What's ahead for me?

Consider facts like:

1. Soon you will be in pain.
2. Eventually, you'll forget.
3. That sad experience is already behind you.

What is needed for making these facts true? Well, someone needs to be in pain, someone needs to forget, someone needs a sad experience. And that someone needs to be you. This identity condition generates all of the familiar questions about personal identity. But there is a third thing needed: the pain and forgetting need to be ahead, with the pain ahead by a little and the forgetting perhaps not a little, and the sad experience needs to be behind. But what does that mean?

The simplest account is just that "ahead" means in the future and "behind" means in the past. But if time travel is possible, this will not do. "Soon you will be in pain" can be true even though the pain is millions of years in the past, as long as what you're about to do is to go into a time machine, quickly go back millions of years, and then experience the pain. Likewise, the sad experience that is already behind you may be one that you experienced a hundred years in the future, traveling to the future and back.

We can, of course, say that "ahead" means in the subjective future and "behind" means in the subjective past. But that is just to give a name to the problem—the problem of what constitutes subjective time for a given person, or, perhaps more generally, what constitutes inner time for a given substance.

The problem of subjective time is related to, but not the same as, the problem of personal identity. Suppose I accept a memory theory of personal identity. Then it is natural to say that some experience E is in the subjective future provided that E is conjoined with a set of quasi-memories that form a chain back to my present state. One might also say this even if one does not accept a memory theory of personal identity. Note that this account of the subjective future, even if accepted apart from the memory theory of personal identity, has some of the counterintuitive consequences of the memory theory. Suppose that in five minutes you will suffer total amnesia immediately followed by horrible pain. Then it seems quite right to say that soon you will be in pain—the pain is in your subjective future. But not if this memory theory of subjective time is correct.

David Lewis in his famous piece on time travel handles this by means of causal connections. What makes person-stage y a subjectively future person-stage with respect to person-stage x is that there is the right kind of chain of causal connections leading from x to y. (Put that way, the memory theory is a special case.) But what sorts of causal connections will do the job? We can imagine here fun time-travel scenarios involving swapping brains, or parts of brains, or memories, with your past self, and we're probably going to get some cases that are at least somewhat problematic for any particular causal connection account.

Note that dualist theories have a much easier time with the various puzzles about personal identity than non-dualist theories. Swinburne shows this: Dualist theories can always make indeterminacies be merely epistemic, and doing so fits very well with our intuitions. But it's much less clear that dualist theories have any easier time with the problem of subjective time.

On the other hand, non-realist or conventionalist accounts, while deeply implausible for personal identity, may be rather more plausible as answers to the problem of subjective time. While it really does matter much whether someone who does some horrible deed or experiences something wonderful is really me, maybe it does not matter much whether the deed or experience is ahead or behind, except insofar as I am causally connected to it. So one could accept a theory on which subjective time is constituted by causal connections, and not worry about the more outlandish counterexamples with mind-swapping, etc., because what matters are the causal connections, not the subjective time relations. One might hold that there can be vagueness in or degrees of aheadness/behindness that is more plausible (to me!) than vagueness in or degrees of identity .

There is a further option. It may be that it is a basic fact about substances in time that they are continuants and come with an internal clock.

A final question is what the relationship between objective and subjective time is. My present view is that external or objective time is constructed out of the inner or subjective times of things. In our universe this can be done because most inner times run in the same direction. There may, however, be universes without much coherence between inner times, and in such universes there will be no objective time, only inner or subjective time.

Reproductive ethics

Much reflection on "reproductive ethics" is in fact about the prevention or nullification of reproduction (e.g., contraception and abortion) rather than the production of life. On the First Things home page, Ryan Anderson urges us to think harder about the production of life. He suggests that in vitro fertilization treats the new human being as a means rather than a person, and challenges us to develop this kind of an insight further. This is a tough challenge, but one that it is important to try to meet.

A radical way to meet the challenge, would be to claim that it is never permissible to deliberately produce a child, because when one deliberately produces a child, one is producing that child for some end. That end is not the good of the child, as that would arguably be justificationally circular, since the fact that the child will exist is presupposed in talking of what is good for the child. Hence, on Kantian grounds, one is not treating a person as an end in producing the person for some purpose. On this view, then, human life can only be licitly produced by a process that has independent value not merely instrumental to the production of human life, such as marital union, and the process must be engaged in for the sake of that independent value. (George and Bradley have an essay where they make the more moderate, but still strong, claim that marital activity engaged in solely for reproductive purposes is wrong.) If the thought of reproduction at all enters into a morally upright decision to engage in the act of marital union on this view, it is not as an end but as a defeater-defeater (e.g., the couple is not in the mood for marital union, and their not being in the mood is a defeater for the reasons that couples have for marital union; but the possibility of reproduction maybe defeats the mood consideration).

This radical move strikes me as deeply implausible. But there is something to the worry that many possible reasons for having a child do treat the child as a means... Is there a way of defending a more plausible position that will rule out in vitro fertilization on the grounds that it treats the child as a means?

A counterexample to the Private Language Argument

Wittgenstein's Private Language Argument contends that it is impossible for one to form a language by oneself. Here's a counterexample. You live on an island that has no people other than yourself. You live for forty years there. Then you step in a time machine that was left there by someone else. You go back forty years. You do this 999 times. (Let's assume that the time machine also fixes up your body so you can live for a subjective length of 40000 years.) To an outsider, the island looks populated by a thousand people of remarkably similar appearance. There is a community there. But that community in fact includes only one person, you. So, it's possible to have a community with only one person. But there is no reason why such a community couldn't develop a language, since it functions just like all other communities do.

A fun question: Suppose Marcy and George join you on the island, but they don't do any time travel, and so there you are located in 1000 places on the island, and then there is Marcy and there is George. In elections, should you get 1000 votes, with each of them getting only one—there does, after all, seem to be a sense in which you have a lot more interests—or should each of the three people on the island get exactly one vote?

By the way, the clip below illustrates the wrong way of imagining the scenario. In my scenario, it is a mistake to think of first the island having you in one place, then of it having you in two places, and so on. Over the 40 year period in my scenario, you always are in 1000 places.

Progress report: naturalism and persons

This is just a progress report, a promissory note without much argument. I've been thinking a lot about naturalism and persons. Specifically, I've been thinking whether there is room for persons in a naturalistic ontology. One lemma that I've become convinced of is that if necessarily all persons are substances, so that if x is a person, then for x to exist is not a matter of something beyond x having some property or standing in some relation, then naturalism is false. In an earlier post, I gave an argument for this conclusion based on speculative physics, but now I am convinced that the conclusion holds independently of the speculative physics. Basically, the idea is that if naturalism holds, strong AI is true (it would be too weird if naturalism were true but minds had to be tied to a biology like ours), but if strong AI is true, then I suspect it is possible for a token computer program to be a person, and token computer programs are not substances (their existence is a matter of a computer having a particular state).

Moreover, it is plausible that finite persons are ontologically homogeneous: if one finite person is a substance, they all necessarily are. If this is correct, then if we are substances, naturalism is false.

Are persons substances? Are we substances? If we adopt an Aristotelian ontology, there are three alternatives to a person being a substance: she might be accident-like (e.g., a trope or a token relation), she might be the essence of a substance, or she might not exist. I take it that persons exist. The same kinds of thoughts that suggest that if naturalism holds, persons need not be substances, also suggest that if naturalism holds, then persons need not be essences of substances. So, on this kind of ontology, the question comes down to: Can persons be accident-like?

