Peers and twins

I just realized something that I should have known earlier. Suppose I have a doppelganger who is just like me and goes wherever I go—by magic, he can occupy a space that I occupy—and who always sees exactly what I see and who happened always to judge and decide just as I do. What I’ve just realized is that the doppelganger is not my epistemic peer, even though he is just like me.

He is not my peer because he has evidence that I do not and I have evidence that he does not. For I know what experiences I have and he knows what experiences he has. But even though my experiences are just like his, they are not numerically the same experiences. When he sees, it is through his eyes and when I see, it is through my eyes.

Suppose that on the basis of a perception of a distant object that looked like a dog I formed a credence of 0.98 that the object is a dog, and my doppelganger did the same thing. And suppose that suddenly a telepathic opportunity opens up and we each learn about the other’s existence and credences.

Then our credences that the distant object is a dog will go up slightly, because we will each have learned that someone else’s experiences matched up with ours. Given that the other person in this case is just like me, this doesn’t give me much new information. It is very likely that someone just like me looking in the same direction would see things the same way. But it is not certain. After all, my perception could still be due to a random error in my eyes. So could my doppelganger’s be. But the fact that our perceptions match up rules makes it implausible to suppose the random error hypothesis, and hence it raises the credence that the object really is a dog. Let’s say our credences will go up to 0.985.

Now suppose that instead this is a case of slight disagreement: His credence that there is a dog there is 0.978 and mine is 0.980, this being the first time we deviate in our whole lives. I think the closeness to me of the other’s judgment is still evidence of correctness. So I think my credence, and his as well, should still go up. Maybe not to 0.985, but maybe 0.983.

What I found in my mailbox

Update: The OUP website says that the official release date is September 16, 2018.

Two kinds of partial causation

It’s interesting that there are at least two significantly different kinds of partial causation. In both of the following cases it seems reasonable to say that x partially causes y:

1. x and z together cause y

2. x causes z and z is a part of y.

I.e., the partiality can be on either side of the causal relation. And one might even combine the two, no?

My previous post was about partial causation where the partiality was on the side of the cause, not the side of the effect.

Partial causation and causeless events

1. If ordinary events can happen without any cause at all, they can happen with a partial cause and no full cause.

2. A partial cause is a part of a full cause.

3. Nothing can happen with a partial cause and no full cause.

4. So, ordinary events cannot happen causelessly.

The argument for (2) is that (2) is the most obvious way to define a partial cause.

The argument for (1) is as follows. Suppose you and I lift a sofa in world w₁ in such a way that the exertion of each of us only partly explains the rising of the sofa, as neither exertion is enough to cause the rising. If ordinary events can happen without any cause at all, there is a world w₂ where the sofa rises causelessly, with neither you nor I doing anything. But if w₁ and w₂ are possible, likewise a world w₃ is possible where only I exert myself just as in w₁ and you sit back and the sofa rises in response to my exertion, and nothing else causally impacts the sofa’s rising. Since my exertion is not enough to cause the rising of the sofa in w₁, and in w₃ I exert myself to the same degree, my exertion is no more a full cause of the sofa’s rising in w₃ than it is in w₁. Hence, in w₃, I partially causes the sofa to rise, without there being a full cause, just as the consequent of (1) claims.

If I were inclined to deny (4), I would want to argue that (2) is not the right way to define a partial cause. But I don’t know a better way.

Internal time and God

1. The internal time of a substance is constituted by the causal order within its accidents.
2. But God is a substance that has no accidents.
3. So God has no internal time.

Pity that both premises are controversial.

Beliefless Christianity

A number of authors have claimed that it is possible to practice the Christian faith without assigning a high epistemic probability to central doctrines of Christianity. Here is an interesting problem with such a practice. A central part of Christian practice is to worship Jesus Christ as God. Now, Jesus Christ is uncontroversially a man. Christianity adds that he is also God. If that additional belief is false, then we who worship Jesus Christ as God are idolaters. But it is wrong to undertake a serious risk of idolatry. Thus, it is only permissible to practice the Christian faith if by one's lights the risk of idolatry is not serious. And the only way that can be is if one assigns a high epistemic probability to the doctrine that Jesus Christ is God. Thus, it seems, at least this central doctrine of the Incarnation needs to have a high epistemic probability if one is to be morally justified in practicing the Christian faith.

