to some C and B is Z understood with respect to some D, and (3) C and D are really distinct from one another.

We saw some examples of virtual distinctions when discussing potential wholes recently, and we’ll repeat two of them here. First, faith is thinking with assent. Of itself, faith is a single action, but it has an intellective aspect (thinking) and a volitional aspect (assenting) each of which involves the use of a different power (the intellect and will respectively). These two aspects of faith, then, are virtually distinct from one another, because they are the same act understood with respect to distinct powers. Second, a water molecule arises from a single bond configuring two hydrogen atoms with one oxygen atom. Now, we can consider the configuration of one of the hydrogen atoms, and we can consider the configuration of the oxygen atom. These two concepts pick out the same underlying reality — the configuration making up the whole water molecule — but do so with respect to distinct elements of the water molecule. As such, they are virtually distinct from one another.

These, then, are the two non-real distinctions, and in each case we could say when such a distinction occurs. Can we do the same thing for real distinctions? One common proposal is that two concepts are really distinct when the realities they pick out are separable, that is when one can exist without the other. Now, certainly separability is a sufficient condition for a real distinction, but is it a necessary condition? For Thomists the answer is no, since we think that a real distinction can occur between inseparable things. In cases where two things are inseparable, then, what is the condition that accounts for their real distinction?

I want to suggest that what we said about virtual distinctions can help us answer this. Looking at the three sub-conditions I listed for virtual distinctions, the second is critical and what links the other two. It is because being understood with respect to C does not exclude being understood with respect to D that there can be one reality picked out by the two concepts. If one of these relations did exclude the other, then the two concepts must pick out distinct realities, and therefore be really distinct. We’ll call this the exclusion condition to distinguish it from the separability condition.

Now, if the exclusion condition is to be of value to us it cannot apply in all and only those cases the separability condition applies. There are clearly cases where the two conditions coincide. To give a simple example, let A pick out me thinking something, and let B pick out me thinking the opposite. Assuming I’m not beset with doublethink, these two realities exclude one another. And they are certainly separable from one another. To find a case of exclusion without separability we need to look a bit harder. Perhaps the most famous (or infamous) example is the distinction between essence and existence in created beings. Aquinas argues that this is a real distinction, despite the two being inseparable from one another. His argument is fairly involved, so here we’ll just sketch enough for illustrative purposes.

Sherlock Holmes and I have a number of important things in common. We are both composites of form and matter, for instance, and we have similar sets of natural powers, even if he has some of these to a greater degree than I. The most salient point is that we share a common essence, on account of which we are both called human and by which we are distinguished from other kinds of substances. As far as I’m aware, however, I exist and he doesn’t. What this means is that our common essence itself cannot differentiate between an existing human and a non-existing human. Put another way, our essence of itself is indeterminate between existence and non-existence. I exist, then, because my essence has something else added to it which determines it to existence rather than non-existence. This something else is called esse in Latin, and is variously translated into English as “being” or “existence.”

All of this might sound like a convoluted way of saying what amounts to the tautology that I exist because I have existence. But such a complaint rides on an ambiguity. When I speak of a common essence shared by myself and Sherlock I do not have in mind some abstract universal that lies outside of each of us, but rather the particular feature found in each of us in virtue of which each of us fall under that universal in the first place. To illustrate the difference between these two consider the simple example of two groups of wood, each organised into a square shape. In this picture there is (1) the universal squareness which is instantiated twice, (2) the particular square organisation which is in the first group, and (3) the particular square organisation which is in the second group. It is in virtue of each of the groups having the organisation in itself that it can fall under the universal in the first place. So too with the common essence shared by Sherlock and myself.

Just as my essence is in me, so too its determination to existence is in me. It is because my essence is determined by esse and Sherlock’s is not that I exist and he doesn’t. So, then, our earlier conclusion really amounts to the non-tautologous claim that a certain fact about me (that I exist) is true in virtue of some feature in me (my esse).

Now, the argument I ran with myself and Sherlock can be applied to any being, so that all beings exist in virtue of esse within them. Esse, therefore, accounts for the similarity between all existing beings insofar as they exist, which is to say it unifies all existing beings qua existing. Essence, on the other hand, diversifies and differentiates these beings from one another, by qualifying their existence in different ways. For instance, two beings A and B are similar to each other in that they both have esse and thereby exist, but differ from one another in that A’s essence makes him an existing human whereas B’s essence makes him an existing angel. The essences of material beings additionally requires that their existence be qualified to a place and time, which allows multiple beings of the same species to exist.

Since esse unifies and essence diversifies, it follows that these two concepts exclude one another. And since a being can’t exist without its essence and esse these two are also inseparable from one another. So we have an example of a real distinction on the basis of exclusion without separability.

Before we close, we must introduce an important nuance. Strictly speaking, all that is needed for A to be a distinctly existing being from B is for A’s essence to qualify its existence in a way that B’s does not. Notice, however, that this leaves open two options regarding B’s essence: either it qualifies B’s existence in a way A’s essence does not, or it doesn’t qualify B’s existence at all. In the latter case, B’s essence would do nothing to exclude it from being really identical with B’s esse. Nevertheless, it is clear from the foregoing that at most one being can have unqualified existence, and so in all other beings there will be the real distinction between essence and esse we’ve been talking about.

Essentially ordered series

The notion of a series, or chain or regress, comes up a number of times in philosophical discussions. In this post, we’re going formalize the notion in general, and then develop this into a formalization of essentially ordered series in particular.

Intuitively, a series is when we start with some member and from there we trace through the other members one at a time, possibly indefinitely. The order in which we trace or discover the members in the series can be (and often is) the inverse of their order in reality. This happens with causal chains, for instance, when we start with some effect A, which is caused by some B, which in turn is caused by some C, and so on. Here, tracing up the series — as we just did — involves tracing backward through the causes. In other words, later members in the tracing correspond to earlier causes in reality.

To give this a formal notation, we can write a series as S = (→sn) = (… → s3 → s2 → s1), where the index of each member represents the order of our tracing backward through the members, while the order of the members represents the order of reality. Thus, because s1 has the first index it is the first of in tracing, but because it is the last member it is the last in reality.

Technically we could drop the requirement that a series has a last member, allowing it to be infinitely extended in both directions. But for our purposes here this would just clutter the notation unnecessarily, so we’ll keep the requirement for the sake of clarity. Nevertheless, the central result of this post does not hinge on this requirement.

Mathematical underpinnings of our notation

Note: if you’d rather not read a bunch of maths, and are happy with our above notation, then you’re welcome to skip this section.

We can give our series notation a mathematical underpinning by analyzing it in terms of a well-known mathematical structure: a sequence. The idea is simple: start with the sequence of indices (which represent our tracing backward up the series), match them up to members in the series, and then give those indexed members the reverse order to that of the indices. More formally, a series (or chain, or regress) is a structure S = (S, I, <, σ) where:

S1.
S is a non-empty set of members and I is a non-empty set of indices,
S2.
σ:I→S is a map from indices to members,
S3.
< is a strict total order on I,
S4.
For each i∈I, if the subset of all indices greater than i is non-empty, then it has least element,
S5.
I has a least element, written 1.

In (S1) we separate S (the members) and I (the indices) because, in general, the same member might appear multiple times within the series.

In (S2) the map σ connects the two sets and captures repetition in the series when two distinct indices map to the same member.

(S3) and (S4) tell us that the indices form a sequence. (S3) guarantees that for any distinct indices i and j, either i < j or i > j, and (S4) guarantees that each index (except the last) has an index immediately after it, which we can label i+1.

(S5), which is technically optional, allows us to write this sequence starting with a first member as (in) = (1, 2, 3, 4, …).

Using the map σ, we can move from this sequence of indices to a series of indexed members, which are the true members of the series. For each i∈I, we have the indexed member si = (σ(i), i). They’re called indexed members because they’re members with an index attached. How do we order these indexed members? In order to get what we had earlier, we need the indexed members to be in the opposite order of their indices. So, if i and j are distinct indices with i < j, then their two corresponding indexed members will be si and sj respectively, with si > sj. Given that the starting order on I was a strict order, there is no problem with inverting it into a strict order on the indexed members, and so we can safely write our series with the above notation of S = (→sn) = (… → s3 → s2 → s1).