But consider the following thoughts: (a) if naturalism is true, then the best theory of personal identity will be a memory-based theory, (b) programs can seamlessly move between processors and even between computers, and (c) accident-like entities cannot move between substances. To me, these thoughts suggest that if naturalism holds, persons can't be accident-like, unless appearances are deceiving and moving from one body to another, or one computer to another, wouldn't involve a movement between substances. But the only way this could be is if the persons are accidents of some grand global substances, like the Cosmos, or Spacetime, or the Fields of a unified field theory.

Thus, assuming an ontology that has only substances and accident-like entities, the conclusion I draw is that if naturalism holds of persons, we are all modes (to use Spinozostic terminology) of one or more global substances. I doubt that on a sparse theory of properties and relations there will be enough modes to do the job. So the ontology will have to be one on which there are one or more global substances, of which everything else is a mode, and the modes are abundant. Moreover, since we have properties, this ontology will have to be one on which accident-like entities can be nested. I suspect that abundance will cause Unger-like problems with identifying who exactly we are, but I would like to have a better argument against such a Spinozistic ontology.

So this is where I am at right now in the argument: either some non-naturalistic account of persons is true, or a Spinozistic naturalistic ontology of one or more global substances, with nestable modes, probably abundant, holds. Of course I am convinced that the Spinozistic account is false (if only for ethical reasons: it doesn't do justice to the ethical importance of the body), but it would be nice to have a good ontological arguemnt here. With some modal imagination we might make progress: for instance we might think that even if in fact such an ontology holds, surely it would be possible to have persons apart from such an ontology, and this is enough to sink the naturalistic account. But I would rather not rely on modal imagination.

There is a lot of detail here that can be questioned. But the basic idea is, I think, sound: further progress on the question of whether the existence of persons is compatible with naturalism is going to be a matter not just of metaphysica specialis but of metaphysica generalis (i.e., of ontology).

The cause has at least the reality of the effect

A traditional staple of cosmological arguments is that at some point after one has established that there is a First Cause, one applies the Reality Principle (RP): If C is the cause of E, then C has at least the reality of the effect. If true, the RP is very helpful. Since among the things caused are intelligent beings, we immediately conclude that the First Cause has at least intelligence, i.e., has intelligence or some attribute greater than intelligence. This helps with the Gap Problem—the problem of showing that the First Cause is appropriately identified as God.

Aquinas, Descartes and Clarke all use a version of the RP in at least one of their respective arguments. Aquinas and Descartes, as far as I know, give no argument. Clarke gives arguments (see p. 49ff), but they are not very plausible to those not already persuaded. The basic intuition behind the RP is either that one cannot give what one does not have (Clarke, ibid.) or that the cause must be relevantly like the effect (Freddoso, email communication). I think there is something to the intuition but don't at present have a better argument.

Note that the RP would make emergentism quite implausible. So figuring out whether the RP is true would advance the discussion in areas other than natural theology.

Age and time

Say that an entity E has age T at t if and only if E began to exist exactly at t-T[note 1] Observe that the age of an entity can be positive, zero, or negative. What kind of property of E is the having of a particular age?

Here is the problem. An entity continues to change in respect of age even when it no longer exists. But when an entity does not exist, the only change it can engage in is pure Cambridge change—the sort of "change" that Napoleon "experiences" when he changes from not being thought about by the Duke of Wellington or Bill Clinton to being thought about. I will assume that the age is the same kind of property during a substance's lifetime as afterwards.[note 2]

Now, Cambridge change is in the end grounded in something else undergoing non-Cambridge change. The Duke of Wellington or Bill Clinton change from not thinking to thinking about Napoleon, and thus Napoleon "changes" from being not thought about by them to being thought about by them. So the change in the age of an entity must be grounded in an something else's undergoing a genuine, non-Cambridge change. But what is that something else? And what does that something else change in respect of?

One intuitive thing to say is that "the time changes". E comes to have age T when the time changes from not being equal to t₀+T, where t₀ is the time E first came to exist, to being equal to t₀+T. But what kind of a change is that? Time surely isn't literally some enduring entity that has a succession of temporal properties like "being noon", "being 3pm", etc. Maybe what we want to say is that reality itself or the cosmos changes in respect of time: it changes from being such that it is not t₀+T to its being such that it is t₀+T.

Suppose that our ontology includes moments of time, and that if t is a moment of time, then t exists at t and only at t. We can then say that the age of E changes to T precisely when reality changes so as to include the moment t₀+T. If our ontology does not include moments of time, but, say, is relational, we may need to do some more work, but I do not see any obvious in-principle bar to defining the time.

We now have a seemingly well-defined property of age, defined in terms of reality's inclusion of a particular moment of time. Now, here is an oddity. This property of age can be equally well defined on a B-theory as on an A-theory. Indeed, I alluded to nothing A-theoretical in the account. A first consequence—Dean Zimmerman has a paper that among many other interesting things says something like this—is that it won't do to define the difference between the A- and B-theories in terms of the objective futurity, presentness and pastness of events, since such properties can be defined in terms of age, and both the A- and B-theories can define the property of age, and the definition seems mind-independent. Nor will it do to define the distinction between the A-theory and the B-theory in terms of an A-theorist's being committed to age being a non-Cambridge property. For the above argument shows that age is a Cambridge property (and by the same token, so are futurity, presentness and pastness), so it would be grossly unfair to the A-theorist thus to define the A-theory. A third consequence is that a reductio, like McTaggart's, of the very idea of futurity, presentness and pastness properties is apt to equally attack the B-theory as the A-theory, since both the B-theory and the A-theory can define such properties.

How, then, to define the A-theory, if not in terms of objective futurity, presentness and pastness of events? I see only one way at present: in terms of the idea that propositions change in truth value. The A-theorist, then, is one who gives up on the eternity of truth: p can be true at t₀ but false at t₁. This Aristotelian theory of propositions is, I think, false (on this theory, tomorrow I will no longer believe the same things as I believed today about my actions from today, even in cases where I have not forgotten these actions), but it is not clearly absurd.

Induction and the A-theory

According to the A-theory of time, there is an objective difference between past, present and future. What the difference consists in depends on the particular A-theory one has. The growing block theorist thinks the difference is that there are no future events, but there are past and present ones. The presentist thinks there are no past and future events, but there are present ones. The spotlighter thinks that one moment, the present one, has a special property of presentness (it is in the moving temporal spotlight).

I will argue that the A-theory decreases the strength of many simple inductive inferences in a way that is implausible. Suppose I engage in simple induction. I observe many ravens. They all are black. I am then asked about Smitty, a raven whose color I have not yet observed. I say he's black. This inductive inference presupposes that the observed sample was not biased in some significant way. But suppose now that I knew that the unobserved raven had some natural property P that the observed ravens do not have. Unless P were the property of being unobserved or something like it (the strength of inductive inference in general already takes this difference into account), or unless we had evidence that the possession of P is irrelevant to properties like blackness, this would weaken the inference. Suppose, for instance, all the ravens I observed were male, and the unobserved raven were female. I would have good reason to take the inference to be significantly weaker in this case. Moreover, the more "significant" the property P, the more it weakens the simple induction.

