Moral reasons

What are moral reasons?

I don't want to say "moral reasons trump". That's misleading. Deontic constraints do trump, by definitions, but not all moral reasons are deontic constraints. Imperfect duty reasons are "moral" but don't trump.

One can roughly delineate a family of reasons that roughly corresponds with the ordinary notion of "moral reasons". Some of the reasons in the family always trump (namely, the deontic constraints). Others don't (e.g., imperfect duties; promises on some views). When I think about the variety of reasons to put in this family (e.g., reasons arising from promise-like speech acts, needs to prevent the pain of others, deontic constraints, etc.), I really doubt that there is a natural kind that covers these reasons.

There are some natural distinctions among reasons:

• Those that always trump and those that don't.
• Those that concern the flourishing of other persons and those that don't.
• Those that concern the flourishing of persons and those that don't.
• Those that concern the flourishing of conscious things other than self and those that don't.
• Those that concern the flourishing of conscious things and those that don't.

But while these distinctions cut at the joints, none of them has the property that all and only the members of the messy family lie on one side.

Here's another argument. A reason is something that connects an action with a good, as furthering the good, respecting the good, detracting from the good, etc. One would expect natural kinds of reasons to be delineated in one of two ways (or a combination): by kind of good and by the nature of the relation to the good. But no natural delineation of either variety sorts the reasons into the moral and non-moral, as per the ordinary notion. And I bet no combination does either.

Rather than taking the messy family to be the "moral reasons", it strikes me as a better way to talk to say that all reasons are moral reasons. Each reason has the property that one fails in the love of God when one knowingly fails to follow the reason in the absence of sufficient countervailing reason. To fail act in accordance with a reason, absent sufficient countervailing reason, is to be bad qua person. If I make something ugly, when at insignificantly higher cost I could have made it prettier, I thereby failed to glorify God in creation as I should have. And so I failed as a person.

Christianity and paradox

Suppose we have a religion whose central tenets are paradoxical, verging on the contradictory. What would we expect? We might predict that the religion would be unsuccessful. But that would be too quick. The religion could be successful by adopting strategies like the following:

1. Hiding the central tenets from the bulk of the members.
2. Obscuring the paradoxical nature of the central tenets from the bulk of the members.
3. Downplaying the central tenets as unimportant.
4. Appealing almost only to the uneducated and ignorant.
5. Denigrating reason, and thus appealing to anti-intellectual impulses among uneducated and anti-rational impulses among the educated.

But now consider Christianity. It has central paradoxical doctrines, including Trinity, Incarnation and Real Presence. It does not hide them from the members. Nor is there any attempt to hide the paradoxical nature of these doctrines: that paradoxicality is plain to see, and if anything it is gloried in. Through much of the history of Christianity, the central tenets have been insisted on very publicly and are central to the liturgy. While Christianity has always had a special love for the downtrodden, its appeal has always also included many men and women of very high intellectual stature. Finally, while there are occasional instances of Christians denigrating reasons in history, the main thread of Christianity has been a defender of the importance of reason, even to the point of a significant part of the tradition embracing the Greek idea of humans as distinctively rational animals. How did it do it? Well, in addition to the five strategies above (and perhaps some others) there is also a sixth possibility:

6. Having true central tenets and having God work in the hearts and minds of members and nonmembers.

Instructable for python coding for Minecraft

If anybody is interested, I wrote up an Instructable for python coding for Minecraft using my Raspberry Jam Mod.

Quantum Mechanics and functionalism

Some theories suffer from the too-many-minds problem. Here I'll say that a theory suffers from a too-many-minds problem if the theory predicts that most minds are aberrant, say because they experience very unlikely scenarios (cream forming into words on their coffee, etc.) or because they live a truncated or disconnected life like Boltzmann brains.

Thinking about the main interpretations of Quantum Mechanics, I was struck by the following curious fact:

• Each main interpretation either suffers from the too-many-minds problem or requires a non-functionalist (typically, dualist) theory of mind or both.

Why? Well:

1. Everett's multiverse interpretation: Obviously suffers from the too-many-minds problem.
2. The many-minds interpretation of Everett: Probably suffers from too-many-minds, but anyway requires dualism.
3. The traveling minds interpretation: Doesn't suffer from too-many-minds, but is predicated on dualism. (OK, this isn't one of the leading interpretations, but I am a little fond of it, though I don't endorse it.)
4. Bohm: If functionalism is true, Bohm suffers from too-many-minds. See Section 7 here.
5. GRW collapse theories: There will be Boltzmann-brain type low-probability short-lived functional isomorphs of minds at the tails of the wavefunction, hence if functionalism is true, the theory suffers from too-many-minds.
6. Consciousness-causes-collapse: It is hard to see how this could work without dualism. (In addition to the obvious point, I suspect that if minds are physical, the quantum Zeno effect is apt to prevent the emergence of consciousness.)

This is inspired by lots of recent discussions with Josh Rasmussen and Rob Koons.

Absolute simultaneity and common sense

It's common sense that there is absolute simultaneity, whether directly so or because it's common sense that there is an objective present. It is sensible for philosophers to want to hold on to what is common sense. But here we should not be so quick. For consider some common sense claims:

1. There is absolute simultaneity.
2. If A and B are absolutely simultaneous and C and D happen t units of time after A and B respectively, then C and D are absolutely simultaneous.
3. Properly functioning clocks correctly measure lengths of time.
4. Clocks continue to properly function when moving, as long as they are not accelerated so quickly as to damage them.

But while (1)-(4) are all common sense, we have empirical data (assuming some uncontroversial claims of how to determine cases of absolute simultaneity for side-by-side events) that they are not all true, namely the data confirming the Twin Paradox.

