Decisions on Decisions on Decisions on...

When you really, really, really, re... don't know what to do

1. A Day at the Station

Desma is standing—as people in thought experiments so often do—by a trolley track. On the track, a supervillain has placed a large box. Desma knows that before this pandemonium, the villain spun a fortune wheel with 1000 equal squares, and if it landed on square 1, he stuffed 1001 people into the box. This means that, based on Desma’s information, there is a 0.1% probability that the trolley on the horizon will convert the entrails of 1001 people into a very long and very red stripe on the tracks. Fortunately for the potential people in the box, there is also a single person wearing an improbably heavy coat standing right next to the tracks. Even though Desma cannot move the box, she can push this person onto the tracks, which, in addition to brutally killing the person, will stop the trolley before it reaches the box. Oh, the horror!

How does Desma figure out what to do in this situation? It seems that she must find a normative theory that can tell her what to do in situations of descriptive uncertainty. If she does not find such a theory, she has no criteria under which she can weigh up different options, and a normative theory is therefore necessary to ensure that her choice isn’t arbitrary. For example, she might be convinced of utilitarianism, which tells her that she should always take the action that has the highest expected value. Given that she attributes equal value to all lives involved, it follows that she should push the person with the heavy coat, thereby saving the box.

But from her ethics classes all that time ago, she now remembers that there are several proposals for normative theories. For example, she remembers that there were actually quite good arguments for deontology, and if that theory is true, it would be strictly forbidden to push the person off the rails. Nevertheless, she still leans more towards utilitarianism, and gives utilitarianism a credence of 0.6, and deontology gets a credence of 0.4.

As with the box, however, we now have a situation where we give positive credences to different options, where what we should do depends on which one is true; and the choice isn’t obvious: Utilitarianism has higher credence and prefers one course of action, while deontology prefers the other much more. This then requires a new principle that can tell us how we should act, all things considered—a second-order principle that can tell us how we should act under moral uncertainty, just as decision theories such as expected value theory tell us how we should act under descriptive uncertainty.

There are, of course, remedies for this. Desma, as the diligent philosopher she is, has read Ted Lockhart's Moral uncertainty and its consequences (or my old post on the topic), meaning she knows that she should maximize expected Rightness. She has sadly been a little too diligent with her studies, and has also read Johan E. Gustafsson and Olle Torpman's In Defence of My Favourite Theory, so she also gives some credence to the idea that she should simply act in accordance with the normative-ethical theory she gives the highest credence.¹ After considering the various arguments, she gives Lockhart's theory a credence of 0.6, and Gustaffson and Torpman's theory gets 0.4. The astute reader may begin to see the beginnings of a regress here.

Let us call descriptive uncertainty 0th-order uncertainty, uncertainty about normative-ethical theories 1st-order uncertainty, uncertainty about meta-normative theories (such as Lockhart's ) 2nd-order uncertainty, etc. As we have seen, we need a 1st-order theory² to make decisions given 0th-order uncertainty, etc. More generally, we need a kth-order theory to make decisions given k-1st-order uncertainty. As long as there is no order, such that one theory in that order has a credence of 1 (which I hope the reader will agree seems very unlikely), this regress will be infinite, since there will be uncertainty no matter how many orders we consider.

2. The Good, the Bad, and the Infinite

Is this a problem? Well, it’s not obvious that all infinite regresses are vicious. For example, there seems to be nothing immediately problematic about God writing “1,” on a piece of paper on the first day, erasing it on the second day and writing “2,” and so on ad infinitum. Similarly, we should not worry about the following regress: P, it is true that P, it is true that it is true that P… On the other hand, it seems quite vicious if the reason the earth does not fall is that it rests on a turtle; and the reason this turtle does not fall is that it rests on another turtle; and…

It’s one thing, of course, to identify examples of vicious and benign regresses; it’s quite another to identify what qualifies a regress into this or that category. What I say here is only tentative.

In one-way infinite regresses like the examples here, the answer seems to lie in the order of dependency. Take God’s eternal number series as an example. Let the starting point—what is written on the paper on the first day (i.e. “1 ”)—be called element 1. Likewise, we call what is written on the paper on the second day element 2, and so on. Note that the content of larger elements in this case depends on the content of smaller elements—that is, which number God writes depends on which number he wrote the day before. The same applies to the series of truths.

We can now generalize our naming scheme: Here P is element 1, “it is true that P” element 2, and so on. Again, the content of element n always depends on the content of elements <n. However, the reverse is true in vicious regresses. In the above example, the position of the Earth (element 1) depends on the position of the first turtle (element 2), which depends on the position of the second turtle, and so on. It seems, then—at least from these hand-picked examples—that a possible diagnosis is that a regression is vicious if lower elements depend on higher elements; and that it is benign if higher elements depend on lower elements (or possibly that no elements depend on each other).