Now, consider two special cases of induction: induction from past events to present or future events. Our observed sample consists of a set of past events. For instance, we've observed strikings of matches, and noted that they are all followed by the match's bursting into flame. We are told (Case 1) that George will strike a match, or (Case 2) that he is now striking one. How strongly should we expect that the match will burst into flame?

If the A-theory is true, then George's striking the match is significantly different from the observed strikings. The observed strikings were all past. George's striking is future or present. This is a particularly significant difference on Case 1 for growing block theories, on which the observed strikings fall within the realm of the real while George's striking does not, and on Case 2 for presentists, on which the observed strikings fall outside the realm of the real while the George's striking is real. On these two theories, this is even more significant a difference than finding out that the unobserved raven was of a different sex from the observed ones, because there is an ontological difference between the observed strikings and the unobserved one.

Note that this temporal difference between the observed cases and the unobserved one here is not a general difference of a sort that induction automatically takes into account, such as the bare difference between observed and unobserved. It is quite possible to do induction based on past observed events and draw a conclusion about an unobserved past event, and that kind of inductive inference will be unaffected by this argument. So this is not a general sceptical argument. Moreover, the argument simply makes use of a principle—viz., that disanalogies between observed and unobserved cases weaken inductive inferences—that is intrinsic to inductive practice, rather than making use of any sceptical hypotheses.

Could one argue that the temporal difference is one that we know is insignificant vis-à-vis induction? If the unobserved raven had an even number of feathers and the observed ones all had an odd number of feathers, we wouldn't take this to weaken the induction, particularly in light of the fact that we know that the parity of the number of feathers changes faster in birds than their color (they keep on losing feathers). Some properties, we know, are insignificant. Is the temporal difference like that?

If it is, the onus is on the A-theorist who wants to keep past-present and past-future induction unweakened to show that it is. I do not know of any good a priori arguments here. Could we know this inductively? I think not. For consider what an inductive argument would look like. Maybe it would say: "We have found in the past that inductive inferences from past to future or present were just as likely to succeed as inductive inferences from past to past, so we should conclude that inductive inferences from past to future or present are just as likely to succeed as inductive inferences from past to past." But this inductive argument would be precisely an instance of those inferences whose force is weakened by my argument. So even if this inductive inference weakens my weakening, inductive arguments from past to present/future will still be weaker than ones from past to past.

If this argument works, it shows that if A-theory holds, then induction from past to present or past to future is significantly weaker than induction from past to past. But our inductive practices do not take into account any such difference. If our inductive practices are nonetheless correct, then the A-theory is false.

All this is particularly problematic on presentism for the following reason. One way to understand presentism is to say that the most basic propositions are propositions about the present. However, we have two modal operators (actually a continuous family of them describing different degrees of pastness and futurity, but I will neglect this for simplicity), "Pastly" and "Futurely", which shift the proposition's tense (as it were: strictly speaking, tense is linguistic rather than propositional). Now in inductive reasoning from past to past, we reason from claims that start with a "Pastly" modal operator to ones that also have it. This is unproblematic. But to reason inductively from claims that start with a "Pastly" modal operator to ones that have no such modal operator or that start with a "Futurely" modal operator is very fishy. The modal operators "Pastly" and "Futurely" for the presentist are like the modal operators "In a novel" and "Possibly"—they are potentially truth-canceling (something that holds pastly, futurely, in a novel or possibly need not hold). But to make inductive inferences from what happens possibly to what happens actually, or from what happens in a novel to what happens in the real world, or from what happens possibly to what happens in a novel, or even from what happens in a novel to what happens possibly, is dangerous. (The last is the safest, except when one is dealing with time-travel novels.)

Circular lives and time travel

1. Necessarily, having the same kind of genuine bliss for an infinite amount of time is intrinsically better for one than having it for a finite amount of time. (Premise)
2. Leading a genuinely blissful life over a temporal circle that wraps around from t₀ to t₁ (you have a blissful life from t₀ to t₁, and time wraps around so that t₁ is actually the same as t₀) would be intrinsically just as good as living out an eternal recurrence of a genuinely blissful life of the same kind and length as the temporally circular life. (Premise)
3. If both of the scenarios in (2) are possible, then (1) is violated. (Premise)
4. The scenario of an eternal recurrence of a blissful life is possible. (Premise)
5. The scenario of a life arranged on a temporal circle is impossible. (By (1)-(4))
6. If a circular life is possible, so is a blissful circular life. (Premise)
7. Therefore, a circular life is impossible. (By (5) and (6))
8. If circular time is possible, so is a circular life. (Premise)
9. Therefore, circular time is impossible. (By (7) and (8))
10. If time travel is possible, so is a circular life. (Premise)
11. Therefore, time travel is impossible. (By (7) and (10))

In (2), the life of infinite recurrence is the circular life "unwrapped". I am open to the possibility that (2) in the argument is false, and that it is due to the "infinitely many times around" misapprehension of what circular time would be. It could also be that experiencing the same kind of bliss twice is no better than experiencing it once. I am also open the possibility that (8) is false—maybe there can be circular time, but lives of persons might not be circularly arrangeable. Likewise, I am not that sure of (10).

In any case, the thought experiment embodied in (2) seems worth thinking about. As you approach t₁, you become more and more like you were at t₀, and then, lo and behold, t₁ is t₀. If I lived on a circular time, I would never be facing death. Yet my life would be finite. It would not only be finite in the objective way of a life of someone whose functions got faster and faster, thereby ensuring that over a finite span of objective time he accomplished a life that was of infinite subjective span (i.e., a super-task life), but the circular life would be a life that has only a finite subjective span, though no beginning or end.

Psychological identity and faster than light causation

In 2010, data from your brain is scanned and recorded in duplicate on two hard drives, while the original is destroyed. One hard drive is sent off to a station in orbit in the alpha-Centauri system, and it arrives there within ten years. The other remains on earth, in a special vault. An automated process in the vault is guaranteed to grow a new brain in 2050, and imprint the saved data on that brain. If that is the whole story, then according to materialist psychological identity theorists who ground personal identity in chains of (quasi-)memories, you will thereby be resurrected.

But now consider this oddity. Suppose that at the same time (in respect of some reference frame—it shouldn't matter which one), the scientists on the station around alpha-Centauri happen to grow a brain and imprint your data on it. Then you have undergone fission: there are two copies of you. The standard resolution of fission cases is to say that you then do not exist—all the other options are more absurd. This means that the scientists on the station have it within their power to prevent your being resurrected on earth, simply by imprinting your data on a brain at the same time as the machines on earth are doing so. And this ability of theirs is not limited by the speed of light. In fact, in some reference frames it will be true to say that because they imprinted your data on a brain shortly after the vault on earth has done its work, you weren't resurrected in the vault on earth (but instead were the victim of fission). This may well seem absurd.

The scientists near alpha-Centauri, then, have counterfactual control over whether you're resurrected on earth. Is this counterfactual control a form of causal control? Well, on theories of causation on which counterfactual dependence between wholly distinct events (the scientists' pushing of buttons is wholly distinct from your resurrection, it seems) entails causation, the answer will be affirmative. So, materialist psychological identity theorists who accept accounts of causation like that seem to have to admit that faster than light causation is physically possible (I say "physically", because no part of my story seems to violate any law of nature).