Now when a number of common sense claims cannot all be held together, it is not responsible simply to say that one of them is common sense and therefore true. For the same thing could be said about the others. One would need to say something about how one's preferred claim is more commonsensical than the others, and that's a judgment that may well go beyond common sense.

I think most defenders of absolute simultaneity will reject (3) or (4). But if we look at how we actually acquire our concepts of durations of time by using clocks, watches and internal timers, it's plausible that we are committed to (3). And our practices of blithely using clocks even after coming to think that the earth is rapidly moving around the sun suggest (4).

I actually think that an interesting strategy for defending absolute simultaneity is to deny (2). This would lead to a view with absolute simultaneity but purely relative temporal durations.

That said, I am happy to deny (1).

Divorce

A marriage forges the couple into something analogous to a new person. Divorce is intended to be destructive of that something analogous to a new person. Thus divorce is at least presumptively wrong.

Objection: What if a marriage fails to forge that something analogous to a new person?

Response: I think we should see persons as through and through normative beings. What makes the married couple be something analogous to a new person is not that they actually make decisions together, become aligned to one another's needs and so on, but that such joint decision-making, this kind of alignment to one another's needs and so on are normative for them—are what they should strive for. A ceremony that fails to make this normative reality come into existence is not a marriage. We have something analogous to a new person even in a bad marriage.

People are not fungible

If people are fungible—can be exchanged for exact duplicates without this making any significant difference of value—then any two situations where there is the same number of exactly similar people are equivalent in value. After all, we can get from one situation to the other by just replacing the people in the one situation by the people in the other.

But suppose there are infinitely many exactly similar happy people and every second one ceases to exist. Obviously, something bad has happened—a lot of value has gone out of the world. But the number of exactly similar happy people is the same. So people are not fungible.

Prostitution and sex only for pleasure

Suppose Sid is the beneficiary of a trust fund which yields just enough money to live, but not to have much pleasure in life. Sid works as a prostitute solely in order to get more money in order to buy pleasures like fine dining. Thus, Sid has sex for the sake of pleasure. Compare this to Flynn who has sex solely for the sake of pleasure in the more ordinary way--it's the sex that he enjoys. Is there any interesting moral difference between Sid and Flynn? Both Sid and Flynn are having sex solely for the sake of pleasure: they are both ultimately being paid with pleasure. (The intermediate presence of money in the case of Sid may be a red herring. We might suppose Sid is having sex with a great chef and he doesn't enjoy the sex, but she is going to give him great culinary pleasures in exchange.)

I think a case can be made that Sid and Flynn are close to morally on par. (And clearly Sid is morally in a less good position than the more typical prostitute who has sex to provide for the necessities of life.) This would suggest that:

• If sex solely for money is always wrong, then sex solely for pleasure is always wrong.

When I think of ways of challenging the above argument, I think about how there is something interpersonally significant about the pleasure of sex, and so I think that maybe there is something less perverse about Flynn's case than Sid's. But on the other hand, I've described Flynn as just pursuing the pleasure, not any interpersonal significance of the pleasure.

Are there more nonmeasurable sets than measurable ones?

Assume the Axiom of Choice.

Consider the subsets of the interval [0,1]. There 2^c subsets of [0,1], where c is the cardinality of the continuum. Since the Cantor set C has measure zero, and every subset of a measure zero set is (Lebesgue) measurable, there are at least as many measurable subsets of [0,1] as subsets of the Cantor set. But the Cantor set has cardinality c, so there are 2^c measurable subsets of [0,1].

On the other hand, however, if A is any nonmeasurable set, then adding and/or subtracting a set of measure zero to A won't change the nonmeasurability, so there are 2^c nonmeasurable sets as well, since there are 2^c ways of varying A by adding and/or substracting a subset of C.

But notice the curious role that the Cantor set played in my above arguments. The reason there are 2^c measurable sets and 2^c nonmeasurable sets is because there are 2^c sets of measure zero, and we can vary any set by a measure zero set and preserve measurability / nonmeasurability.

This suggests another question. Say that two sets are equivalent provided that they differ by a set of measure zero. Are there more equivalence classes of nonmeasurable sets than of measurable sets?

Assuming the Axiom of Choice, the answer is yes. In fact:

• Theorem: There are 2^c equivalence classes of nonmeasurable sets while there are only c classes of measurable sets.

Why? Well, any measurable set differs from a Borel set by a set of measure zero, so there are no more equivalence classes of measurable sets than there are Borel sets, and there are c Borel sets. (And of course there are no fewer than c equivalence classes measurable sets: just consider the intervals [0,x].) Responding to a question I had asked on MathOverflow, Eric Wofsey yesterday showed that there are 2^c equivalence classes of subsets of [0,1]. Since there are only c equivalence classes of measurable ones, there must be 2^c equivalence classes of nonmeasurable ones.

In fact, we can say something stronger. Say that a subset A of [0,1] is saturated nonmeasurable (I used to call this "maximally nonmeasurable") provided that it is not only nonmeasurable but that every measurable subset of A has measure zero and every measurable superset of A has measure one. In other words, there is nothing measurable about A: we can't even give a non-trivial range of Lebesgue measures for A. (Technically: the inner measure is zero and the outer measure is one.) Then:

• Theorem: There are 2^c equivalence classes of saturated nonmeasurable sets.