So, the members of the series S are the indexed members ordered inversely to their indices. So, s1 is the last member in the series. Notationally, we will refer to the series with either a bold-face S or the arrowed (→sn), depending on which is easier to read at the time. These two notations are interchangeable.

Some examples

I admit that all of this is quite abstract, and so before continuing, we’ll consider some examples. As mentioned before, a familiar class of examples is causal chains. These start with some final effect (s1), and trace backwards to its cause (s2,), and then to the cause of that cause (s3), and so on. For instance, consider the causal chain of me moving my arm, which in turn moves a stick, which in turn moves a stone. We would write this series as (me → arm → stick → stone). Similarly, we could we depict the series of the successive begetting of sons as (… → grandfather → father → me → son → grandson).

But causal chains are not the only kinds of series. Say we define word1 in terms of word2, word2 in terms of word3, and so on. This would give us a series of definitions (→wordn) = (… → word3 → word2 → word1). And, as we saw in a previous discussion, some good1 might be desirable as a means to some other good2, where this good2 is itself desirable as a means to some other good3, and so on. This would give us a series of desires ordered from means to ends, (→goodn) = (… → good3 → good2 → good1). Let’s say we took members from the moving chain above and ordered them as a desiring series: I desire to move my arm, as a means to moving the stick, as a means to moving the stone. This desiring series would then be written as (stone → stick → arm), which has the members in the opposite order from a causal chain.[1]

Each example so far is a series where earlier members depend on later members. Call such a series a “dependent series.” We’ll return to these below, but for now, we note that not every series is a dependent series. Imagine, for instance, we had three lights of different colors (red, blue, and green), such that only one light is on at a time, and where the light that’s on switches randomly and endlessly. The series of switched-on lights up until some time might then be something like (… → red → green → blue → blue → red).

Some notes

Two final points on notation before we proceed.

First, sometimes it will be helpful to talk about sub-series, which are taken from a series by excluding some of the later members. So, the sub-series as (→sn)n>i consists of all the indexed members of (→sn) that come before s(remember that the order of the indices is the inverse of the order of the indexed members in the series). Unsurprisingly, we write this as Sn>i = (→sn)n>i = (… → sn+3 → sn+2 → sn+1).

Second, in the interest of not cluttering everything with brackets, we say that entailments have the lowest precedence of all logical operations, so that a statement like A ∧ B ⇒ C ∨ D is the same as a statement like (A ∧ B) ⇒ (C ∨ D).

Active series

For any series or member thereof, we can talk about its activity, in the sense of whether it is active or not. What it means to be active is determined by the series we’re considering: to be moving, to be begotten, to be defined, to be desired, or to be on are what it means to be active in each of our examples above respectively. The notion of activity enables us to distinguish genuine series from merely putative ones, and compare them within the same formalism. To see what I mean, consider the moving stone example again. Let’s say the stone is moving and there are two putative series that could be causing this: me moving it with a stick, and you kicking the stone with your foot. These would be depicted as (me → arm → stick → stone) and (you → foot → stone) respectively. Both series are putative because each would account for the movement of the stone if it were active. Nevertheless, only the one which is active actually accounts for the movement of the stone.

We encode the activity of a member with a predicate α, which is true of a member if and only if that member is active. The necessary and sufficient conditions for α will depend on the kind of series we’re considering, and sometimes we will be able to give an explicit formulation of it. Nevertheless, it is safe to say that a series is itself active only if each of its members is active, so that:

AS.
α(S) ⇒ (∀siS) α(si),

As an illustrative example, consider the lights from earlier. Imagine we had three putative series for which lights went on in which order: (green → blue → red), (red → blue → red), and (blue → red). Now assume the lights went on in the order specified by the first of these. In this case, both the first and third series would be active, but the second series would be inactive because it would have an inactive member.

Dependent series

Now, we want to focus specifically on dependent series. In such series, the activity of later members depends on the activity of earlier members. More formally, si depends on sj if and only if α(sj) factors into the conditions of α(si). We’ll call the inverse of dependence acting: an earlier member acts on a later member if and only if the latter being active depends on the former being active.

Before we continue we need to make a technical note about how the series and its members are being considered. A series is always considered in terms of an order given by a particular activity (and dependence) on the members themselves. Take the example of me moving the stone with the stick with my arm. When we write this as (me → arm → stick → stone) it must be understood that we are considering me, my arm, the stick, and the stone in terms of the movement only. This series is not meant as a universal description of dependence between the members, but just dependence with respect to a particular instance of movement. So, in the present series “me → arm” just means that on account of some activity within me I am imparting movement on to my arm; it says nothing about other ways my arm may or may not depend on me.

Essentially ordered series

The particular kind of dependent series we’re interested in here is called essentially ordered. In such a series, we distinguish between two types of members. A derivative member is not active of itself, but is active only insofar as the previous member is active. Or, put another way, a derivative member continues to be active only so long as the previous member continues to act on it. A non-derivative member, by contrast, does not need another to be active but is active of itself — it has underived activity. An essentially ordered series is a dependent series because deriving activity from something is one way of depending upon it.

The moving example from earlier is an essentially ordered series: the movement originates with me as the non-derivative member, and propagates through the derivative members (my arm, the stick, and the stone), each of which moves something only insofar as it is moved by something else. Something similar can be said for the defining series and the desiring series, each of which is also essentially ordered.

Traditionally essentially ordered series have been contrasted with accidentally ordered series, in which later members depend on earlier members for becoming active but not for continuing to be active. The begetting series from earlier is accidentally ordered: me begetting my son does not depend on my father simultaneously begetting me.

Now, the fact that in essentially ordered series the dependence in view is derivativeness, makes it relatively straightforward to give a necessary condition for the predicate α. Let η be a predicate which is true of a member if and only if that member is active of itself, so that η(s) if and only if s is a non-derivative member. Then we can explicitly give the following necessary condition of α:

ES.
α(si) ⇒ η(si) ∨ α(Sn>i).

This formulation captures both the non-derivative and derivative cases. Non-derivative members are active of themselves and so can be active irrespective of the activity of the chain leading up to them. Derivative members, by contrast, are not active of themselves but by another, and so will only be active if the chain leading up to them is active.

From (ES), we see that the following holds for essentially ordered series:

α(S)
⇒ α(s1)
⇒ η(s1) ∨ α(s2)
⇒ η(s1) ∨ η(s2) ∨ α(s3)
⇒ …
⇒ η(s1) ∨ η(s2) ∨ η(s3) ∨ ….

Given that a disjunction is true only if one of its disjuncts is true, it follows that any active essentially ordered series must include a non-derivative member:

EN.
α(S) ⇒ (∃u∈S) η(u).

From (AS) and (EN) it follows fairly straightforwardly that in an active essentially ordered series, every derivative member is preceded by some non-derivative member:

ENP.
α(S) ⇒ (∀s∈S) (∃u∈S) η(u) ∧ u ≤ s.

Now, because non-derivative members are active regardless of the activity of the members before them, it follows that they do not depend on any members before them. And because essentially ordered series are a species of dependent series, we can say that if a member is non-derivative, then there are no members before it. We’ll call this the non-derivative independence of essentially ordered series, and formulate it as follows:

ENI.
η(u) ⇒ (∀s∈S) u ≤ s.

Together, (ENP) and (ENI) entail that any active essentially ordered series will have a first member which is non-derivative, which we call the primary member. We call this the primacy principle and formulate it as follows:

PP.
α(S) ⇒ (∃p∈S) (∀s∈S) η(p) ∧ p ≤ s.

This is the central result of this post.

Questions and objections

This property of essentially ordered series — that they must include a primary member — can and has been leveraged in a number of ways. It is perhaps most well-known for its controversial usage in first cause cosmological arguments arising from the Aristotelian tradition. We’ve seen previously how Aristotle uses it when arguing for the existence of chief goods. It is also the formal reason behind the intuition that circular definitions are vacuous. For the remainder of this post, we will address various questions and objections that might be raised, first two shorter ones and then two longer ones.

First, some will be quick to point out that what we’ve said here doesn’t prove that God exists. And this is true: the result given here is very general, and any successful argument for God’s existence would need additional premises to reach that conclusion.