Substance and intrinsic properties

A standard necessary condition for a property P of a substance x to be intrinsic is the loneliness condition: x could have P without anything other than x existing. There is good reason to doubt the necessity of this condition. For if the condition holds, and if there is a contingent substance that has an intrinsic property, then (a) there are no necessarily existing substances (like God), and (b) the principle that, necessarily, every contingent substance is caused to exist by a substance is false. It is implausible that a mere account of intrinsicness should immediately have such consequences.

Here, however, is a simple replacement for the loneliness condition: a substance x has P (where "P" is a name of a property, not a definite description of a property) intrinsically only if the truthmaker of the proposition that x has P does not involve any substances other than x. To explicate this further, one needs to say something about what it is for a truthmaker to "involve" y. Since all I'm trying to give is a necessary condition on intrinsicness, all I need to do is give some sufficient conditions for involvement. Here are three:

1. If y is a part of the truthmaker of p, then the truthmaker of p involves y.
2. If y's having Q is a part of the truthmaker of p, then the truthmaker of p involves y.
3. If x's standing to y in R is a part of the truthmaker of p, then the truthmaker of p involves y.

Love of truth

You are a philosophical researcher who has concluded that the only four metaethical positions that have any serious plausibility are nihilism, Natural Law, Kantianism and utilitarianism. You plan to devote the rest of your life to figuring out which of these four theories is correct. But God speaks to you—and you know it's God speaking—and makes you an offer. First he tells you that you're right that the correct metaethical theory is one of the four you listed. But you must now choose between two options:

1. You continue on your career as before, and God makes no guarantee whether you'll come to an answer, and whether, should you come to an answer, the answer will be correct.
2. God will tell you which of the four theories is true, and will do so in such a way that you will know that it is God speaking, but the price you will have to pay is that you will lose the creative abilities that are necessary for good philosophical research. Nonetheless, God promises to ensure you will still be able to teach philosophy in a way that is just as beneficial to students and both renumerative and satisfying to yourself.

Never mind the epistemological question of how you know it's God speaking and how you will know the answer is from God. What should you do?

On the face of it, this is a question whether you love truth more than the search for truth, and my own gut reaction to a question like this is to say: "I want to know the truth, and I don't care about the means by which I get it (except insofar as I am a sinful and vain man, who wants to get it by his own power, but this sinful desire is one that I do not endorse)."

But this gut reaction is simplistic. Aquinas distinguishes faith from science (which includes philosophy, of course, in his terminology) as follows: faith gives one certainty of the truth, but science also gives one understanding of why something is so. Faith ensures that we know with greater certainty that God is a Trinity than we know that the planets move in approximately elliptical orbits; but while our knowledge that God is a Trinity is more certain, we have better understanding of the ellipticity of the orbits—we can say something about why the orbits are elliptical (something about the curvature of space or the law of gravitation). There are pluses and minuses of knowing by faith versus knowing by science: certainty versus understanding.

In choosing option (1), one may never get the right answer; however, one may also get the right answer plus an understanding of why it is the right answer. Option (2) gives one a certainty of knowing the right answer, but it is less likely that one will know why it is the right answer, because one will have lost the creative abilities needed to find that out. It seems, then, that there are incommensurable goods involved in the two options. It may be that both choices are rational.

But suppose now that the offer is different. Option (1) is as before. But in the case of option (2), God will not take away one's philosophical abilities—one will still be free to try to find out why the given metaethical theory is true. While one might worry that knowing the answer ahead of time will make one less good at figuring out the why question (e.g., more apt to glibly accept arguments for the answer one already knows is right), this does not seem to me to be a compelling worry. Barring that worry, it seems that the modified version of option (2) is what one should choose. To fail to opt for option (2) is likely to care more about searching for truth than about having truth, and that, I think, is to have one's priorities backwards.

If this is right, then likewise those philosophers who also know various doctrines by faith need not be shy about making use of this knowledge, about drawing out the entailments of this knowledge. I might work dozens of years trying to figure out if there is such a thing as substance, and fail. But significantly less effort might yield the conclusion that there is substance based on the my knowledge that transsubstantiation occurs (even there, some non-trivial philosophical work is needed to rule out non-substantival accounts of transsubstantiation). And to fail to make use of that knowledge, and instead to search for years, could be a case of loving philosophy more than truth. Of course some will dispute whether we have knowledge by revelation. Here I take my stance by faith: I believe (on the authority of the First Vatican Council, for instance) that faith yields knowledge and proper certainty. (I also have some philosophical stories about how this might happen.)

A non-vicious circle in the order of explanation

Say that p is prior to q in the order of explanation provided that p enters into some explanation of q. One might think that a circle in the order of explanation is impossible. (Some background: Robert M. Adams has once constructed an elegant argument against Molinism that, among other premises, assumed that there were no circles in the order of explanation. William Lane Craig, however, has responded by arguing that circles in the order of explanation are quite possible, but the examples of his that I've seen I've found unconvincing.)

Suppose I promise that if this year you make a donation either to CRS or Caritas of Waco, I will this year make a donation to CRS. You make a donation to Caritas. I thus make a donation to CRS. This example inspires you, and you respond with a donation to CRS yourself. Let p be the proposition that you made a donation to CRS or Caritas. Let q be the proposition that I made a donation to CRS. Let r be the proposition that you made a donation to CRS. Then, p helps explain q, and q helps explain r. But r is a disjunct in p, so it seems q helps explain p. Thus, it seems, p is explanatorily prior to q and q is explanatorily prior to p.

Is this a good argument? I am not so sure. One problem is that the thesis that the truth of a disjunct a explains the truth of a disjunction a-or-b may not be true when a is itself explained by b.

But suppose one accepts the example. Is there still a way of capturing the intuition behind the idea that there can't be circular explanations? I think so, but it will take some hard work. And that I want to leave for another post.

Note, also, that the above example fits with a principle I've defended that if there is a circle of explanations, then the circle also has an explanation from beyond the circle. (If this principle is true, then Adams can probably regroup and defend his anti-Molinist argument.) In this case, your initial choice to make a donation to Caritas together with my promise are an explanation for the circle.

... is the set of ...

The locution "...is the set of..." occurs all over philosophy (2365 times in JSTOR's philosophy collection). Sometimes the phrase is used innocently to introduce a stipulation, to draw out the consequences of a stipulation or as part of the philosophy of mathematics. But some uses are far from innocent. The non-innocent uses I want to focus on are ones in metaphysics where something non-mathematical and non-stipulative is identified with a certain kind of set. An example is David Lewis's identification of a property with the set of the possible objects that exemplify it. There is also a whole slew of examples that use the related locution "...is a function from...to..." (a function is, after all, a certain kind of set): thus, some take the meaning of a sentence to be a function from situations or worlds to truth values.

Such non-innocent identifications of things with sets (and, as a special case, with functions) are almost certain to be false. My first argument is very simple. A set is any (necessarily?) existing object that, together with other objects and a member-of relation, satisfies the axioms of set theory. The set of F's is the set to which all and only F's stand in the member-of relation. But if there is one collection of objects and member-of relation that satisfies the axioms of set theory, there are infinitely many such. With a perverse member-of relation, we can identify any necessarily existing entity as the set of F's. Let o be the number 7 or any other necessarily existing entity (for the sake of the argument, I assume there are sets and that they exist necessarily). Then we can take o to be the set of all possible hot objects, just by reinterpreting the initial member-of relation into another relation, say member*-of, that still satisfies the axioms of set theory. (The sun will then be a member* of o.) So we can't take seriously the idea that "the" set of all possible hot objects is the property of hotness if we think there is non-stipulatively such a thing as the property of hotness.