Why? Well, this uses the same trick that Wofsey's proof did. Sierpiński showed in 1938 that you can find a disjoint family of perfect, and hence of cardinality c, subsets of the square [0,1]² with the property that any set obtained by choosing one member from each element in the family is saturated nonmeasurable. Since as measure spaces [0,1]² is isomorphic to [0,1], there will be a disjoint family F of subsets of [0,1], each of cardinality c, such that choosing one member of each element in F yields a saturated nonmeasurable set. For any A∈F, let φ_A be a one-to-one function from [0,1] to A. Define U_x={φ_A(x):A∈F} for x∈[0,1]. Then each U_x has inner measure zero and outer measure one, and the sets U_x are disjoint for different values of x. Any union of the sets U_x that (a) contains at least one of the sets (i.e., isn't empty) and (b) doesn't contain all the sets then also has inner measure zero and outer measure one. Why? Well, since it contains at least one of the sets, its outer measure is one. And since there is at least one that it doesn't contain, its complement has outer measure one and hence it itself has inner measure zero. But there are 2^c such unions (since there are 2^c possible unions given c nonempty disjoint sets, and throwing out the union that has no sets and the one that has all sets doesn't change that). Moreover, any two distinct such unions differ by at least one of the sets U_x, and hence differ by a set with inner measure one (and outer measure one for that matter), and so are not equivalent up to sets of measure zero.

Why is marriage sacred?

Many religions that disagree on many other things treat marriage as something sacred, not just a contract. Moreover, many non-religious people—though not all—have intuitions that point in that direction. Let's take all these intuitions at face value. Marriage is sacred.

Why?

Well, a paradigm of the uncontroversially sacred—something that we except to see connected to rituals across religions—is life. We are not surprised to see funerals or baptisms in a religion. Maybe at some deep level it is puzzling why human life is sacred (if materialism is true, this may be especially puzzling), but that human life is treated as sacred is not puzzling.

A student pointed out to me this morning that we can attempt to account for the sacredness of marriage by pointing to the sacredness of the new joint life of the couple. They become one flesh after all. Indeed, it is as if a new human life came into existence. And if the analogy is tight enough, that makes sense of its as being sacred.

But while I think this is all true, I suspect that the reason why marriage has been so widely treated as sacred may be a more literal connection to new life: it is a relationship tied to literal new human life, to procreation. Literal new human life is sacred. The sacred infects what is related to it. The message of a book is sacred, so the volume it's in is treated as a holy book. Marriage, on this picture, is tied to procreation.

But of course we and our ancestors know that not every marriage results in procreation and that procreation can happen outside of marriage. So the tie between marriage and procreation has to be carefully formulated. I don't think we want to say it's just a statistical tie. That would undermine the reason for taking marriage to be sacred. Rather, I suspect it's a normative tie. There is more than one way one could expand on this tie.

One option is to say that marriage is a relationship that normally results in children. One would expect a relationship that normally results in something sacred to have something sacred about it.

However, this option has the consequence that a marriage without children is lacking something normal to it, like a three-legged sheep lacks a leg. But is it right to say that a couple who got married in their 60s has a defective relationship? Well, the phrase "defective relationship" leads astray. It suggests that there is something wrong with what the people are doing. And in that sense, the couple who got married in their 60s don't have a defective relationship just because they don't have children. But if we think of it as a defect in the same way that a sheep having three legs is a defect, then that phrase may not be incorrect. A couple who gets married late in life may well have a quite appropriate sadness that they were unable share a larger portion of their life, and in particular a sadness that they were unable to share their fertility. So I don't think the case of elderly couples is a serious problem for the view that the tie between marriage and procreation is that children normally result from marriage. And the view explains why it can feel so tragic to be infertile.

Another option would be that marriage is a relationship that makes having children morally permissible. It is a relationship that licenses procreation. One shouldn't here have a picture of the state or the church giving one a license to procreate: marriage comes from an exchange of vows between the future spouses, and it is their giving themselves in marriage to one another—something that in principle can happen without a state or a church being involved—is what morally licenses the procreation on this view. It is only with the kind of commitment that is found in marriage that a couple could permissibly tie themselves to each other by having a child together. But it makes some sense that taking up the commitment which makes the production of human life permissible would be infected with the sacredness of human life. Still, in the end this doesn't seem quite to get the full story. For instance, if a married unemployed couple is so poor that they cannot adequately care for their children, then it could be morally impermissible for them to procreate. Getting a job could then render procreation morally permissible. But that doesn't make the job be a sacred thing, at least not in the way marriage is.

In the end, I suspect that all three stories—the story of the new joint life of the couple, of marriage normally resulting in children, and of marriage in principle morally permitting a couple to have children—are a part of the truth. And, as a colleague reminded me, there is the mirroring of the life of the Trinity.

The essential properties of our spacetime

Suppose that spacetime really exists. Name our world's spacetime "Spacey". Now, we have some very interesting question of which properties of Spacey are essential to it. Consider a possible but non-actual world whose spacetime is curved differently, say because some star (or just some cat) is in a different place. If that world were actual instead of ours, would Spacey still exist, but just be curved differently, or would a numerically different spacetime, say Smiley, exist in Spacey's place?

There are three different views one could have about some kind K of potential properties of a spacetime:

1. All the properties in K that Spacey has are essential to Spacey.
2. None of the properties in K are essential to Spacey.
3. Some but not all the properties in K that Spacey has are essential to Spacey.

Suppose K is the geometric properties. It's plausible that at least the dimensionality is essential to Spacey: if Spacey is four-dimensional, it is essentially four-dimensional. Any world with a different number of dimensions doesn't have our friend Spacey as its spacetime. If so, we need only to decide between (1) and (3).