Second, some might wonder if our use of infinite disjunctions is problematic. While infinitary logic can be tricky in some cases, our use of it here is fairly straightforward: all it requires is that a disjunction of falsehoods is itself false. As such, I see nothing objectionable in our use of it here.

Third, astute readers will notice that we have not shown, namely that every active essentially ordered series must be finite. This is noteworthy because it is at odds with traditional treatments of such series. For example, in his Nicomachean Ethics Aristotle argues for a chief good by denying an infinite regress of essentially ordered goods:

If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. (NE, emphasis mine)

And in his Summa Contra Gentiles Aquinas argues for the prime mover by arguing against an infinite regress of essentially ordered movers:

In an ordinate series of movers and things moved, where namely throughout the series one is moved by the other, we must needs find that if the first mover be taken away or cease to move, none of the others will move or be moved: because the first is the cause of movement in all the others. Now if an ordinate series of movers and things moved proceed to infinity, there will be no first mover, but all will be intermediate movers as it were. Therefore it will be impossible for any of them to be moved: and thus nothing in the world will be moved. (SCG 13.14, emphasis mine)

Our result in (PP), however, is perfectly consistent with the series being infinite: all we need is for it to have a first member. This, for instance, is satisfied by the following series:

ω+n → … → ω+3 → ω+2 → ω+1 → ω → … → 3 → 2 → 1

where ω is the first ordinal infinity and n is some finite number. The question, then, is what the present result means for the validity of the traditional treatments.

On the one hand, the key property leveraged by thinkers like Aristotle and Aquinas is not that there are finitely many members, but rather that there is a primary non-derivative member. Now it’s possible that they conflated the question of finitude with the question of primacy, but it’s also possible that they merely used the language of infinite regress to pick out the case where there is no such primary member — something we might more accurately call a vicious infinite regress. Either way in the worst case they were slightly mistaken about why a primary member is needed, but they were not mistaken that it is needed.

On the other hand, in the kinds of essentially ordered series Aristotle and Aquinas were considering, it is a corollary of (PP) that there are finitely many members in the series. In general, (S4) guarantees that every member in the series (except the first) has a previous member, but it does not guarantee that every member in the series (except the last) has a next member. It’s precisely because of this that there can be series with beginning and end, but with infinitely many members in between. However, if a series is such that every member (except the last) has a next member, then given (PP) that series will also be finite.[2] Now, each series discussed by Aristotle and Aquinas have this second property. And so they are somewhat justified in talking as they do.

Finally, we might wonder why it is not sufficient to have a chain of infinitely many active derivative members, where each is made active by the one before it.[3] After all, if the chain were finite we could pinpoint one derivative member not made active by a previous member. But in an infinite chain, it can be the case that each member is made active by the previous.

Now, behind this objection lies the unfortunately common confusion between a series considered as a part and a series considered as a whole. When we consider a series as a whole we’re considering it as if it is all there is, so far as the series is concerned. For a series considered as a whole to be active, then, it must contain within itself the necessary resources to account for its members being active. By contrast, for a series considered as a part to be active, it need only be part of a series which, considered as a whole, is active. To illustrate this, imagine we see a stone moving, then realize it’s being moved by a moving stick, and stop there. In this case, we’d be considering the two-member series (stick → stone), where both members happen to be active. The series is active, but not when considered as a whole, since it needs additional members (like my arm, and me) to be able to account for the motion of its members.

Given this distinction the central question is what the conditions are for a series, considered as a whole, to be active.[4] Naturally, the answer will depend on the kind of series we’re considering, but merely pointing to a series in which all members are active is not enough to show that such a series considered as a whole can be active — as the previous example illustrates. What we need is an account of the distinctive characteristics of such a series, and a derivation from these what the conditions for activity are when such a series is considered as a whole.

Now, as we’ve seen the distinctive characteristic of essentially ordered series rests on the distinction between derivative and non-derivative members. Derivative members are only conditionally active, whereas non-derivative members are unconditionally active. Derivative members propagate the activity of earlier members, whereas non-derivative members originate the activity. The result encoded in the (PP) is that no members have their conditions actually met if all members are only conditionally active. Again, it’s that no member can propagate without some member originating. The point is not about the number of members, but about their kind. It doesn’t matter whether you have finitely or infinitely many pipes in a row, for instance, they will not propagate any water unless something originates the water. It doesn’t matter how many sticks you have, they will not move the stone unless something originates the movement.[5]

In short, then, the mistake of the objection is that it confuses the activity of an infinite series considered as a part, with the activity of an infinite series considered as a whole. The example does not contradict the present result because the objector has given us no reason for thinking the series in question is active when considered as a whole.

Updates

This page was significantly rewritten on 26 Aug 2017. The notation for series was made easier to follow, by distinguishing the sequence from the series so that the latter could follow the order of the series in reality. I also reordered the conclusions and formulated more in symbolic terms.

On 15-16 Dec 2017 I reworked the introduction and order of formalizations, so that the maths section is now optional. I also changed the Greek letters used to be closer to their English counterparts (sigma for the map into the series, and alpha for the active predicate).

Notes

  1. Well, an efficient causal chain. The chain here is, in Scholastic nomenclature, a final causal chain.
  2. We leave the proof of this as an exercise to the reader.
  3. This objection is inspired by Paul Edwards’ famous objection to first cause arguments for God’s existence.
  4. From a formalization perspective, this means that our formalism of series considered as wholes can include the answer if done correctly. Indeed, this is why we introduced the active/inactive distinction so that we can “step outside” and analyze the differences.
  5. To be sure, there is a difference between finite and infinite cases, in that a finite inactive series there will always be a first inactive member. This will sometimes happen in the infinite cases, as we saw above with our ω+n example, but not always. This difference, however, does not entail that infinite series can be active without non-derivative members.

The threefold whole

In his Metaphysics Δ Aristotle says there are two senses of the term “whole”:

Whole means that from which none of the things of which it is said to consist by nature are missing; and that which contains the things contained in such a way that they form one thing.

The first sense corresponds to our usage of the word when we say things like, “he managed to eat the whole sandwich” and “she read the whole book in one day.” The second sense corresponds to what we refer to when we speak of general part-whole relations, for instance when we say that my arms and legs are part of my body. This second sense is what we’re interested in here. Aristotle further divides this into two kinds:

But this occurs in two ways: either inasmuch as each is the one in question, or inasmuch as one thing is constituted of them.

These are two very different kinds of whole. The second kind is perhaps the one we’re most familiar with: bodies are constituted by organs, tables are constituted by legs and tops, computers are constituted by transistors and other electronics. This kind is referred to as integral, so that integral wholes are constituted by integral parts. We might not think to talk about the first kind as a whole, but it does fit one sense of the general definition. It’s a whole in the sense that a universal applies to (and thereby “contains”) all the particulars that instantiate it: humanness contains all individual humans, treeness contains all individual trees, and so on. This kind is referred to as universal, so that universal wholes apply to universal parts.

Aristotle construes the difference between these two kinds of whole in terms of how the parts are made “one” in different senses. Integral parts come together to form one individual which we call the whole. We refer to this as numerical unity. Universal parts are each themselves an individual which instantiate a common universal. We refer to this as specific unity.

Later the Scholastics discovered a third kind, which they called potential. How potential relates to integral and universal depends on how you analyse the differences between the kinds. Aquinas, for instance, analysed them in terms of the presence of a whole in its parts, which in turn correlates to how truly the whole can be predicated of its parts. This led him to placing the potential as midway between the integral and universal:

… the universal whole is in each part according to its entire essence and power; as animal in a man and in a horse; and therefore it is properly predicated of each part. But the integral whole is not in each part, neither according to its whole essence, nor according to its whole power. Therefore in no way can it be predicated of each part; yet in a way it is predicated, though improperly, of all the parts together; as if we were to say that the wall, roof, and foundations are a house. But the potential whole is in each part according to its whole essence, not, however, according to its whole power. Therefore in a way it can be predicated of each part, but not so properly as the universal whole. (ST I, Q77, A1, ad1)

Intrinsicality

My preferred analysis is in terms of the intrinsicality of the potency and act by which the parts of a whole are distinguished and unified respectively. For the remainder of this post we will unpack this, and reflect on how the different kinds relate to one another on this account.