Unless there is a privileged interpretation of set theory, such identifications simply have no hope. But do we really have reason to suppose there is a privileged interpretation of set theory? I doubt it. I don't have an argument here, just a strong intuition.

But even if there were a privileged interpretation of set theory, anything that one might identify with a set can be equally well identified with some other set. For instance, instead of taking a property as a set of possible objects having that property, one might take it as the set of possible objects lacking that property. All the theoretical benefits are still there. Granted, Lewis's approach might be slightly simpler. But a slight difference in complexity does not justify a strong epistemic reason to believe one theory rather than another. So one's reason for believing Lewis's theory over this competitor will be weak. But there will be many such competitors. (Here is one that seems quite natural: a property is a function f from the set of all possible objects to the set {0,1}, where f(x)=1 iff x has the property.) One's reason for believing Lewis's variant to be true will be low. Moreover, it just seems somehow unlikely that of these variants one would actually be right in an objective sense.

This argument is even more obvious when we look at the idea of identifying meanings with functions. A function f from a set S to a set T is a set of ordered pairs <x,y> where x is in S and y is in T, satisfying the condition that each member of S appears in the first place in exactly one pair in the set. But we can equally well define a function* f from a set S to a set T to be a set of ordered pairs <y,x> where x is in S and y is in T, satisfying the condition that each member of S appears in the second place in exactly one pair in the set. Any reason to think a meaning is a function can be turned into an equally good reason to think a meaning is a function*. And, besides, there is more than one way to define an ordered pair <x,y>.

At the same time, what I said is in an important way unfair to Lewis and others. For a charitable reading (supported by things that Lewis actually says) of claims like "a property is a set of possible objects" is that the writer does not actually believe in properties. Rather, he means that all the work that property-talk does in our language can be equally done by set-of-possible-objects-talk. And that claim is immune to my criticisms. However, it is important to note that this claim either has no metaphysical consequences (after all, any work that talk of elephants does in our language can be equally well done by talk of ordered pairs of the form <7, e>, where e is an elephant, with some modifications of the rest of the sentences, but this does not mean elephants are ordered pairs, pace indeterminacy of translation claims) or else is tantamount to a denial of the real existence of properties. Not that there is anything obviously wrong with the latter. But what would be very bad would be to take the claim to give a realist metaphysics of properties.

Species, biological and metaphysical

The concept of a species is quite important to an Aristotelian metaphysics. All the members of an Aristotelian species have qualitatively exactly the same nature. But it is difficult to figure out exactly which individuals are conspecific in this metaphysical sense.

It would be mistaken to think that metaphysical species are always co-extensive with biological ones. Biological species are defined in terms of populations that exhibit gene interchange. Thus, some biologists think there are six giraffe species. Suppose this hypothesis is right—if it's not right of giraffes, there will be some related case where it will be right. In nature, these different putative species of giraffes do not appear to interbreed, though in captivity they apparently do. If we thought metaphysical species to be coextensive with biological ones, we would have to answer tough questions about the offspring of different giraffe species. Suppose that the father is of metaphysical species A and the mother of metaphysical species B. Then any reason to think the offspring to be a metaphysical conspecific of the father is a reason to think it to be a conspecific of the mother, and these reasons seem to cancel out. So it seems better to suppose the offspring to be a member of a third metaphysical species. But if so, then with six species of giraffes, we could get up to 18 or maybe even 36 offspring metaphysical species. And when those bred, the metaphysical species would seem to keep on multiplying. This seems excessive, and so it seems better to suppose that, whatever the biologists say, the different giraffes are all members of one metaphysical species.

But all this reasoning strikes me as seriously ad hoc. If different biological giraffe species are metaphysically one species, why stop there? Why not suppose that all the members of the biological family Giraffidae, including giraffes and okapis, are one biological species?

It is not clear whether this is a metaphysical or an epistemological question. It might be that if we were clear enough on what metaphysical species are, we would make some progress here. On the other hand, people not sympathetic to Aristotelian metaphysics will take these difficulties as significant arguments against Aristotelianism.

I suspect that the answer here has a lot to do with teleology and the notion of normalcy. The Aristotelian nature encodes or defines how an organism ought to be, what its normal arrangement of parts is, what behavior is normal to it. Perhaps on the epistemological side, one can make a move here rather like that which David Lewis makes in regard to laws of nature. The metaphysical species provide a level of classification that offers the best balance between simplicity of normative description and richness of normative implications. If the metaphysical species included both giraffes and okapis, then the common nature would have to encode many conditional normative claims such as: if the individual has such-and-such features, then it should have a short neck, but if the individual has such-and-such features, then it should have a long neck. On the other hand, if giraffes and okapis are separate species, then we get a classification system with greater simplicity—the giraffe nature encodes having a long neck with no complicated conditionals, and the okapi nature encodes having a short neck again with no complicated conditionals.

How, then, do we know male and female giraffes to be members of one species? Because just about all the normative properties of males and females are the same, and we get a simpler classification system that just includes conditionals like if the individual has such-and-such features, then it should have ovaries, but doesn't reduplicate other normative claims.

But what about species, like Osedax worms, where male and female individuals seem to be very different? Maybe we Aristotelians just have to say that the balance of simplicity and richness account is only epistemic, and in this case is trumped by an analogical argument from other metaphysical species in which males and females are more easily seen as members of the same metaphysical species.

Two accounts of lying

There are two accounts of lying. If one asks a child, one will likely hear that to lie is to say something that isn't true, and the child is likely to count any statement she thinks is false as a lie. Adults do this, too, but reflective adults tend to grow out of this, and see a lie as a statement that the speaker takes to be false. On this more sophisticated view, a lie is opposed to sincerity, not truth. If one is mistaken about the truth, One can lie and say the truth, or one can speak falsely and not lie.

I think the more mature account is probably truer to the English word "lie". But the interesting question isn't about linguistics, but about ethics: The question is whether what morality in the first instance forbids (whether absolutely or prima facie—I think absolutely) is insincere speech or false speech.

I want to argue that what is forbidden in the first instance is false-telling. The obvious objection, of course, is that (a) one is innocent if one is convinced that the falsehood one tells is true, and (b) one is guilty if the truth one tells is something one believes to be false.

This objection, however, is one that the defender of the false-telling theory can easily handle. First, consider (b). If it is wrong to do A, it is wrong to do what one takes to be the doing of A. The person speaking a truth and believing it to be false takes herself to be speaking a falsehood, and hence she acts wrongly.

It is not obvious that claim (a) is actually correct. If I believe a falsehood p, but I have no right (moral or epistemic, say) to believe p, it is not clear that I am excused for affirming p. It is a merit of the false-telling theory that it draws one's attention to this. In any case, the false-telling theorist can say that when one sincerely affirms a falsehood p, and one has the right to believe p, then one is not culpable, though one has acted wrongly. One is like the person who handed out poison at the party, believing it to be water—it is wrong to hand out poison, but one is not culpable if one was not reasonably expected to know that it's poison.