There is, however, a hole in the argument. Idolatry is only a great evil if God exists. Now imagine someone who assigns a high conditional probability to the Incarnation on the condition that God exists, but who assigns a low unconditional probability to both the Incarnation and the existence of God. Such a person can reason as follows. Either God exists or not. If God does not exist, there is not much evil in idolatry, and so not much harm in worshiping Jesus as God. If God does exist, however, then probably the Incarnation is true, and the value of worshiping Jesus outweighs the risks, since the risks are small.

So, what I think my overall argument shows is that it is wrong to practice the Christian faith without assigning a high epistemic probability to the doctrine of the Incarnation if one assigns a significantly higher epistemic probability to theism. Thus, someone who comes to be convinced that theism is true but assigns a low epistemic probability to Christianity should not practice Christianity.

Objection: Perhaps it is just as morally evil to fail to worship as God someone who is in fact God as it is to worship as God someone who is not. In that case, by not practicing Christianity, one also takes on a great moral risk, and perhaps the risks cancel out.

Response: I think it not just as morally evil to fail to worship as God someone who is in fact God. As far as we know, John the Baptist did not worship Jesus as God, but we have no reason to think that this was a great evil, on the par of idolatry.

Another way out of the closure argument

Consider this standard closure of the physical argument for physicalism (Papineau gives one very close to this):

1. Our conscious states have physical effects.

2. All physical effects are fully caused by physical causes.

3. There is (typically) no overdetermination.

4. So, our conscious states are (at least typically) physical.

Many dualists question (2), and epiphenomenalists question (1). But there is another move that seems to me to be promising.

When we say that our conscious states have physical effects, we don’t mean that our conscious states are the full causes of physical effects. Descartes himself would say that the movements of the particles in the pineal gland are partly caused by the conscious choice and partly caused by the prior state of the particles.

In other words, (1) just tells us that our conscious states are partial causes of physical effects. Given this, what (1)–(3) license us in concluding is only:

5. Our conscious states are (at least typically) parts of physical causes.

But to conclude from (5) that our conscious states are physical, it seems we need some premise like:

6. All the parts of physical things are physical.

But (6) is worth questioning. Note first that it is easier to find false than true cases of principles like:

7. All the parts of Fs are Fs

(E.g., electrons are parts of red things, but electrons aren’t red.) So why think (6) is true?

So, it seems that (6) needs some argument.

And in fact there are serious metaphysical views on which (6) is false. Consider, for instance, bundle theory: substances are bundles of properties. Well, rocks are physical objects, but a part of the bundle that makes up a rock will be the abstract entity of rockiness. But abstract entities aren’t physical.

Or take a reading (perhaps a misreading) of Leibniz on which physical objects are constituted by non-physical monads, and suppose that constituents count as parts.

Or, most promisingly, take Aristotle’s view on which all physical objects have form. Form is immaterial, and plausibly non-physical. Hylomorphism thus escapes the closure argument.

More generally, for all we know, the fundamental structure of reality is such that physically fundamental things are not ontologically fundamental but themselves have parts that are not physical.

Evan Rosa's interview with me

I just happened to come across an interview that Evan Rosa did with me about half a decade ago, when my One Body book came out. As far as I can tell, the interview was only posted last month.

Justice and gratitude

It is galling to be punished or even criticized unjustly. But it can also be galling to be rewarded or even praised unjustly. Over the past two years, two of my graduate students have received grants. They did all the work. But because of university policy, I had to be listed as the PI on the grants. And I’ve been getting multiple letters from the administration congratulating me on the grants. That’s galling.

I think God would be similarly galled if he were thanked for something he didn’t do, unless he did something just as good or better. And so God would have strong reason to act to ensure that such thanks would not be forthcoming.

Thus, we have reason to think that whatever people sincerely thank God for, God has either done that—or something at least as good—for them. In particular, we have reason to think that God has become incarnate and died for our sins or has done something at least as good.