Now, any material being is a mixture act and potency (or, equivalently, actualities and potentials). By this we mean that it has capacities for various states or behaviours, some of which are realised. We call these capacities potentials, and insofar as a potential is realised we call it an actuality or an actualised potential. For example a coffee cup has potentials for being various temperatures, a person has potentials for being various levels of educated in some subject, and a squirrel has potentials for jumping and running. That last example indicates that potentials aren’t always potentials for static states, but can also be potentials for dynamic activities. So also actualities can be static or dynamic, depending on the kind of potential they’re the actualisation of.

These two things, namely (1) the distinction between act and potency and (2) the realisation that individuals are mixtures of various acts and potencies, enable us account for very fundamental features of reality like change and multiplicity. We’ve spoken about change before, but it’s worth saying something about multiplicity here. Parmenides famously held that multiplicity is impossible since if A and B have being, then the only thing that can distinguish them is non-being, which is nothing. But if nothing distinguishes them then they are not distinguished, and therefore they are identical. Thus everything is one, a unity without multiplicity. His mistake was failing to realise (as we have) that being is divided into act and potency, and that beings are mixtures of these two principles. Two things can be unified by being actual in the same way, but diversified (or multiplied) by this common actuality resulting from the actualisation of distinct potencies. So you and I can be unified in our both being educated, but diversified by the fact that my being educated is the actualisation of my potency for being educated and your being educated is the actualisation of your distinct potency for being educated. So long as we properly divide being into act and potency, then, we can affirm both unity and multiplicity.[1]

So that’s act and potency, next we turn to intrinsicality. Intuitively, to be intrinsic to something is to be wholly contained within it. Slightly more formally, A’s being B is intrinsic to A relative to some C insofar as A’s being B doesn’t depend on C. Alice’s being educated is intrinsic to her relative to Bob’s being educated, for example, because it does not depend on Bob’s being educated. Intrinsicality is, naturally enough, contrasted with extrinsicality. In a water molecule, the hydrogen’s bonding to the oxygen is extrinsic insofar as it depends on the cooperation of the water molecule.

It’s clear enough that the primary sense in which we talk about the acts and potencies of something is as intrinsic acts and potencies, since these are what constitute the being of that thing. In order to outline all three kinds of whole, however, we will need to expand our focus to secondary senses. That being said, when considering something in terms of an act and potency at least one of these must be intrinsic to that thing, since if this weren’t the case, no sense could be made of our considering that thing rather than something else.

In general a whole, in the sense we’re interested, is “a unity of ordered parts.”[2] Parts, of themselves, are diverse and are brought together into a unity through an ordering of some kind, like an arrangement or structure or process. Now, since act unifies and potency diversifies, it follows that a whole arises through the actualisation of the potencies by which the parts are distinguished from one another. So for each part we can talk about the actualisation that unifies it with the other parts, and potency that distinguishes it from the other parts.

This allows us to state our taxonomy of the kinds of whole. For any part, either this unifying actualisation is intrinsic to the part or it is not. If it is extrinsic then, as we said above, the diversifying potency must be intrinsic to the part. If the actualisation is intrinsic, then either the potency is also intrinsic or it is not. An integral whole arises when we have an extrinsic act and intrinsic potency, a universal whole arises when we have an intrinsic act and intrinsic potency, and a potential whole arises when we have an intrinsic act and an extrinsic potency.

Breakdown of the three kinds of whole
Breakdown of the three kinds of whole

Integral wholes

All of this is rather abstract, and some examples might help for clarity. Starting with integral wholes we’ve already seen an example: a water molecule made up of hydrogen and oxygen molecules. Each of the parts has an intrinsic potential to be bonded with the others. There is one bond which actualises all of these distinct potencies resulting in one water molecule, and so this actualisation is extrinsic to the parts. Second, there’s a simple wooden table made up of a tabletop on four legs. Here each of the five pieces have potencies for being structured in various ways, and the binding of them together into the table is an actualisation of these potencies. And finally, there’s a living animal. What the parts are here is not totally obvious; they might be the various organs, the interconnected organic systems, or the cells, bones, and other organic materials. Whatever they end up being, the point of interest is that the extrinsic actualisation here is a dynamic process involving the parts, rather than the static structure of the table. This process is what constitutes the difference between a living animal on the one hand, and a corpse on the other.[3]

With these three examples in hand, we can introduce some technical vocabulary. In an integral whole call the extrinsic actualisation the configuration, and call a part with the configuration abstracted away an element. The element is that in which the intrinsic potency inheres. If we consider a hydrogen molecule while abstracting away whether it is free or bound in some other molecule, then we’re considering the hydrogen molecule element. When we consider a free-hydrogen-molecule or a water-bound-hydrogen-molecule, then we’re considering the element together with a configuration.

Universal wholes

Moving on to universal wholes, let’s consider the example of the wooden table and how it differs depending on which kind of whole we’re considering. The integral whole in this case is the table itself, with the integral parts being the tabletop and legs. The universal whole, on the other hand, is tableness and the universal part of this whole is the individual table (that is, the particular instantiating tableness). Each table — each universal part — will have its own intrinsic actualisation that accounts for its being a table as opposed to something else. This actualisation is common to all tables (it is in virtue of this that we call them tables in the first place), but it is not some numerically one thing. Rather, each has their own instance of this actualisation, each being actualised in the same way.

Again we can introduce some technical vocabulary. Well actually, we can re-introduce some technical vocabulary first introduced by Aristotle. The common actualisation intrinsic to each universal part is called the form, and when we abstract away the form of a part we’re left with its matter. Of itself matter is indeterminate between a number of alternatives, and form is the determination to one of these. (Put in terms of act and potency, of itself matter has potencies for alternatives, and form actualises one of these potencies.) The difference with integral wholes may now be apparent: with integral wholes the elements are the individual pieces of wood, but with universal wholes the matter is the wood itself. After all, if we have a table of wood and we abstract away the table bit all we have left is the of wood bit.

Because much of modern science has focused on integral wholes, we as moderns will always be tempted to confuse form and matter for configuration and elements.[4] We’ve already seen the difference with the wooden table: the elements are the pieces while the matter is the wood. With the living animal the elements are often said to be the cells, and so the configuration would be the organising process of those cells.[5] For universal wholes, however, the matter of a living thing is called its body and the form of a living is called its soul.[6] Considered broadly, there are three classes of living things: plants, animals, and humans. The soul of a plant makes it vegetative, the soul of an animal makes it sentient, and the soul of a human makes it rational.[7] If we abstract away the particular soul of a living thing, then all we know is that it is living; and this matter we call a body. The lesson here is that form and matter carve up the world very differently from configuration and element.

One more example should do to get this point across: consider the case where my hand moves into your face. The motion of my hand alone is indeterminate between me attacking you, and me reaching to get something and hitting you by mistake. The form that determines which of these is the case is my intention. Together the motion (as matter) and the intention (as form) constitute my action. The configuration of my action, by contrast, would presumably pick out how I hit you with my hand, like the path my hand took through the air. This something very different from the intention of the action.

Potential wholes

Finally, potential wholes. Of the three kinds this is the most foreign to us, and it is also arguably the most fundamental. The key here is this: in both integral and universal wholes we have cases where a single act can actualise multiple potencies at once. This is clear enough in integral wholes, but it can also apply with universal wholes: an animal’s soul actualises potencies for walking, grasping, flexing, seeing, smelling, touching, and so on. Now, whenever a single act involves the actualisation of a number of potencies, we can distinguish between sub-acts of that act. If some act A is involves the actualisation of potencies P, Q, and R, then we can consider the sub-acts of A as the actualisation of P and the actualisation of Q and the actualisation of R. The potential whole is the act, and the potential parts are these sub-acts which are distinguish by extrinsic the potencies found in the elements.