The false-telling account has the advantage that it situates the paradigmatic case of lying as an offence against truth, rather than against sincerity, and that seems right. Moreover, it appropriately parallels the prohibition against lying with the prohibition against promise-breaking and similar objective moral rules. What is forbidden (at least prima facie) is to fail to do what one has promised. A person who thinks she is acting contrary to a promise is, of course, acting viciously, but she is not breaking her promise—she merely thinks she is, though in doing what she thinks is a breaking of a promise she does wrong. If one has fulfilled a promise without knowing one has done so, one is off the hook as far as the promise goes. And if one has innocently forgotten a promise, say due to amnesia, then one still has gone against the promise and acted wrongly, but one is not culpable. We would say the same thing about adultery. What is forbidden in the first instance is for a married person to engage in sexual relations with a non-spouse. It would be odd indeed to say that what is in the first instance forbidden is sexual relations with someone one takes to be a non-spouse.[note 1]

On an account on which what is in the first instance wrong about lying is insincerity, we need to posit an additional duty, the duty to ensure that what one speaks is not only sincere but sufficiently investigated by the speaker. To speak when one has made insufficient investigation of the matter on which one speaks is not a lie, but is nonetheless wrong, since in speaking one invites trust. But on the false-telling account, the duty to investigate the relevant matters follows from the general duty to make sure in all our actions that we have sufficiently investigated whether the action isn't wrong. For if what is wrong is the telling of a falsehood, then one must sufficiently investigate to ensure that one isn't unknowingly doing that, and this one does by investigating whether the matter is true or false. The false-telling account, thus, neatly fits with the idea that by speaking we put our authority behind something, inviting others to trust us—and we should only put our authority behind the truth.

I also think the false-telling account fits better with Example 1 in this older post.

On the other hand, the false-telling account of the wrongness of lying has the counterintuitive consequence that when we make a mistake, we have done wrong. Here I am willing to bite the bullet. In speaking falsely, I have said what was not to be said. If one thinks, as I do, that there is only one form of normativity, it is plausible that a moral misdeed was done here. One might try to press this harder—does the student who makes a mistake on an exam do morally wrong (assuming she studied hard enough)? Here, I could bite the bullet, but one might also question (I got this idea from one of our grad students in a different context) whether one makes assertions on exams.

A final reflection. It seems that if I am right, then personal virtue/vice here tracks not whether one has acted objectively rightly/wrongly, but whether one is subjectively praiseworthy/culpable. The person who speaks sincerely (at least if after sufficient investigation) is the honest person, and the insincere person is the dishonest one. That virtue/vice doesn't track right/wrong may seem implausible, at least to virtue ethicists. But the cases of promises and adultery suggest that this is indeed so—virtue does not seem to be lost in failing to keep a promise when you honestly think you've kept it but have innocently mistaken the terms of it, or by committing adultery with someone one believes to be one's long-lost spouse but who is in fact an impostor. (Nonetheless, there will likely be some trauma to the virtuous agent once she finds out what she did, and this might cause moral damage.) If I am right here, then virtue ethicists would be mistaken to try to derive rightness/wrongness facts from virtue facts.

Frankfurt and free will

Here is a version of the Principle of Alternate Possibility that is immune to all of Frankfurt's counterexamples:

If x freely does A and Mr Black is nowhere near, x could have refrained from doing A.

An approach to the Sleeping Beauty problem

Experiment 1:
A fair coin is flipped on Sunday, without you seeing the result, and then you go to sleep.
Tails: You get woken up Monday and Tuesday and each time shown a red flag. Your memory is erased each time, and you don't know whether it's Monday or Tuesday when you wake up.
Heads: You get woken up Monday and shown a red flag.
So, you're awake and see a red flag. What probability should you assign to heads? The two most common options are 1/2 and 1/3.

Experiment 1 is equivalent to the Sleeping Beauty problem, with a red flag added, which changes nothing.

Experiment 2:
Same as Experiment 1, except that on heads, you get woken up on both Monday and Tuesday, but on Tuesday you see a white flag.

It seems clear to me that in Experiment 2 you should assign 1/3 to heads. It's a standard Bayesian thing—you start with 1/2, and update on the additional information of a red flag: given heads, the chance of a red flag is 1/2, and given tails, the chance of a red flag is 1, so the red flag is evidence for tails, and the numbers work out to a probability 1/3 for heads.

I now claim that you should give the same answer for both experiments. This implies you should assign 1/3 to heads on Experiment 1.

Two arguments for equivalence. First, we can imagine a continuum of cases between Experiments 1 and 2, where the amount of awareness you have on Tuesday given heads varies continuously from zero (Experiment 2) to full human awareness (Experiment 1). Where exactly you would be on this spectrum on a white flag Tuesday does not seem to me to affect what credence is rational when you see a red flag and are fully humanly conscious.

Second argument. You can imagine that you're not told ahead of time whether you're in Experiment 1 or 2, but when you wake up and see a red flag you can press a button that you know has the following effect. If the coin was tails, the button has no effect. If the coin was heads, in which case it's Monday (since on Tuesday you don't see a red flag, if you're awake at all), and you press the button, then you'll wake up on Tuesday and see a white flag; if you don't press the button, you won't wake up on Tuesday in that case.

If you press the button, you're effectively in Experiment 2. If you don't, you're effectively in Experiment 1. If different credences of tails are appropriate in the two experiments, then how you decide about the button press after the coin toss affects what credence you should assign to tails. That's weird. (Is there a better choice of button press, one that will provide me with a better credence?)

Variant on second argument: You either do or do not see an independent random process depress the button when you wake up—you don't control the button. Should the outcome of this random process affect your credence about the initial coin toss? Certainly not: the outcome of this process is ex hypothesi independent of everything else. So, you should assign the same credence to tails in Experiments 1 and 2, and this credence should be tails.

I've been told that the claim that 1/3 is the right answer for Experiment 2 would be controversial. If so, then the argument only shows the credence is the same in the two cases, not that it's 1/3. But I think 1/3 is the right answer for Experiment 2.

Morality and Relativity Theory

Einstein tells us that basic laws of physics should be invariant under change of reference frame. Is the same true of basic laws of morality? What would that mean? I think it would mean that any law of morality which is not invariant under change of reference frame can only be a consequence of a more general moral law that is invariant together with some conditions explaining why, contingently, things are arranged in some particular manner in space-time as to give rise to the non-invariant law. (Similarly, the non-invariant law about dropped objects near the earth moving in the direction of the center of the earth follows from an invariant Einsteinian law together with contingent facts about how matter is distributed in our vicinity.)

Could this abstract observation have any actual consequences? Suppose Georgina believes that when she works unowned land, by natural law the land becomes hers (cf. Locke), and by natural law she gains mineral rights to what is below the surface of the land she has worked. That doesn't seem right. What counts as being "below the surface of the land she has worked" depends on the reference frame. So it can't just be a basic moral law that one gets whatever unowned stuff is below where one worked. A story must be given explaining the lack of invariance. And probably the easiest way to do this is to say that if there is any such acquisition of mineral rights, it comes from a non-invariant positive law. This isn't very interesting, since I assume we knew that there is no natural acquisition of mineral rights.