Certainly in a case like the one we have here, this structure seems problematic! Perhaps if there is some ontological chain, it doesn’t matter if it’s turtles all the way down, but in a case like this where your mind has to traverse an infinity of orders before making a decision, we’re in a lot more trouble, as you could never actually do that.

I think the idea that this kind of dependency is problematic on a more fundamental level is also intuitively captured well by Leibniz's example with Euclid's Elements:

Let us imagine the book on the Elements of Geometry to have been eternal, one copy always being made from another; then it is clear that though we can give a reason for the present book based on, the preceding book from which it was copied, we can never arrive at a complete reason, no matter how many books we may assume in the past, for one can always wonder why such books should have existed at all times; why there should be books at all, and why they should be written in this way.

This is of course the most surface-level diagnosis you could give of this question. But I hope that you—even if you’re unconvinced by my brief sketch—will indulge my feeling that these types of regresses are problematic, so that the attempt to find a solution makes sense.

3. A Tale of Two Solutions

Let’s now return to the regression we began with, namely different orders of uncertainty. Do larger elements here depend on smaller ones, or vice versa? It should be clear from the story we began with that it’s the latter. Let’s call what Desma should do element 1. Element 2 is then principles for action under descriptive uncertainty, element 3 is principles for action under uncertainty regarding the principles in element 2, and so on.

As we saw, element 1 depends on element 2: Desma can have no answer for what she should do given uncertainty until she has a principle that takes the uncertainty as input and gives her an action as output—until then she has merely descriptive facts about a situation. But element 2 similarly depends on element 3: As long as Desma gives positive probability to several different principles in element 2, she can have no answer for what she should do until she has a way to convert the uncertainty among these different principles into a unified judgment about what she should do, and then the train to infinity is on. And since each element depends on the next, this regression is likely to be vicious; thus Desma will never be able to come to a decision about what she should do. If this is true, however, it means that we never have reason to make any decision at all—but if anything is absurd, it must be this! What should poor Desma do?

3.1. The Factual Solution

An appealing option might be, as Brian Weatherson, to be a normative externalist. On this view, it doesn’t matter if you’re unsure which theory is correct; the fact is that there is a correct theory, and what you should do is act in accordance with it. We’re of course still in trouble if there are infinite dependent orders as above—but this also seems pretty easy to avoid.

One option is that there are only 1st-order normative theories, and no higher orders. For example, it could be that utilitarianism is true and you should therefore maximize expected value. Whether or not you’re 99% sure of deontology, it doesn’t matter—you should still maximize the good! This is the model Weatherson himself adopts.

Another possibility is that there are facts about higher-order principles, but that the higher-order facts depend on the credence distribution of the lower orders. For example, it could be that utilitarianism is true at first order, and that My Favorite Theory is true at the second order.

However, to avoid a vicious regress here, we need to introduce different kinds of oughts—one for each order. This is obvious, as we might otherwise have to do two contradictory things. If utilitarianism and My Favorite Theory were both true, but you had a 0.9 credence on deontology, it would be true according to utilitarianism that you ought to push the person in the coat, and true according to My Favorite Theory that you ought not push the person! Therefore, we should instead say that you ought-1 push the person and ought-2 not do it.

It may be appealing here to try to find an ought-all-things-considered, i.e. an ought that depends on the full series and includes all the other ought’s (let's call it ought-X). This is a mistake, though. What you ought-all-orders-<n-considered is precisely what you ought-n, i.e. the content of the nth order. So to look for what you ought-X is to look for the content of the highest order. But given that the regress is infinite, there is no highest order, which is why ought-X doesn’t exist either.

Perhaps you think that ought-X is not a link in the chain, but stands completely outside it. It could be, for example, that ought-X is determined as a function of the set of ought-k's for choosing actions. So it’s not a theory in an order, but a theory of what one should do, given what all the infinite orders each recommend. The problem here is that this specific function itself will not get a credence of 100%—there will be a number of candidate functions with different ways of weighting different orders etc. So one has to find a new theory for choosing given uncertainty among these functions, and we already know how that story ends (or doesn’t).

On the externalist front, one must therefore either say that the right thing to do is always what the correct first-order normative theory recommends, or that there is an infinite series of higher-order normative theories, each with incommensurable types of normativity.

3.2. The Epistemic Solution

But even if we can solve the regress problem externally by saying that Desma should act in accordance with the correct theory, she’s none the wiser, as she’s not sure which theory is correct. There is also a fact about whether there are 1001 people in the box or not. If there are not, she should not push the person in the coat, and if there are, she should (say, if utilitarianism is correct) push the person. This is all well and good, but it doesn’t help Desma figure out what she should do, since the number of people in the box is precisely one of the facts she does not know, and she cannot act on unknown facts.

Let us therefore disambiguate two problems: the factual and the epistemic. The factual problem we looked at above, and it can be solved externally by saying that we should actually act in accordance with the true normative theory. But we have no direct access to what the true normative theory is (if there is one), as is clear from the extremely long normative-ethical literature. So even if there is something we should do “out there,” we still need some principles for how we should act most responsibly when we don’t know what we should do. We call this the epistemic problem.