Notice the difference here: the parts do not have potencies, but are just sub-acts we differentiate by reference to extrinsic potencies. Consider the water molecule again as an integral whole, so that we have a configuration of elements. Each part is the result of an element being actualised with the configuration, and so each part includes some potency inside it. The whole water molecule includes both potency (from the elements) and act (from the configuration). But now abstract away the elements so that all you’re left with is the configuration itself. This doesn’t include a potency; it is just an act. And when we sub-divide this configuration into sub-configurations (each the actualisation of a different element), these are also just acts: the configurings of the hydrogen molecules and the configuring of the oxygen molecule. Potency plays a role is distinguishing the sub-acts from one another, but the potencies are extrinsic to these sub-acts.

Something similar happens in the case of a form informing matter. For each distinct potency actualised by the form, we can discern a sub-act which is that form considered with respect to that extrinsic potency. The potential parts of a human soul are roughly the various powers it gives a human: vegetative powers like digestion, animal powers like walking and seeing, and rational powers like abstraction and judgement.[8]

So far we’ve illustrated potential wholes by reusing examples from integral and universal wholes. This is partly because we want to show the sense in which potential wholes are most fundamental, but also because it helps us gain some initial intuitions. There are other examples of potential wholes, two of which we’ll go through now. First, communities are potential wholes. This is true in general, but focus on one for now: an orchestra playing a piece of music. The playing is the result of a co-ordinated effort from all the members of the orchestra, and is a single activity of the orchestra. We can consider the sub-activities of this activity as the playing of the individual members, and these would be the potential parts of the playing of the orchestra as a whole.

Second, there are what we might call “composite actions” like faith. At its most general level, faith is thinking with assent. “Thinking” involves having intellectual confidence in something, less than certitude.[9] “Assent” picks out the mood of the thinking: that which I think I also desire. So thinking uses the intellect and assenting uses the will, but these are being used together in one and the same act, which we call faith. So then the act of faith is a potential whole with the potential parts of thinking and assenting, each distinguished by the rational faculty they are the use of.

With both integral and universal wholes we introduced technical vocabulary to capture the specific kind of act and potency at play in each case (configuration-element and form-matter). With potential wholes, however, the act in view seems to be as varied as actuality in general. As such, it seems the best we can do is distinguish between super-act and sub-act, where the super-act is the potential whole and the sub-act is the potential part. Depending on which kind of act we’re considering we’ll restrict the vocabulary, and we’ll usually drop the “super-” bit from the whole. We’ve been doing this all already: configurations and sub-configurations, activities and sub-activities, actions and sub-actions. We also sometimes spoke about the potential parts by using a proxy, as when we used powers as a proxy for sub-forms of an animal soul.

Conclusion

Aristotle discovered two kinds of whole: integral and universal. The Scholastics discovered a third, the potential whole, and extended Aristotle’s analysis of wholes in terms of predication. We saw an example of this in Aquinas, and in that case potential wholes fell between the other two kinds. With the present analysis in terms of intrinsicality there doesn’t seem to be a linear way of ordering the different kinds, although their relations are captured well in the diagram we saw earlier.

Notes

  1. One might wonder if we haven’t just pushed the question about what multiplicity is back a step, since multiplicity of things arises from multiplicity of potencies. But this misses the point since we’re not trying to give an analysis of multiplicity, but rather trying to account for the reality of multiplicity with our principles. Because Parmenides had just being and non-being he could not account for multiplicity. But because we have divided being into being-in-potency and being-in-act, we are thereby able to account for it.
  2. See Svoboda’s Thomas Aquinas on Whole and Part.
  3. Rob Koons discusses in some detail how this process interacts with the parts in his Stalwart vs. Faint-Hearted Hylomorphism. David Oderberg argues in his Synthetic Life and the Bruteness of Immanent Causation the process of life is one involving immanent causation.
  4. Even Eleonore Stump, who is a very careful expositor of Aquinas, falls into this trap. I made the same mistake in an earlier post.
  5. While it is common to refer to the elements of an organism as a cell, this is technically wrong. But the details are not particularly important to our present point.
  6. See Mike Flynn’s blogpost series In Search of Psyche (introduction, part 1, part 2, part 3, and part 4).
  7. This is a technical term: any animal we take to be rational is a human. See David Oderberg’s Can There Be a Superhuman Species? for a related discussion.
  8. We say they are “roughly” the powers, since strictly they are the vehicles of the powers. Every power is grounded in a particular intrinsic actualisation, which we call the vehicle of that power. But such technicality is not necessary here.
  9. As Aquinas said, “[Thinking] is more strictly taken for that consideration of the intellect, which is accompanied by some kind of inquiry, and which precedes the intellect’s arrival at the stage of perfection that comes with the certitude of sight.” (ST II-II, Q2, A1, corp)

Because God said so

In a recent discussion with some friends, the question of why murder was wrong came up (actually, it was why Aquinas would say murder was wrong, but the discussion equally applies to the more general discussion to be had here). The answer “because God said so” quickly came up and, being a natural law theorist in the tradition of Aquinas, it left me unsatisfied. During later reflection on this, it occurred to me that there are at least three different questions at play here. Each of these questions might be answered in part with “because God said so,” but how each is fully cashed out is very different from the others. The three questions are as follows:

  1. Why is it bad to murder?
  2. How do I know whether it’s bad to murder?
  3. Why should I not murder?

The first question is a meta-ethical question about what makes things good, bad, virtuous, vicious, and so on. The second is a question of ethical epistemology about how we come to know the truth of the notions grounded by our meta-ethical answers. And the third is a question of normative ethics about what I should and shouldn’t do given the answers to the first two.

The three questions are related but very different from one another. Let’s take each of these questions in turn, discuss them in more depth, and outline what “because God said so” might look like as an answer. Now, of course, the details of the answers will depend on the meta-ethical framework we’re working from. For the majority of this post I’ll be working from a Thomistic natural law perspective, which I’ve discussed a number of times on this blog (eg. herehere, and here). Towards the end of this post, I’ll consider how another theistic meta-ethic (divine command theory) would differ from what was said.

Why is murder bad?

The fundamental thing that determines whether something is good or bad is whether it contributes to the fulfillment of your nature, the realization of your natural ends. Initially, it’s obvious why this would account for certain things being good or bad for me, such as not hurting or unnecessarily damaging myself. On the other hand, it is less clear how this would extend to the good of others, as when we say it is bad for me to murder another person. There are a number of ways to “extend” the notion of my good to include the good of others. I’ve sketched one before, and we can very briefly sketch another — in my opinion better — one by combining some previous discussions.

The fulfillment of our natural ends — and therefore the realization of our good — is achieved by us through the measured and unified expression of our natural powers. The active frustration of these powers would, therefore, be to that extent bad for us. Our natural ability, as rational animals, for co-operating toward a common end enables us to acquire what we might call “common powers” which are expressed through the participation in common endeavors. Consider the following example: by myself, I have the power to sing within a certain vocal range, but only with someone else am I able to harmonize within my vocal range. Here harmonization is a common power. Now, just as my frustrating a power is bad for me, so my frustrating a common power is a common bad for us. (Recall the kind of commonness we have in mind here.) Now, living amongst others gives us certain common powers, albeit ones less easily describable than “harmonization”. Murder would involve the frustration of some (or even all) of these powers and therefore be something bad.

Of course, much more needs to be said before this is a full account. The point to take away is that, however we flesh out the details, the way good and bad are grounded is ultimately based on the kind of beings we are (our natures). At this point is there any place for an answer like “because God says so”? Yes and no. Insofar as God creates and sustains us with the natures we have, he is the author of what is good or bad for us. But, he cannot do the impossible, and so he cannot arbitrarily decide what is good or bad for us any more than he can make a married bachelor or a square circle. So long as he creates a living being, he cannot make it good for that being to die. So long as he creates a rational being, he cannot make it good for that being to murder. So when it comes to natural law the “because God says so” answer needs to be understood in an indirect and qualified way.

But wait, there’s more. In section 2.5 here I mentioned that Aquinas distinguishes between four different fundamental kinds of law, one of which is the natural law we’ve been discussing so far. There’s also eternal law, which we’ll leave to one side. Then there’s positive law, which is law given by a legislator, and which is divided into human law (positive law given by a human legislator) and divine law (positive law given by a divine legislator). Now, natural law is often very vague and general and its application in particular cases requires careful consideration by wise people. So, as John Goyette says, “human law is essential for living the good life because it makes the general precepts of the natural law more specific.”[1] The same goes for divine law, with the obvious difference being that God is the legislator as opposed to humans.