There could, however, be some slightly more interesting consequences in other areas. For instance, in sexual ethics, it follows that considerations based on the shapes of organs, as well as ones based on inside-outside distinctions (what is in one reference frame a cup that is red on the outside, green on the inside, with juice within is in another reference frame a cup-shaped object that is green on the outside, red on the inside, with juice adhering to the outside due to odd gravitational fields), should not be of basic relevance, absent some further story. Instead, basic moral rules about sexuality should involve reference-frame invariant concepts such as contact, causation, teleology, intention, and consent. This is helpful—it focuses the philosopher's mind on what the morally relevant features of the activities are. (I've used this in a comment to argue that the use of condoms to prevent HIV transmission within a married couple is unacceptable within a Catholic sexual ethics.)

Magic and Humean theories of causation

Humean theories of causation make causal facts supervene on facts about correlations between events. The simplest theory was Hume's: A causes B if and only if A type events always cause B type events. Perhaps the best contemporary version is Lewis's: (1) the laws of nature are true propositions which optimize a balance of brevity and informativeness; (2) similarity of worlds is defined in large part by local sameness of law; (3) counterfactuals are defined in terms of similarity of worlds; and (4) causation is defined in terms of counterfactuals.

I claim that if Humean theories of causation are true, then I have a magical power—the power of causing events in another galaxy just by muttering incantations. Let's suppose that the Andromeda Galaxy contains a billions of intelligent aliens, whom I shall call Andromedans, who are going to have a long and exceedingly complex political future, but a finite future with a finite description of it being possible. The events I can magically cause are the political activities of the Andromedans. (If Andromeda has no intelligent life, I can modify the example.) I now claim that if Humean theories of causation are true, there is a long incantation that has the following two properties: (a) it is physically possible for me to chant it, and (b) if I chanted it, the chant would be the cause of every major political event among the Andromedans from now until the end of Andromedan history. If that's not enough to establish I have a magical power, I don't know what is.

Now my argument. There are infinitely many incantations that it is possible for an analog being like me to chant. Fine details of the tone, timbre, etc., of an incantation can be used to encode information. It is easy to come up with very simple ways of encoding information in a chanted incantation, and still keep the incantation within my physical powers. Let Q be a detailed and correct description of the political future of the Andromedans in a simple and straightforward language L. Then, Q is a very, very long but finite text. However long Q is, we can encode it with a simple encoding scheme into an incantation I that it is physically possible for me to chant. (I don't mean I know how to intentionally chant it; but it is possible for me to chant it, perhaps by accident.)

Let w be a world as much like ours as we can make it but where I chant I. What would w be like? Well, presumably, all the Andromedan events described in Q would still happen in w. However, in I, these events would be foreshadowed by being encoded in I. If there are enough of these events (that's why I assumed that the Andromedans will have a long and exceedingly complex political future; moreover, to ensure that there are enough events, I need only be sufficiently detailed in Q), then this correlation will be one that the Humean will have to take cognizance of and make be a part of the laws—making it be a part of the laws does increase the complexity of the laws, but the gain in informativeness is worth it. So, in w, there will be a Humean law about the correlation between aspects of I and aspects of the Andromedan political future. Moreover, on Humean views, this law will support counterfactuals (laws do, of course) and will (on Lewis's view we can insert "therefore" here) be such as to ensure causation between the aspects of I and the Andromedan political events therein described. Hence, in w, I cause the Andromedan events if Humeanism is correct.

Thus, it is physically possible for me to do something, viz., chant I, which is such that were I to do it, I would be causing all Andromedan political events.

And this is absurd. So Humean theories of causation are false.

The twist

Consider the Truth-Teller Paradox:

1. This sentence is true.

You may not think this is a paradox at all. But ask yourself: is (1) true or false? No contradiction arises from either supposition, but it also should become plausible that there is no way of settling the question, and one may start to think that there just is no answer. We could stipulate a truth value, but stipulating a truth value will not give a meaning to the sentence. (I can stipulate that it is true that mimsy were the borogoves, but I have not thereby given the sentence meaning.) The sentence seems to, as it were, pull its content out of itself, and as such has no content. Now maybe you're not convinced by this—maybe you only feel a vague discomfort at (1). So now I apply the twist, by changing (1) slightly to something that is clearly paradoxical:

2. This sentence is false.

That (2) is paradoxical is clear (it's true if and only if it is false). The twist that took us from (1) to (2) made clearer that there is something fishy about the kind of self-dependence that (1) involves.

This kind of twist can be found in other cases. One might be vaguely worried about the set of all sets that contain themselves, and then make the twist and get the clearly paradoxical set of all sets that do not contain themselves. Or one might be worried about the causal loops that time travel would permit, say one's getting the plans for the time machine from one's future self, and then after building the time machine going back in time to hand those plans to one's then-past self. There is something fishy about such a causal loop. So you give it a twist, and you turn it into a clearly paradoxical story about shooting your grandfather before his children are conceived. I think one can argue that in this same way, Thomson's Lamp Paradox is a twist on Zeno's Achilles Paradox, and the Grim Reaper Paradox is a twist on Zeno's Dichotomy.

I wonder if there is anything interesting and general one can say about the logical structure of the twist. (There may be something in the literature.) In particular, I am curious whether one can infer the impossibility of the untwisted situation from the impossibility of the twisted situation.

The Principle of Avoidability of Guilt

(PAG) If the world at t₁ is in a state S₁ sufficient to cause it to be the case that I am guilty at a time t₂>t₁, and no aspect of S₁ is the product of backwards causation, then I am already guilty at t₁. (Note: The state of the world includes my state.)

To be guilty is to be guilty of something. However, I am not claiming here that I am guilty at t₁ of the same things that I will be guilty of at t₂. For instance, at t₁, I might be guilty of getting drunk, while at t₂, I am guilty of killing people with my car.

PAG should be compared the Principle of Alternate Possibility (PAP: if I act freely, I could have acted otherwise). PAG implies that if we are guilty of anything, and our world has no backwards causation, then our world is not causally deterministic. PAG might be compatible with acausal determinism as well as with causal determinism with backwards causation (if there is backwards causation, then my later self could have corrupted my earlier self). PAG captures part of the intuition behind PAP that nothing but ourselves can make us be guilty, that if our character forces us to act wrongly, then either we are not culpable for the wrongful action or we are culpable for having had that character.

Some nice things about PAG:

1. PAG escapes standard Frankfurt examples. The neurosurgeon can make sure that I kill someone, but he can't make sure that I am guilty of killing someone.
2. Defending PAG does not require us to make a distinction between derivatively and non-derivatively free actions, in the way that a defense of PAP may (a derivatively free action is an action which is determined by the agent's state and the character, but the agent is still responsible in virtue of an earlier, libertarian-free choice, which is a non-derivatively free action[note 1]).
3. PAG is clearly compatible with God's being free and unable to do evil, since PAG is only a principle about wrong action.
4. For the same reason, PAG is clearly compatible with the thesis that God's grace makes us act rightly.
5. Notice that we see nothing unjust about rewarding Jane for her courageous deeds even if given her upbringing she couldn't but have acted courageously, while we at least worry about the permissibility of punishing Patrick for his cowardice when given his upbringing he couldn't but have shown cowardice.
6. That we have a particularly strong commitment to something like PAG explains why it is that defenders of PAP tend to gravitate towards using examples involving responsibility for wrongful action instead of responsibility for right action.
7. At the same time, PAG is compatible with the truth of a stronger view that includes not just guilt but also merit, which stronger view may have trouble with God's freedom and grace and the rewarding of virtues that a person didn't have a choice about. So PAG lets us remain open on a number of issues.