Here is an argument for (3). Spacey's properties can be divided into earlier and later ones, since one of the four (or more) dimensions of Spacey is time. Further, according to General Relativity, some of Spacey's later geometric properties are causally explained at least in part by Spacey's own earlier causal influences. But if (1) were true, then Spacey would not have existed had the later geometric properties been different from how they are, and a part of the explanation of why it is Spacey that exists lies in the exercise of Spacey's own causal influences. But nothing can even partly causally explain its own existence. (Interesting consequence: If Newtonian physics were right, we might think that view (1) was true with respect to geometric properties. But this is implausible given General Relativity.)

Similar arguments go for the wavefunction of the universe, if it's a fundamental entity.

Decision theory, evidence and Sleeping Beauty

I've been thinking about the following variant of Sleeping Beauty. A coin is tossed on Sunday, out of your sight. As usual, if the coin is heads, you'll wake up on Monday, and then sleep through until Wednesday. If it's tails, you'll wake up on Monday and Tuesday. But this isn't standard Sleeping Beauty. Your memory of the Monday wakeup won't be erased on Tuesday. Instead, you will be given a drug that makes it impossible for you to update your credence as to heads on Tuesday.

You wake up. It's Monday. You know it's Monday, because you don't remember an earlier wakeup. How should you set your credence?

Evidentially speaking, it's clear and uncontroversial. Your credence in heads evidentially should still be 1/2. A Monday wakeup is no evidence for or against heads. (Now, a Tuesday wakeup would a different matter—it is conclusive evidence against heads, but it would be evidence you are unable to update on due to the drug.)

But suppose that both on Monday and, if it's tails, on Tuesday you will be offered choices from a single broad and diversified portfolio of bets regarding whether the coin landed heads. Suppose, further, that you will be unable to decide except on the basis of maximizing expected utility (with respect to your credences). Then decision-theoretically, you should assign credence 1/3. A simple argument is that if the experiment is repeated, then in 1/3 of the times you're choosing from the portfolio it will in fact be heads and 2/3 of the times you're choosing from the portfolio it will in fact be tails (remember that once you set the credence on Monday, it won't be able to change on Tuesday). So you should gamble as if you had credence 1/3, and to do that you need your credence to be 1/3 since I assumed that you cannot but bet on the basis of your credence.

Interestingly, the same result follows if you're maximizing total lifetime expected epistemic utility with respect to a proper scoring rule: You should assign 1/3 to heads.

Yet evidentially your credence should be 1/2. This illustrates the fact that when you expect your future credences to have a chance of being irrational—because of your inability to update on Tuesday—then we have a conflict between what, on the one hand, the evidence supports and what, on the other hand, decision theory and epistemic utility maximization support.

The original Sleeping Beauty case, where you can't tell if it's Monday or Tuesday because your memory has been erased, has some similarity to this. For while in my modified case, Tuesday's credence is forced by a drug to be the same as Monday's, in the original Sleeping Beauty case Tuesday's credence is forced to be the same as Monday's due to memory loss and the fact that, presumably, you will make up your mind in the same way given the same data.

This similarity suggests that we should be suspicious of concluding that evidentially your credence should be 1/3 from the fact that both decision-theoretic and epistemic utility considerations lead to 1/3 in the original Sleeping Beauty case.

I only want to make this modest point. I think that's the only point the analogy supports. The analogy is not strong enough to support the conclusion that one should assign 1/2 in the original Sleeping Beauty case. But it is enough, I think, to show that cases like Sleeping Beauty are going to be exceptions to the correspondence between evidential and utility (whether pragmatic or epistemic) considerations.

Internal time, external time, probability and disagreement

Suppose that Jim lives a normal human life from the year 2000 to the year 2100. Without looking at a clock, what probability should Jim attach to the hypothesis that an even number of minutes has elapsed from the year 2000? Surely, probability 1/2.

Sally, on the other hand, lives a somewhat odd human life from the year 2000 to the year 2066. During every even-numbered minute of her life, her mental and physical functioning is accelerated by a factor of two. She can normally notice this, because the world around her, including the second hands of clocks, seems to slow down by a factor of two. She has won many races by taking advantage of this. An even-numbered external minute subjectively takes two minutes. Suppose that Sally is now in a room where there is nothing in motion other than herself, so she can't tell whether this was a sped-up minute or not. What probability should Sally attach to the hypothesis that an even number of minutes has elapsed from the year 2000?

If we set our probabilities by objective time, then the answer is 1/2, as in Jim's case. But this seems mistaken. If we're going to assign probabilities in cases like this—and that's not clear to me—then I think we should assign 2/3. After all, subjectively speaking, 2/3 of Sally's life occurs during the even-numbered minutes.

There are a number of ways of defending the 2/3 judgment. One way would be to consider relativity theory. We could mimic the Jim-Sally situation by exploiting the twin paradox (granted, the accelerations over a period of a minute would be deadly, so we'd have to suppose that Sally has superpowers), and in that case surely the probabilities that Sally should assign should be looked at from Sally's reference frame.

Another way to defend the judgment would be to imagine a third person, Frank, who lives all the time twice as fast as normal, but during odd-numbered minutes, he is frozen unconscious for half of each second. For Frank, an even numbered minute has 60 seconds' worth of being conscious and moving, while an odd numbered minute has 30 seconds' worth of it, and external reality stutters. If Frank is in a sensory deprivation chamber where he can't tell if external reality is stuttering, then it seems better for him to assign 2/3 to its being an even-numbered minute, since he's unconscious for half of each odd-numbered one. But Frank's case doesn't seem significantly different from Sally's. (Just imagine taking the limit as the unconscious/conscious intervals get shorter and shorter.)