In a sense both forms of positive law are authoritative because they’re based on natural law,[2] but they do establish new legal duties on us: so long as I am under a legislator who has imposed just duties on me, it is good for me to fulfill those duties and bad for me to fail in those duties. Because this goodness arises from positive law, we’ll refer to it as positive goodness. This positive goodness differs from the natural goodness mentioned above in an important way: natural goodness applies to us as humans whereas positive goodness applies to us as citizens under the legislator. So whereas natural goodness is applicable insofar as we have our particular nature, positive goodness only applies once the legislator has imposed the duties on us. So, then, with respect to positive goodness “because God says so” has direct relevance.

In the remainder of this post, if we do not specify the kind of goodness (or badness) in view then what we say applies equally to both outlined here.

How do I know whether it’s bad to murder?

This question differs from the first in that while the first concerned itself with ontology (what makes something bad) this question concerns itself with epistemology (how I know something is bad). Because of this, the number of potential answers (and so the potential for “because God says so” answers) increases.

The answers to the first question also apply to this question in the sense that one of the ways I can come to know whether murder is bad is by grasping what in reality makes it bad, or in other words, I can come to understand the ontological grounds for its badness. Indeed, this way of knowing the badness is in a sense primary in that it does not derive its correctness from other, deeper, reasons.

But I can come to know things in other ways, beyond the primary sense of grasping their underlying ontology, because I can come to know from others who know. I can come to learn the badness of murder from my parents, my school teachers, mentors, church leaders, the broader culture I find myself in, or some combination of authorities like these. If God has revealed himself (as some religions think he has), then he also stands as an authority that we can learn from. If God is concerned for our well-being and infallible in his judgments (again, as some religions think he is), then he is the uniquely perfect authority. And so, in this sense, “because God says so” takes on a special significance.

At this point, we must be careful not to forget the distinction between ontology and epistemology. Unlike in the previous section, here God’s revelation does not constitute the badness of murder but only perfectly informs us of it. All things being equal, we are justified in believing what we’re taught by the relevant authorities, and so a fortiori we are justified in believing what we’re taught by the perfect authority.

So we come to know what is bad by grasping the underlying ontological truths or by being taught by others. In the first case, all the “because God said so” answers in some sense carry over to the epistemological answers. In the second case, we have new “because God said so” answers insofar as he is a perfect authority on our nature (for natural goodness), and his will (for positive goodness).

Why should I not murder?

The first question was ontological, and the second was epistemological. This question is normative: it asks why I should act in a certain way. And just as the epistemological question was in a sense broader than the ontological one, so the normative question is broader still. Indeed, here the answers become manifold.

In general, a hypothetical imperative is a statement of the following form:

  1. If I want to achieve X, then I should do Y.

In cases where these apply, there’s something in the notion of X that entails that the way to achieve it is by means of Y. And this is largely mind-independent in that I should do Y even if I don’t understand enough about X to see that I should do Y. Consider a toy example:

  1. If I want to draw a straight line, then I should use a ruler.

This is true just by virtue of what drawing a straight line involves and the possible tools for achieving it. And it remains true even if I don’t know about rulers, or have temporarily forgotten about them, or hadn’t thought to use one, or any number of other reasons.

Now just as there are many motivations (X’s) for action, so too there are many of these imperatives and therefore many answers to the normative question. We’ve explained before that the imperative involving natural goodness is particularly interesting, because of the structure of the human will (section 2.4 here, cf. this and this). Taking the answer about natural goodness from the first question, an argument might be framed as follows:

  1. If I want what is good for me, then I should act so as to fulfill my natural ends.
  2. I do want what is good for me.
  3. Therefore, I should act so as to fulfill my natural ends.
  4. If I should act so as to fulfill my natural ends, then I should not murder.
  5. Therefore, I should not murder.

What’s interesting about this is that (2) is always true, since whenever we desire something it’s precisely because we see some good in it, and as noted above this remains true even in cases where our relevant judgments about what is good are incorrect. As Edward Feser says, “The mugger who admits that robbery is evil nevertheless takes his victim’s wallet because he thinks it would be good to have money to pay for his drugs.”[3]

Can something similar be said for the positive goodness discussed in the first section? It seems so: God is the legislator over all creation in charge of its common good, and since I should seek my good I should also, therefore, listen to his commands. (Again we note the dependence of positive goodness on the notion of natural goodness.)

So the previous “because God said so” answers carry over to answer the current question indirectly. However, these do not exhaust the possible motivations we might have. In addition to these, we might be motivated by a desire to follow God’s will, which itself perhaps follows from a love for him. We could also be motivated by the avoidance of punishment or the acquisition of reward. Each of these has analogs in human affairs too, of course, but we’re primarily interested in “because God said so” answers.

A different meta-ethical framework

How would things have been different if we’d approached these questions from a divine command theory perspective? On divine command theory, anything we’d get from natural law gets ignored, leaving positive divine law as the only form of goodness. Given the importance that natural goodness played in the discussion, it’s not surprising that this move also accompanies shifts in the logical ordering of things. So the normative force of God’s commands are taken as primitive and “morality” gets lifted to this somewhat mysterious and unique notion (cf. sections 1 and 2.1 here). The consequence of all of this is that “because God said so” takes on a more direct relevance more often, and plays a unique role in the ontological answer. The picture becomes flattened and therefore simpler, but wrong.[4]

Conclusion

If we take anything away from this it’s that the answer “because God said so” can be valid for very different reasons depending on what we mean by it. Let’s try and list the options that arose from the above discussion. Why should I not murder? “Because God said so.” In what sense? Well…

  1. Because it frustrates your natural ends established by God’s creative act, which is bad for you, as I know through philosophical investigation.
  2. Because it is bad for you, as revealed by God.
  3. Because it goes contrary to God’s law, which is bad for you, as revealed by God.
  4. Because it is contrary to God’s will.
  5. Because God will punish you if you do.

I’ve tried to capture this diagrammatically in the following:

Solid arrows represent ontological priority. Broken arrows represent epistemological priority.
Solid arrows represent ontological priority. Broken arrows represent epistemological priority.

Notes

  1. John Goyette, On the Transcendence of the Common Good.
  2. Thomas Aquinas, ST I-II, Q. 90, Art. 4.
  3. Edward Feser, Classical Natural Law Theory, Property Rights, and Taxation.
  4. I take the fact that on divine command theory the term “good” is equivocal (as opposed to analogical), that authority and normative force need to be primitive or reduced to something consequentialist, and that “moral” picks out some special and mysterious class of facts. I consider all of these reasons to reject divine command theory as a viable alternative to Thomistic natural law theory.

The metaphysics of gender

I recently listened to this talk by John Finley titled The Metaphysics of Gender: A Thomistic Approach. Below are my notes of this. I skip the introductory remarks and follow the four-section division of the talk. Note that by “gender” here we do not mean the psychological or social construct introduced by modern feminists. Rather, by “gender” we mean the biological distinction between male and female. Some have come to refer to this as “sex” but in the introduction John notes that both terms have ambiguity and so he just picked one. By-and-large parentheses represent my own thoughts, but this is not always the case. And finally, the times for each of the sections are written next to each of their headings.

Aquinas’s position (8:56-20:30)

A man is a male human being and a woman is a female human being. Male and female are distinguished by their mode of generation: the male is that which can generate in another, while the female is that which can generate in itself. Whatever meanings man and woman could have, they need be connected to these meanings.

So, then, what is the connection between male or female on the one hand, and being human on the other? It does not affect that one has a human nature: one’s gender does not elevate or detract from one’s being a human being. Perhaps, it’s better to say that gender affects how one participates in human nature. “It might be better to say that men and women share human nature equally but differently, according to their respective generative abilities. In an analogous way, being blue-eyed and being brown-eyed pertain equally but differently to the human power of vision.” Nevertheless, gender must be a more significant personal attribute than eye-color, since it involves distinct organs, activities, and purposes. It is also more uniform than other less significant attributes, which appear more sporadically throughout the human population.