How many universes in a multiverse?

Suppose that all universes, or all universes which are "good enough", exist. For any object x, let U_x be a universe which contains exactly one conscious non-divine being, where this being is an angel who spends most of his time thinking virtuously and pleasurable precisely about x. This kind of world is surely "good enough". Thus, it seems there are at least as many universes in the multiverse as there are sets, since for any set S there is a universe U_S. That's not a problem yet—after all, maybe the collection of universes is a proper class. But now for any proper class K, we can imagine the universe U_K. Now the number of universes is really creeping up on us—it seems that we have at least one universe per set or proper class. Maybe we can introduce some higher order way of counting, beyond sets and proper classes. Sure. But the same problem will occur again.

A complication for theistic multiverse theories

On Donald Turner's theistic multiverse theory (recently ably defended by Klaas Kraay), God, out of his perfect goodness, necessary creates all possible universes that are "good enough", i.e., whose value is above a cut-off line, below which a universe is not worth creating. Thus, the world is a multiverse consisting of infinitely many universes. A God who actualized the best possible world can only create such a multiverse. The metaphysics is similar to that of David Lewis, but with only "good enough" worlds there. This gives a lovely answer to the problem of evil: "Ah, you think this universe would be better without evil E? It sure would—and there is another universe, a better one, in existence that lacks E, but it is better that both this universe and the other one should exist, than that just one of the two should. We see what we would expect to see on the theistic multiverse theory, a world with a lot of evil, but still worth creating."

I want to make a bit of trouble for the notion of a universe worth creating: Whether a universe is worth creating can depend on what other universes, if any, there exist.

Imagine a possible universe U that is just around the cut-off line between good-enough and not-quite-good-enough, and which contains a thousand philosophers who care about little but whether the multiverse hypothesis is correct, and who come to a justified[note 1] belief that there is only one universe concretely in existence. Assuming the notion of a cut-off line makes sense, it seems we could imagine that the universe is so close to the cut-off line that whether the universe falls above the cut-off line or below it depends on whether the philosophers' justified belief that there is only one universe concretely in existence is true. If so, then U is worth creating on its own, since then that belief is true, but it is not worth creating as part of a multiverse, since then that belief is false, and U is so close to the cut-off line that having this belief be wrong pushes it below the cut-off line.

So, the notion of the cut-off line is not so clear: whether a universe is below or above the cut-off line can depend on what other universes there are. Moreover, it seems one can have a pair of universes U₁ and U₂ such that each is worth creating as part of a multiverse only if the other is not included in the multiverse, and such that neither of the two is better than the other. If we can have such a pair of universes, then there is no unique optimal multiverse. For there will, presumably, be one possible optimal multiverse (i.e., multiverse than which there is no better) that includes U₁ but not U₂, and another possible optimal multiverse that includes U₂ but not U₁. How to construct such U₁ and U₂? Well, again, suppose that the two universes are marginal—very close to the cut-off line—and what decides whether U₁ is above it or below it is whether the justified beliefs of U₁'s philosophers that U₂ is non-actual are true, and what decides whether U₂ is above it or below it is whether the justified beliefs of U₂'s philosophers that U₁ is non-actual are true.[note 2]

Deep Thoughts VI

Every cause has an effect.

A certain kind of conservative

There is—and if there isn't, we can imagine her—a certain kind of conservative who both likes to have laws prohibiting various kinds of behavior that she takes to be immoral and in the name of freedom believes in a small government and is opposed to much government regulation in business (e.g., minimum wage laws) and other areas of life. The position seems inconsistent or at least ad hoc: she opposes certain kinds of regulation but not others. (It is sometimes said that people like want to have the freedom to do the things they like, but not to give others the freedom to do the things they like, but that is an unkind jibe, for instance because such a person might well want, for the good of her own soul, that the state prohibit immoral behaviors that she herself is tempted towards.)

I will argue that, whatever the substantive merits of positions like that, the position can be quite consistent, and indeed the restriction of immoral activity is quite consistent with setting a high value on civil freedom.

For it may well be that the activities that our conservative wishes to prohibit are ones that she takes to be absolutely wrong in all cases. Now it is possible to value civil freedom, without valuing the civil freedom to do what is wrong. Rather, one might value the civil freedom to choose between multiple morally permissible options. One might hold that no civil freedom worth having is lost to one through a prohibition on what would anyway be wrong to do.

However, the regulations that this conservative opposes on the grounds of the value of liberty are ones that prohibit, or at least penalize, activities some instances of which would be morally permissible but for the law. Consider, for instance, a minimum wage law. While there is a moral duty to pay a just wage, it is false that absent such a law it is always wrong to pay less than $5.85 per hour to an American worker in our day. It is not wrong, for instance, to pay $4 per hour to a kid who has no need for the money, who wants to work to get some experience, and whose productivity is significantly below that of an older worker. It is not wrong to pay workers $4 per hour if the owner is only making $4 per hour herself and the only available alternative for the business is to go broke and leave the workers destitute. The latter case is pretty rare but physically possible, but the former is less rare. In any case, it is clear that the minimum wage law prohibits some activities that are reasonably taken by our conservative not to be independently immoral, and indeed I suspect that even the proponents of such a law (I have no principled problem with minimum wage laws) are going to agree.

Our conservative takes the regulations she opposes to make illegal, or at least penalize, some actions that otherwise would have been morally unexceptionable. Moreover the proponents of the legislation are going to agree about this fact. They will, however, insist either that in most cases the activities prohibited or penalized would be wrong, or that some of the evils prohibited or prevented by the legislation are so great that it is worth prohibiting some otherwise permissible activities to prohibit these evils, or that great social goods are promoted by the legislation. The conservative lover of civil freedom will not be impressed, but may insist that we should leave unprohibited ten wrong actions rather than prohibit one permissible action just as we should leave unpunished ten guilty people rather than punish one innocent one.

Observe, too, the following. Legislation that prohibits something that is already immoral (e.g., fornication or unjustified breach of contract) does not decrease the number of actions that are morally open to one. But legislation that prohibits some actions that are not already immoral does decrease the number of actions that are morally open to one—for while the action wasn't immoral before the legislation was put in place, it becomes immoral afterwards to do it, since we are morally bound to obey the state (within certain limits). So it is quite consistent to believe in civil freedom, and to attack all kinds of otherwise reasonable laws on the grounds that they limit civil freedom, while yet wanting to prohibit fornication, unjustified breach of contract, suicide, medically unnecessary amputations, etc., as long as one believes the latter actions to be always wrong.

I am not saying that the position I described is above criticism. I think in any well-run state, we will need a lot of legislation that prohibits antecedently morally permissible activities (such as driving on the left side of the road). But at least it should be clear that one can consistently call for legal prohibitions on some activities one takes to be immoral while setting a very high value (perhaps too high a value) on civil freedom.

Deep Thoughts V

"Truth" is a word. So is "tenure".

Here you get two thoughts for the price of one. The first of these Deep Thoughts was reported to me as said by someone at an English Department with "is just" in place of "is". The second seems a useful supplement. I generally want the Deep Thoughts to be tautological. I do not know if these count as tautological; perhaps they do; at least they are necessary truths if strings plus quotation marks refer to types relativized to a language, so that "Gift" is a different type from "Gift", if the former is contextually in German and the latter in English.