A third way is to think about time travel. Suppose you're on what is subjectively a long trip in a time machine, a trip that's days internal time long. And now you're asked if it's an even-numbered minute by your internal time (the time shown by your wristwatch, but not by the big clock on the time machine console, which shows external years that flick by in internal minutes). It doesn't matter how the time machine moves relative to external time. Maybe it accelerates during every even-numbered minute. Surely this doesn't matter. It's your internal time that matters.

Alright, that's enough arguing for this. So Sally should assign 2/3. But here's a funny thing. Jim and Sally then disagree on how likely it is that it's an even-numbered minute, even though it seems we can set up the case so they have the same relevant evidence as to what time it. There is something paradoxical here.

A couple of responses come to mind:

• They really have different evidence. In some way yet to be explained, their different prior life experiences are relevant evidence.
• The thesis that there cannot be rational disagreement in the face of the same evidence is true when restricted to disagreement about objective matters. But what time it is now is not an objective matter. Thus, the A-theory of time is false.
• There can be rational disagreement in the face of the same evidence.
• There are no meaningful temporally self-locating probabilities.

Two motivations for Bohmian quantum mechanics

There are two different motivations for the Bohm interpretation of quantum mechanics. One comes from a philosophical affinity for determinism. The other comes from the desire to have the Schroedinger equation, with all its mathematical elegance, hold without the exceptions that collapse leads to, while avoiding the multiverse excesses of Everettian quantum mechanics.

Now, deterministic hidden variable theories like Bohm's match up with the stochastic predictions of indeterministic quantum mechanics by supposing that the initial state is chosen according to a "special" probability distribution. But there are serious philosophical problems with justifying the assumption of that special probability distribution.

Interestingly, if all one is after is avoiding the Scylla of collapse and the Charybdis of an Everettian multiverse, one can find indeterministic hidden variable theories that avoid the initial distribution problem that deterministic hidden variable theories suffer from. A dualist example is what I call the "Traveling Minds" interpretation. But one should also be able to cook up physicalist hidden-variable theories that mimic something like the dynamics of the Traveling Minds interpretation.

It may seem silly to have indeterministic hidden variable theories, given the history of positing hidden variables in order to regain determinism. But I see no good reason to try to regain determinism, while I do see good reason to try to keep unitarity, i.e., to avoid collapse. And there is good reason to avoid the Everett multiverse, because of the serious probabilistic problems facing it. And so there is actually good reason to consider indeterministic theories. (I understand that there already is a Bohmian field theory with stochastic particle creation/destruction.)

Gunky ontology and virtual points

Gunk is subdivisible into smaller parts, and these are subdivisible into yet smaller parts, and this happens ad infinitum, with no smallest indivisible parts or atoms.

But here is an interesting fact: One can introduce ersatz atoms or virtual points into a gunky ontology, given some plausible mereological axioms. Suppose that O is a gunky object. Then the set M(O) of the parts of O has a partial order ≤ where x≤y if and only if x is a part of y. Now we can say that an ersatz atom of O is any ultrafilter on O with respect to the ordering.

Thus, ersatz atoms are subsets U of M(O) such that:

1. U is a non-empty proper subset of M(O)
2. if x is in U then everything that has x as a part is also in U
3. if x and y are in U, then there is a z in U such that z≤x and z≤y
4. U is maximal: any larger subset satisfying (1)-(3) is all of M(O).

We can then say that an ersatz atom U is an ersatz part of x∈M(O) provided that x∈U.

To get the existence of ersatz atoms, we need some axioms of mereology in addition to the Axiom of Choice. Fortunately, pretty weak mereological axioms suffice:

5. parthood is a partial ordering
6. O has two parts x and y that do not overlap

As usual, two things are said to overlap provided that there is something that is a part of both.

In general, given any two parts x and y that do not overlap, there will be an ersatz atom U that is an ersatz part of x but not of y. Let's further assume the strong supplementation axiom that if y is not a part of x, then there is a z that is a part of y such that z does not overlap with x. Then whenever x≠y, there will be an ersatz atom that's an ersatz part of one but not of the other. Hence, we can identify every part of O with a set of ersatz atoms. However, given gunkiness, not every set of ersatz atoms corresponds to a part. In particular, singleton sets of ersatz atoms do not correspond to parts.

So the gunk theorist can talk as if objects were made out of atoms. Now, if we have a gunky ontology, then I think we should take the parts to be non-fundamental, and grounded in the wholes rather than the other way around on pain of a grounding regress. But if we allow non-fundamental parts in our ontology, then one may worry that the gunkiness of the ontology is merely verbal and non-substantive, dependent on the verbal decision not to talk of the ersatz atoms as real parts.

Privacy and knowledge

Our privacy is violated when people improperly come to know private things about us. Note, however, that all the harms that violation of privacy causes can be equally had without a violation of privacy. For instance, suppose that Sally the clever hacker breaks into my computer and figures out my credit card number while Jim the inept hacker tries to break into my computer and extract a credit card number, but due to a bug in his hacking script he never gets into my computer, but his hacking software reports a random number to him as my credit card numbers. If the random number happens by chance to match my credit card number, I am equally exposed to harms from Jim as from Sally. Yet only Sally has actually violated my privacy.

So I am not harmed by Sally's knowing my credit card number as such. Rather, I am harmed by Sally's (and Jim's) having a correct belief as to my credit card number.

In fact, in the case of some violations of privacy, it's the belief, not even the correctness of the belief, that harms me. If someone I thought to be a friend has communicated to people that I confessed to an embarrassing moral failure, my reputation is equally harmed just as much when the supposed friend is lying and I never committed the failure as when my supposed friend has violated my privacy. Typically it is easier to remove the harm when the belief about one is false, namely by presenting evidence as to its falsity, but even that is only typically true.