Thomas has two classifications of accidents: (1) a logical classification (in terms of genus, species, etc.) in The Disputed Questions on the Soul and (2) a metaphysical classification (as arising from form and matter) in On Being and Essence:

On the logical classification there are three sorts of accidents: proper accidents (eg. risibility in humans) result from the principles of the species and so characterise all members, inseparable accidents (eg. masculine and feminine) result from the principles of the individual through permanent causation and so characterise that member in a lasting fashion, and separable accidents (eg. sitting and walking) flow from the principles of the individual through temporary causation and so only characterise that member at particular times. The main focus here is the inseparable accidents, however it’s not clear what other examples of such accidents there are. Aquinas gives examples like eye color, bone structure, and natural temperament, but as noted above these seem less significant than gender. A question arises as to which principles of the individual (soul, or body, or both) bring these accidents about. This is addressed by his metaphysical classification in On Being and Essence.

Regarding the metaphysical classification, we note that the whole substance is the true subject of all accidents, but since humans are composed of two principles (form and matter) certain accidents flow more from form and others more from matter. Thomas describes four kinds of accident (two following from form primarily, and two following from matter primarily). First, of those following from form, rational activities — understanding and willing — occur entirely in the soul and have no share in matter (though there is a measure of dependence on the physical sense organs). “Other accidents following from form, like sensation, do have a share in matter since they properly reside in the composite substance. The soul, that is, originates powers of sensation but it can’t sense on its own.” “Moving downward, accidents following from matter will always have some relation to form since matter on its own is pure potency, uncharacterized by any feature.” So, in the third case, some accidents following from matter relate to a particular kind of form. For Aquinas, masculine and feminine are accidents that follow from matter but precisely in relation to an animal form. So when the animal dies, and the animal form is separated from the body, it is no longer gendered in a univocal way. Finally, “other accidents following from matter relate to a more general form, as one’s skin color occurs through matter’s relation to the form of some elemental mixture. The color thus remains even after the person has died.”

Combining the two accounts, Aquinas takes gender to be an inseparable accident following from one’s matter in direct relation to one’s substantial form as an animal. This helps us distinguish it from other inseparable accidents, as they would follow from one’s matter in direct relation to some form other than one’s animal substantial form. It seems that gender is the only example of this special class of inseparable accident we have, and so it is in this sense a metaphysically unique feature.

“Now, if being male or female relates necessarily to the form of an animal why does Thomas assigns gender’s origin to matter?” He gives two reasons:

First, for both Aristotle and Thomas, the male and female roles in generation are active and passive respectively. The male semen contains the formal principle of generation whereas the female seminal fluid contains the material principle, such that when the two come together a human is generated. Insofar as every act of generation is directed toward producing one’s likeness and since the male is more active is the generative act, the act naturally tends toward a male offspring, and a female results from an accidental alteration in the male semen. Since gender is determined by the manner in which the seminal matter has been affected, it is seen to follow from matter as opposed to form. Aquinas agrees that one’s reproductive power — as all powers — arise because of the soul, but the difference in gender is owed to a defect in the matter of the female (since the male, insofar as he is more active, has the more reproductive power more perfectly).

Second, for both Aristotle and Thomas since form is what makes matter to be a certain kind or species, a difference in form must result in a difference in species. Thus differences applying to individuals of the same species must be differences originating from matter.

Note that genders origination from matter does not mean that it has no bearing on the soul. “While the soul in its own right is not gendered, just as the soul on its own possesses no sensation, presumably the soul of a male can be derivatively considered a male soul and the same in the case of the female, since the soul’s identity is marked by it’s being the soul of a male or female body. One’s gender then, as following from the principles of the individual, characterizes the person as a whole.”

Brief evaluation of Thomas’s account (20:31-23:15)

Thomas’s logical classification of gender as an inseparable accident makes sense insofar as gender doesn’t apply to the species as a whole, but individual members. “Moreover, current biology’s understanding of genetic systems, chromosomal patterns, gonadal structures, and sexual organs affirms that the principles of the individual exercise permanent causation in their originating one gender or another.” In spite of this, the fact that gender seems to be in a class of its own — separate from other accidents — calls for further inquiry. And this inquiry would have to focus on Aquinas’s metaphysical account of gender arising from matter in relation to a specific form.

It’s not totally clear what it means for an accident to follow from the matter in relation to a specific form. If this is taken to mean simply that the accident flows from the principles of the individual as such, then it is well-taken since evidently, one gender is not a characteristic of the species. This would still leave open, however, which of the individual’s principles is at work here (soul, matter, or both). But Aquinas, in saying that the female gender arises from an accidental alteration of the semen, answers this second question. “That is, he holds not just that gender stems from the principles of the individual, but also that being male or female stems concretely from the side of one’s matter, rather than one’s substantial form or soul.”

Now, current biology, of course, has shown that the female reproductive abilities are not imperfect versions of the male ones. Man and woman, respectively, do not supply the active formal principle of generation and the passive material principle of generation. That a man’s production of semen and a woman’s ovulation each supply distinct elements of the offspring’s genetic material reveals that, in this capacity, the two are co-contributors to the offspring. Since man and woman do not relate generatively as perfect to imperfect it is not the case that any given act of generation seeks the male. As contemporary science shows, the male and female are equally intended at the biological level. So Thomas’s empirical reason for attributing gender to matter — the first reason I mentioned earlier — is no longer tenable.

This leaves us with the question of whether the second reason given still works. Is it true that gender must arise from the matter and not the form because the form cannot account for something that arises from the individual?

A revised account (23:16-36:42)

The aim here is to argue that the Thomistic principles suggest that gender flows more from substantial form than from matter, that is more from the soul than the body.

As both Aristotle and Aquinas saw, male and female are of a different category to black and white. The former are tied up with the essential teleos of the human being and contain the substance’s essence within their definitions, whereas the latter are not and do not. “The presence of an organ indicates a particular configuration of matter for the sake of one of the soul’s powers, which in turn flows from the essence of the soul. The soul itself arranges material structures as organs so that they might fittingly serve as means through which the soul’s various powers can operate effectively.” As Thomas says in The Disputed Questions on the Soul, “the soul constitutes diverse parts in the body even as it fits them for diverse operations.”

To unpack this we might say that like the vegetative powers the reproductive powers slowly manifest as the being matures, and as the soul actualizes and shapes the individual it constitutes these powers in particular organs within the body. Just like the sensory powers, if the soul were to leave the body so too would the generative powers. Unlike the sensory powers, however, not all humans share the same set of generative powers (instead we have something like a 50/50 split across the population).

The generative powers of man and woman should be considered, strictly speaking, co-generative, since they possess a two-fold formal object distinguished hierarchically. As “generative” they possess the same ultimate object, namely procreation of another human being. While as “co-” their proximate objects differ by way of offering distinct sexual organs and activities yet in relation with each other. The ultimate object of the co-generative powers points to the unity of nature shared by man and woman since another of the same species, whether male or female, is generated. The proximate object of the co-generative powers points to the distinction within human nature as found in either man or woman, albeit only at the level of the reproductive capacities.

Since the reproductive powers are two distinct co-generative — as opposed to one at varying levels of perfection — it seems clear that they must be accounted for by the substantial form of the individual. Of course, since the generative powers intrinsically depend on organs they would this should not be thought of as an attempt to separate the soul from the body, but rather to highlight the soul’s role in constituting the powers in the body. Thus we provisionally include gender in those accidents that stem from the soul and have a share in matter, as with the senses. In order to develop this account further, we address three objections.

The first objection is that modern biology seems to support Aquinas’s position that gender is better attributed to matter than soul. This is because modern biology teaches us that gender is intimately connected with various genetic networks, especially the chromosomal patterns XY or XX found in the zygote. But this does not so much entail that gender differentiation arises from matter primarily as show us more clearly how intimately related substantial form and matter relate to one another in the constitution of a human being. Any becoming of a substance requires appropriately disposed matter; after all, the being is generated by the actualization of potencies in the matter. But it is the resultant form (the actuality) that primarily characterizes the being the is generated.