When it comes to descriptive uncertainty, we solve the epistemic problem by formulating a first-order theory. And even if what Desma should do depends on how many are actually in the box, she needs a first-order theory to solve the epistemic problem, given her zero-order uncertainty—and this even if the actual problem is solved. But like clothes on the bedroom floor, the infinite regress manages to sneak back in, no matter how bravely we try to keep it out. For Desma is not 100% convinced ex hypothesi of one particular first-order theory, etc., etc. How can we solve the epistemic problem now that externalism can no longer come to our rescue?

I think we must consider how our moral reasoning starts: in judgments about particular cases. For example, if you want to argue for deontology, the process is to highlight various examples where your (and hopefully your listeners') judgments agree with deontology's, and against those of other theories. First-order theories are thus attempted summaries of judgments about individual cases, and it is through this that they are justified.

Or, it is not only judgments about individual cases that count. More general considerations about theoretical virtues, about whether a theory's structure and motivation capture what it “should” capture, etc. also play a role. But what’s common is that the normative theories are epistemically justified by their fit with lower-order “data” and not the other way around.

In other words: Maybe it is true that the reason Desma should actually do this or that is that there is a true normative theory that tells her that she should. But the way she figures out what she should do is not by starting with the correct theory and deducing what she should do, but rather simply by acting on 0th-order judgments.

This should not be a particularly foreign thought. When you, for example, avoid running over a kindergarten on a field trip in your BMW, it’s not because you first consult what the various normative theories you give positive credence say, but because you can just see that you should not do it—and if a 1st-order theory says that there is nothing wrong with running them over, then so much the worse for that theory. All of this is consistent with the underlying reason why you should do this coming from the 1st-order theory. Where the actual reasons work “top-down” in the regression, so to speak, the normative cognition works “bottom-up.”

This doesn’t mean, however, that 1st-order theories cannot influence our 0th-order judgments. First, there are many cases in which our 0th-order judgments are not clear and distinct. In such cases, 1st-order theories function as extrapolations from the cases in which we are certain to the cases in which we are not.

Second, our 1st-order theories can correct our 0th-order judgments in reflective equilibrium. For example, if I, through reflection on many 0th-order judgments, come to the conclusion that utilitarianism is correct, I must revise my 0th-order judgment that I mustn’t kill one person to save two. This does not mean that I use 1st-order theory as an epistemic starting point, but simply that, starting from some 0th-order judgments, I arrive at a 1st-order theory that undermines other 0th-order judgments through reflective equilibrium.

The idea is then that we stay at 0th order in our moral life, and make judgments without thinking about major theoretical considerations. But in certain cases—for example, when in doubt—we may have to take the step up to 1st order. The story is the same when it comes to the relationship between 1st and 2nd order. For the most part, it is sufficient to stop at 1st order. But in some cases it may be necessary to take the step up to 2nd order. It may be, for example, that I give utilitarianism a credence of 0.6 and deontology a credence of 0.4. That is, I am reasonably sure that it is not wrong to kill one to save two. But if deontology is true, it is really wrong to kill one. This may then cast doubt on whether I should follow utilitarianism, and in such a case it is necessary to take the step up to 2nd order. And so on, of course, for higher orders.

There is a risk that your considerations at one order will undermine all your previous considerations at lower orders. For example, it may be that I am quite sure of utilitarianism at 1st order, but that at 2nd order I become convinced of “maximize expected choice-worthiness,” (MEC).³ Since I have a positive credence in theory a (e.g. absolutist Kantianism ), which gives the act of lying a choice-worthiness of -∞, this means that my actions involving lies are dominated by it. So even though, before considering the second order, I was pretty sure that I must lie when some Nazis ask if I have Jews in my attic, this view has been undermined by higher-order considerations.

But this doesn’t mean that we have to suspend all judgments until we have examined the entire infinite regress—which leads to all the problems we have considered so far. Instead, we assume that our 0th-order judgments are correct until 1st-order theories undermine them; that we should act on our 1st-order theory until 2nd-order theories undermine it; and so on. All this starts with 0th-order judgments, and these are allowed to remain until we—in the light of higher-order considerations that themselves are grounded in 0th-order judgments—have reason to revise them.

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1. This is not strictly the theory Gustafsson and Torpman give in the article, but it captures the spirit.

2. By a 1st-order theory I mean here a normative-ethical theory combined with a decision theory (to the extent that the decision theory has an impact on what you should do morally). So utilitarianism+expected value theory would count as one 1st-order theory, and utilitarianism+risk aversion would count as another.

3. MEC says that I should always take the action that has the highest expected CW. CW is the value a theory gives to an action. So MEC says that if 1st order theory a gives action h CW of 10, and theory b gives h CW of -10, and I give a and b credences of 0.9 and 0.1 respectively, then the total expected CW of h is 8.