And in the credit card case, while correctness matters, the belief does not. If Jim orders expensive goods with a number that he does not believe to be a credit card number, simply on the off-chance that it might be one, and that number happens to be a valid credit card number, I am equally inconvenienced when that number is mine as in the case where he believed it to be my number.

All this suggests that a violation of privacy—people's coming to know private information about us—is not as such harmful. But the above cases neglect intrinsic harms. Take the case of the moral failure. While a false belief about my secret moral failures seems no less harmful to my reputation than a true belief, people's having true beliefs, and especially their having knowledge (if they just suspect and don't know, then that's a comfort), of my secret moral failures would be much more mortifying. Likewise, it seems one is intrinsically harmed if a voyeur installs a camera which transmits pictures of one getting dressed, but one does not suffer similar harm if the camera is defective and sends back random pixels which by chance look just like the real pictures would have.

So there can be a harm from loss of privacy as such. But it depends on the case. In the credit card number case, there is no intrinsic harm in the loss of privacy. Were there no chance of there being thieves, one could emblazon one's credit card numbers on one's T-shirt. In those cases, the violator's gaining knowledge is no worse than the violator's gaining a true belief. In the cases of shameful misdeeds there is typically an intrinsic harm and an instrumental harm from the violation of privacy. For the instrumental harm, it doesn't matter that the violator knows, or even that the violator's belief is true. But for the intrinsic harm, it does matter. In the case of bodily privacy, there is an intrinsic harm but there need not be any instrumental harm.

The case of instrumental harm is very puzzling. After all, isn't knowledge a good? How could someone's knowing something about me not be intrinsically good? But of course we need to distinguish subjects of goods. It is perhaps intrinsically good for the knower to know this thing about me (though perhaps instrumentally bad, say if it harms relationships). But perhaps it is not intrinsically good for me to have it known about me.

Even so, it's puzzling how knowledge can intrinsically harm the person known.

Perhaps our emotions and intuitions are misleading. I am more mortified if some embarrassing moral failure is known of me than if it is falsely believed of me. But perhaps I am simply confusing the fact that typically false beliefs are easier to refute than knowledge. So maybe it really is just harm to my reputation that is at issue?

Here is a hypothesis. Knowledge of people's past moral failures tends to be misleading information as it tends to lead people to think that the person lacks the dignity of someone in the image and likeness of God. Maybe it's worse when knowledge of one misleads people into seeing one as lacking dignity, just as it's worse when one's sins cause a harm to another than when the harm happens for some unrelated cause.

On the other hand, in heaven perhaps all secrets will be known, but moral failures will no longer mislead the knower into thinking that one lacks dignity. On the contrary, moral failures will be connected with the glory of God who gives the grace to overcome the moral failures and the failures will themselves be evidence of the person's dignity (since only a being with this kind of dignity is capable of sin). If people saw our failures in the perfectly right light, there would be no harm from loss of privacy. If this hypothesis is right, then the loss of privacy with respect to moral failures is not intrinsically harmful.

Bodily privacy is, perhaps, a similar matter. Rather than being evidence of the dignity of a child of God, in our fallen condition one can be led by the sight of a person's body to objectify or otherwise dehumanize the person. And maybe it is worse when one's body, rather than random pixels, is the cause of this unfortunate state of affairs.

I don't really know. All this is puzzling.

What happens when collapse doesn't happen in collapse theories?

On collapse theories like GRW, Quantum Mechanics proceeds deterministically according to the Schroedinger Equation until a random "hitting" event occurs, when collapse occurs. There is a frequency parameter f that controls how often hitting events tend to happen. They tend to happen much more frequently when there are large amounts of matter involved than when there are small.

Nonetheless, the hitting events are random. Thus the physics of collapse theories implies that it is physically possible, with a non-zero (but presumably tiny) probability, that no hitting event happen in the universe over the next year, and hence no collapse happens over a year. Since this is physically possible, it should make sense to ask: What would it be like if this happened? Indeed, if we live in an infinite multiverse governed by a collapse theory with the same frequency everywhere, we can be confident that such no-collapse years do occur.

So what would it be like if no collapse occurred? I can think of three plausible proposals:

• Nothing: A (nomic or metaphysical) precondition of consciousness is a brain in a pure, or at least close to pure, quantum state, so in a no-collapse year, once everybody's brain states came to have a sufficient superposition of states (from the preferred basis), nobody would be conscious. However, after that year passed, there would be a collapse, and there would be false but plausible memories corresponding to the outcome of the collapse.
• Everett: For that no-collapse year, we would be living as if in a branching Everett-style multiverse. Either we would be experiencing different things in different branches, or we would have counterparts in different branches experiencing different things. Then with the collapse at the end of the year, all the branches but one would disappear.
• Weird: We would be having strange superposed experiences, perhaps quite unlike anything we can imagine. We would have superposed neural memory states. Then at the end of the year, when collapse occurred, our memories would also collapse, and we would end up with an ordinary set of memories corresponding to one component of the superpositions.

Here's one curious feature of all three proposals: At the end of the year, we would be back to business as usual, seemingly with normal memories of the past year. We would have no way of telling after the fact that we had a year with no collapse. On the Nothing proposal, we would have no way of telling during the no-collapse year, either, since we wouldn't be conscious during it. On the Everett proposal, some of our counterparts or branched selves would be having strange, improbable experiences. On the Weird proposal, we would be having strange experiences, but then we would have no memory of them.