The second objection comes from the second argument given by Aquinas above, that difference in form constitutes difference in species. Since men and women clearly share the same species, their difference must, therefore, arise from matter. Moreover, the notion of an individual brings forth — for Thomists at least — thoughts of matter insofar as it is the principle of individuation. But we must make a distinction between a universal form and a particular form. Aquinas grants that when a soul is commensurated to a particular body (that is, when they mutually limit one another so as to constitute an individual) in a sense it takes on additional characteristics, an obvious example being individuation even after separation from the body at death. It is inevitable that gender is of the form, since matter does not configure itself into particular organs (being indeterminate between any such configurations) it must be the soul that does so in and through matter “for the sake of the particular powers that work through those organs.”

The position I have argued affirms the notion that particular souls are essentially commensurated to particular bodies, but claims that within this commensuration gender begins at the level of the soul and is received into the corresponding matter accordingly designated by the genetic pattern.

As to the concern about this introducing a distinction between two species of human, we can say two things. Rather than being an additional power that future determines the essence of the individual, gender concerns the maintenance of the essence that the other powers constitute. “As oriented towards the species itself, [the generative powers] cannot in themselves constitute new species.” Second, as noted above gender is a co-generative power which differentiates it from the other powers given by the soul insofar as they are independent in some sense. They exclude each other in definition (“four-legged” excludes “winged”) or in fact (“scaled” excludes “feathered”). Gender’s nature, however, presupposes “one like itself” and so depends on and includes its contrary both in fact and in definition. Male is defined in terms of female and vice versa through the co-generative relation. The reproductive powers are not merely distinct as one sense is distinct from another, but as mutually dependent powers contributing to a single action (ie. generation). They are not to be understood as characterizing distinct species, then, but rather as integral parts of the same species considered at the reproductive level. (This is a consequence of us being social animals: humans are not wholly intelligible in terms of an individual, but require that that individual be understood in the context of some community. This reoccurs again at the higher level with powers that enable us to rationally cooperate, which are a consequence of us being political animals.)

The third objection takes issue with the description of co-generative powers. Why could we not accept that there is one generative power manifested in different ways, depending on the body to which the soul is united? This would entail that gender differentiation stems from matter as opposed to form. Note that this is much like Aquinas’s view insofar as he sees one power actualized to differing levels of perfection. Now in some sense, the objector is right, namely insofar as both generative powers have the same ultimate object. Because of this, they can be naturally grouped together, just as the various sensory powers can be naturally grouped together. But insofar as the generative powers have distinct proximate objects (their organs and activities), they can be distinguished. Interestingly, even in the woman, we see multiple generative powers in a single being: powers for generation, support, and nourishment of the offspring all of which are required for procreation (since the ultimate object of generative powers is a human and not merely a clump of flesh). Since there are really distinct generative powers, their distinction must arise from the substantial form and not the matter.

In order to affirm that a numerically single (that is, really identical) power to be differentiated only by matter, we would need to accept Aquinas’s account which, as we’ve seen, is falsified by modern biology. Otherwise, we’d need a “generic power” had by both male and female, which would need to be an abstract power or a power that includes both. But the first alternative is incoherent in Thomistic metaphysics (and even in much of modern metaphysics), and the second would involve an entire set of the person’s powers being denied and frustrated merely in virtue of them being an individual human. This “opposes Thomas’s thought and the majority of human experience.”

Being male or female, therefore, follows principally from one’s soul in relation to that soul’s correspondingly disposed matter.

Three ramifications (36:43-43:41)

The first concerns “gender’s status in relation to the person.” Gender is closely related to the person but is different from other such attributes. Other attributes (like free will, reason, soul, body, growth, and sensation) are understood when the human essence is abstracted from individuals and reproduction is like this. But it differs that when considered in itself the essence includes both male and female, but when it comes to exist there is a split into the co-generative powers. “The human essence in itself includes male and female; only a consideration of that essence as actually existent entails male or female.”

Turn, then, back to the metaphysical classification given above. We’ve seen that reproduction, like sensation, falls into the second category of those accidents which follow from form that have a share in matter. But given the differences between reproduction and sensation, there must be a real distinction within this category. The difference is between those accidents which flow from the nature itself, and those accidents which flow from the nature as it exists in this or that individual.

And in this sense, one’s gender is not as close to one’s fundamental humanity as are the other powers of the soul. Being man or woman — you might say — is more proper to the human individual than to the human individual. As Thomas would put it being gendered at all is proper to human nature, but being a man or a woman is proper to this instance of human nature, this soul and this matter.

All of the other accidents that flow primarily from the soul characterize the whole species, and so we call them the proper accidents (or properties), like sensation and risibility. But gender differs from the other individual accidents insofar as it characterizes one’s structure, abilities, and purpose. Insofar as the gender so characterises an individual we might say that it is “the primary attribute of the existing person”, not as something that constitutes the person (since this is given by the soul and matter), but as that which is most truly proper to individual person (so, in this sense, it’s like a property at the individual level).

The second concerns “gender’s status to the human essence or nature.” Man and woman are not distinct species of human nature, but nor are they merely individuals of human nature. It is good, therefore, to introduce some notions that can describe the genders with regards to their human nature. Man and woman are principles of the nature, they’re parts of it, they are ways of it existing or ways of a soul incarnating in a body, and they are relational as mutually fulfilling complements. “Thomas compares male and female to odd and even in the numerical realm.” But even this misses out the relational nature of humanity.

The third concerns “gender in its specifically human meaning as the intersection of eros and generation.” A slight modification of the Aristotelian definition of male and female is, “the male is what co-generates in another, the female is what co-generates in itself.” There’s nothing peculiar to humans here; we are gendered because we are animal. But human gender has richer meaning than non-human gender insofar as the procreative activity is integrally marked by rational choice.

By nature the generative act is a human act, and not just the act of a human. Thus, what is distinctively human in gender comes to light most manifestly in the “co-” dimension of the co-generative relationship to the extent that deliberation, choice, and love are integral moments within human sexual activity, which thus transcends merely instinctual limitations.

The distinctive human dimension of all this is one of the reasons that it is considered problematic if the human generative act occurs without proper mutual consent, since it “presents a co-generative act with the co- aspect as distinctively human. Since the entire act is co-generative, if one aspect lacks distinctively human structure, so does the whole.” That the co- aspect is human and therefore higher than mere biological generation, it elevates the generative aspect which is primarily animal. The biological tendency becomes subsumed into a conscious intention in love.

Further, as Thomas points out, generating another like oneself in the case of a human involves continued rational and affective dimensions beyond those of the sexual sphere, since the mature human only comes to be after an extensive period of support, nourishment, training, education, and love.

Beyond metaphysics (43:42-46:55)

Here we comment on some things beyond the metaphysical question but which depends on the metaphysical answer, namely issues in the psychological, social, and ethical realms. There are two putative objections that might be raised from modern concerns against the claim that gender stems from the soul. First is the issue of sex-reassignment surgery, second is the reality of intersex persons.

With regards to the first, if in fact sex-reassignment surgery actually changed one’s sex/gender then it would constitute a concern. However, even if such surgery can change the outward appearance of an organ it nonetheless leaves the patient sterile. So rather than say that one’s gender has changed it is more accurate to say that it has to some degree been lost (or blocked).

With regards to the second, just as with sensation defects and abnormalities are possible so too with gender. This arises from the fact that gender (like the senses) arises from the soul working in and through matter. “Aside from the assistance of medical technologies in such cases, it’s crucial to recall that one’s gender, though integral to the person, is neither the defining nor the most important aspect of the person.” To quote Thomas on the place of gender in human life:

Among animals there is a vital activity nobler than generation to which their life is principally directed. Therefore the masculine sex is not in continual union with the feminine in perfect animals, but only at the time of coition, so that we may consider that through coition male and female are made one. But [humans are] further ordered to a nobler vital activity, which is to understand. Therefore there had to be a greater reason for the distinction of these two forces in [them], so that the female should be produced separately from the male and yet they might be fleshly joined as one for the work of generation.

In commenting on this, John closes with:

The ultimate telos of a human being involving the flourishing of a life suffused with knowledge and love reminds us that relationality and fruitfulness occur in realms higher than the physical. If, with Aristophanes in the Symposium, one were tempted to picture the human being simply as a longing half, the passage just quoted offers a larger view. In his own way, Thomas calls to mind Socrates’ and Diotima’s assent to the beautiful.