If we take the Everett proposal, then the GRW theorist does not avoid the metaphysical oddness of persons in a branching multiverse—her only special contribution is to say that this oddness is unlikely to occur. If we take the Weird proposal, then the collapse theorist still has to deal with the metaphysical and psychological oddness of Schroedinger's cat phenomena—again, her only contribution is to say that such phenomena are unlikely. If these difficulties are really serious metaphysical problems, then the GRW theorist does not avoid them. A die that turns into a square circle once it rolls a million heads is not any less metaphysically problematic than a plain and simple square circle.

I suspect the Nothing approach is the best one for the GRW theorist. For instance, Nothing combined with compact-support-collapse helps with the infamous tails problem for collapse theories (see this for a nice discussion of the tails problem; alas, my suggestion doesn't help with the relativistic problems the author points out). For maybe we are conscious only at those instants when the wavefunctions have compact support. This is good reason to opt for the Nothing proposal if one has a collapse theory.

But the Nothing approach leads to a strange sceptical hypothesis, namely that I have not been conscious over the past week, notwithstanding apparent memories from yesterday. For remember that the collapse theories have a free parameter, f, which governs the frequency of collapses. If that parameter is low enough, then collapses will be rare, say once a month in my vicinity. And what reason do I have on the Nothing proposal to suppose that f isn't that low? The apparent memories of continuous past consciousness are exactly what I would expect with a low parameter, since the apparent memories are induced by the collapse of superposed neural states. We do have some constraints on f. For instance, f had better not be so low that it's surprising why anybody is ever conscious. Maybe there are some stronger constraints than that, though this is not clear to me. But there is no reason given the Nothing proposal to deny a value of f that yields once-per-month collapses.

The Everett proposal may well lead to a sceptical worry about low values of f as well. For how do we know that we're not right now in a no-collapse period?

The Weird proposal does not lead to this sceptical worry that f might be low. For on the Weird proposal, given a low f it's surprising that my current conscious state is non-weird, and so that's evidence against Weird plus a very low value of f. But Weird is weird.

The above sceptical worries about low values of f are ameliorated if in addition to being collapse theorists we are theists. For God likely wouldn't want us to have too many misleading memories, and hence would likely make f high enough to prevent misleading memories.

A wacky metaphysics of time for deterministic physics

Consider a deterministic physical theory on which for each t>0 there is a time-evolution operator U_t on set of all instantaneous states of the universe (i.e., global phase space), so that if u is the state of the universe at time t₁, then U_tu is the evolved state of the universe at t₁+t. For example, Everett-style no-collapse quantum mechanics or Newtonian physics without situations like Norton's dome.

Suppose there is a first moment of time, call it time 0. Here, then, is an odd metaphysics to go with the theory. The universe fundamentally has some initial state. Then what it is for the universe to be in state v at a time t>0 is nothing else than for v to equal U_tu₀, where u₀ is the initial state.

For a simple example, suppose that we have a simple Newtonian theory with point particles and no forces. Then what it is for a particle to be at location x at time t>0 just is for the particle to have an initial momentum p₀, initial location x₀ and initial mass m₀ such that x=x₀+(p₀/m)t.

On this wacky metaphysics, later states are not caused by the initial state, but are metaphysically grounded in the initial state.

What are the merits of this kind of a weird theory? Well, it has a lot of fundamental simplicity:

• Fundamental reality is only three dimensional, and facts about later times are just mathematically derivative from the fundamental facts.
• At the fundamental level of description there is no such thing as time.
• There is no need for causation, laws of nature or nomic simplicity. Temporal evolution just is a matter of metaphysical necessity. Later states reduce to earlier ones.

Yet, we can have genuine explanatory relations between times. If the U_t operator has the right kind of mathematical definition in terms of differential equations, we will be able to say that the state of the universe at time t₂ is explained by the state of the universe at an earlier t₁ which in turn is explained by the state at time 0. The explanation is reductive or metaphysical rather than nomic. Thus the number of types of explanation is reduced.

This is, of course, very wacky. But if one doesn't take our intuitions about modality (say, the metaphysical possibility of miracles, which is ruled out on this account), the fundamental existence of persons, free will, and the like, and one has a deterministic theory, it is hard to avoid falling into a theory like this. Simplicity does, after all, strongly favor it.

The above formulation assumes an initial moment of time, but I think one can formulate it in terms of limiting conditions if one's deterministic theory doesn't have an initial moment.

I've noticed that for a while I've been unconsciously pursuing a curious research project. The research question is something like this: If one throws anthropocentric intuitions to the winds, what sort of interpretations of physics would one take seriously? Call this the estrangement (ostranenie) project. The point of the project is to take estranging approaches to their logical conclusion, and see where they lead. The lesson I am drawing is that when one abandons the kinds of anthropocentric approaches that Aristotelian metaphysics uses, one must go much further, and much stranger, than most people are willing to go.

A quick heuristic for testing conjunctive accounts

Suppose someone proposes an account of some concept A in conjunctive form:

• x is a case of A if and only if x is a case of A₁ and of A₂ and ... of A_n.

It may seem initially plausible to you that anything that is a case of A is a case of A₁,...,A_n. There is a very quick and simple heuristic for whether you should be convinced. Ask yourself:

• Suppose we can come up with a case where it's merely a coincidence that x is a case of A₁,A₂,...,A_n. Am I confident that x is still a case of A then?

In most cases the answer will be negative, and this gives you good reason to doubt the initial account. And to produce a counterexample, likely all you need to do is to think up some case where it's merely a coincidence that A₁,A₂,...,A_n are satisfied. But even if you can't think of a counterexample, there is a good chance that you will no longer be convinced of the initial account as soon as you ask the coincidence question. In any case, if the answer to the coincidence question is negative, then the initial account is only good if there is no way for the conditions to hold coincidentally. And so now the proponent of the account owes us a reason to think that the conditions cannot hold coincidentally. The onus is on the proponent, because for any conditions the presumption is surely that they can hold coincidentally.

Consider for instance someone who offers a complicated account of knowledge:

• x knows p if and only if (i) x believes p; (ii) p is true; (iii) x is justified in believing p; (iv) some complicated further condition holds.

Without thinking through the details of the complicated further condition, ask the coincidence question. If there were a way for (i)-(iv) to hold merely coincidentally, would I have any confidence that this is a case of knowledge? I suspect that the answer is going to be negative, unless (iv) is something weaselly like "(i)-(iii) hold epistemically non-aberrantly". And once we have a negative answer to the coincidence question, then we conclude that the account of knowledge is only good if there is no way for the conditions to hold coincidentally. So now we can search for a counterexample by looking for cases of coincidental satisfaction, or we can turn the tables on the proponent of the account of knowledge by asking for a reason to think that (i)-(iv) cannot hold coincidentally.

Most proposed accounts crumble under this challenge. Just about the only account I know that doesn't is:

• x commits adultery with y if and only if (i) x or y is married; (ii) x is not married to y; (iii) x and y have sex.

Here I answer the coincidence question in the positive: even if (i)-(iii) are merely coincidentally true (e.g., x believes that he is married to y but due to mistaken identity is married to someone else), it's adultery.

Definitely incompatible properties and vague identity

Here's yet another version, probably unoriginal, version of the Gareth Evans argument against vague identity. Say that two properties P and Q are definitely incompatible if it is definitely true that it is impossible for an object to satisfy both of them.

1. (Premise) For any property R, being definitely R and being vaguely R are definitely incompatible.
2. (Premise) If P and Q are definitely incompatible, and x has P while y has Q, then x is definitely distinct from y.
3. For any x, being definitely identical with x is definitely incompatible with being vaguely identical with x. (By 1)
4. (Premise) For any x, x is definitely identical with x.
5. So, if y is vaguely identical with x, then y is definitely distinct from x. (By 2 and 3)
6. So, there are no cases of vague identity.

One might want to weaken (1) to say that being definitely definitely R and being definitely vaguely R are definitely incompatible. We then need to strengthen (4) to say that x is definitely definitely identical with x, and our conclusion becomes the weaker conclusion that there is no definitely vague identity. But I suspect that if there is vague identity, there is definitely vague identity, so we can get the stronger conclusion as well.

Personal identity, continuity and vagueness

It is interesting to sort views of personal identity over time based on the answer to:

1. Are the grounds of personal identity over time capable of continuous variation between cases of identity and cases of non-identity?

Memory, body and brain theories answer "Yes". It is natural for soul and further-fact theories to answer "No". Animalism splits at least into a naturalistic version, which answers "Yes", and a hylomorphic version, which answers "No".

Theories that answer "Yes" require either vague diachronic identity or an arbitrary transition (something like: it's the same person if and only if at least exactly this number of neurons are had in common between the state now and the state one second ago). Moreover, the transition would have to be metaphysically necessary, since we are talking about the grounds of personal identity: we can't have two worlds with the same grounds but different identity facts.

I do not think an arbitrary metaphysically necessary transition here is plausible. What about vague diachronic personal identity? I think that is impossible. For I think the only sources of vagueness in whether I am suffering a horrific pain are the vagueness in "horrific" and in "pain". But if there was vague diachronic identity, then one could have a token case of definitely horrific pain and still have vagueness as to whether I am suffering it. And that is absurd. Moreover, we have the well-known Leibniz's Law argument against vague identity (a does not have the property of being vaguely identical with a; if b has the property of being vaguely identical with a, then by Leibniz's Law, b just isn't a, plain and simple).

Ethics of love

New Testament ethics holds that loving (God and human neighbor, at least, but maybe the rest of creation as well) is sufficient for fulfilling moral obligations. This could be taken in weaker and stronger ways. The weaker view is that:

1. Necessarily, anyone who fails morally fails in loving all.

And "necessarily" might not even be metaphysical modality: it might be something "nomically necessarily", or "necessarily in light of God's commands". But there are stronger readings, such as:

2. Necessarily, every moral failure constitutes a failure in loving all.

For instance, take someone who steals. To have (1) hold of the case of the theft, all we need is that, say, the theft makes perfect universal love psychologically impossible, or that perfect universal love would make the theft psychologically impossible. That's a strong claim but nowhere near as strong as the claim we would get from (2) that the theft constitutes a failure in loving all.

I prefer the stronger view. I don't think the New Testament claims are merely claims about moral failings being correlated, even necessarily so, with failures in love. Given that God is love itself, and we are in God's image and likeness, it is quite plausible that (2) is true.

If this is right, then we can give a sketch of the sorts of questions we would want to answer to get a Christian ethics.

Metaethics:

• What is the modality in the "Necessarily" in (2)?
• Why is (2) true? (Is it a brute truth? Is it true in virtue of a divine command? Is it true in virtue of our nature? Etc.)

Normative Ethics:

• What is it to love?
• Are there any restrictions on the quantifiers in the "all" of (2)?
• What is it to fail in loving? (Is it the same as to fail to love, or can one fail in loving x while still loving x but not the right way?)

Applied Ethics:

• Analyze which particular actions are constitutive of a failure in love in light of the analysis of love and failure in the Normative Ethics section.

I see my One Body book as tackling some of the questions in the Normative and Applied areas. I wish I had the time and wisdom to handle the other questions. Maybe one day I will at least have the time.