Notice an interesting way that this argument makes available something like an implicit faith to non-Christian theists. For non-Christian theists also have reason to believe, on the strength of this argument, that God did something at least as good as what Christianity says he did, and to thank God for doing this. If they then thank God for "doing something at least this good", they would be implicitly thanking God for the Incarnation and Redemption, since in fact that is something God did that was "at least this good".

Dentistry, deontology, Double Effect and hypnosis

You are a dentist and a teenage Hitler comes to you to have a bad tooth removed. You only have available an anaesthetic with this feature: Within eight hours of the start of anaesthesia, a neutralizer must be given, otherwise the patient dies. This is not a problem: the extraction will only taken an hour.

You remove the tooth, and are about to administer the neutralizer when you learn that if Hitler survives, he will kill tens of millions of people. And now it seems you have a question whether to save the life of a person who will kill millions if saved. You apply the Principle of Double Effect and check whether the conditions are satisfied:

• Your end is good: Yup, saving the life of an innocent teenager.

• The action is good or neutral in itself: Yes, administering a neutralizer.

• The foreseen evils are not intended by you either as a means or as an end: Yes, you do not intend the deaths either as an end or as a means.

• The foreseen evil is not disproportionate to the intended good: Ah, here is the rub. How can the deaths of tens of millions not be disproportionate to the saving of the life of one?

So it seems that the Principle of Double Effect forbids you to administer the neutralizer, and you must allow Hitler to die. In so doing, you will be violating your professional code of ethics, and you will no doubt have to resign from the dental profession. But at least you won’t have done something that would cover the world with blood.

This is still counterintuitive to me. It feels wrong for a medical professional to deliberately stop mid-procedure in this way.

One can try soften the worry by thinking of other cases. Suppose that the neutralizer bottle has been linked by a terrorist to a bomb a mile away, so that picking up the bottle will result in the death of dozens of people. In that case it is clearly wrong for the dentist to complete the operation. But the Hitler case still feels different, because it is the very survival of Hitler that one doesn’t want to happen. It is a bit more like a case where the terrorist informs you that if the patient survives the procedure, the terrorist will kill many innocents. I still think that in that case you shouldn’t finish the procedure. But it’s a tough case.

Suppose you are with me so far. Now, here is a twist. You learn of Hitler’s future murders prior to the start of the procedure. You are the only dentist around. Should you perform the procedure?

Here are four possible courses of action:

1. You do nothing. The teenage Hitler suffers toothache for many a day, and then later on kills tens of millions.

2. You perform the extraction without anaesthesia. The teenage Hitler suffers excruciating pain, and then later on kills tens of millions.

3. You perform the procedure, including both anaesthesia and neutralizer. The teenage Hitler’s pain is relieved, but then later on he kills tens of millions.

4. You administer the anaesthesia, remove the bad tooth, and stop there. The teenage Hitler dies, but the world is a far better place.

Assume for simplicity that it is the same tens of millions who die in cases 1, 2 and 3.

So, now, which course of action should you intend to embark on? Option 4, while consequentialistically best, is not acceptable given correct deontology (if you are a consequentialist, the rest won’t be very interesting to you). For if you intend to go for Option 4, you will do so in order to kill Hitler by administering the anaesthesia while planning not to administer the neutralizer. And that’s wrong, because he is a juridically innocent teenager.

Option 3 seems clearly morally superior to Options 1 and 2. After all, one innocent person—the teenage Hitler—is better off in Option 3, and nobody is worse off there.

But you cannot morally go through with Option 3. For as soon as you’ve applied the anaesthesia, the Double Effect reasoning we went through above would prohibit you from applying the neutralizer. So Option 3 is not available to you if you expect to continue to act morally, because if you continue to act morally, you will be unable to administer the neutralizer.

What should you do? If you had a time-delay neutralizer, that would be the morally upright solution. You give the time-delay neutralizer, administer anaesthesia, remove the bad tooth, and you’re done. Tens of millions still die, but at least this innocent teenager won’t be suffering. It seems a little paradoxical that Option 3 is morally impossible, but if you tweak the order of the procedures by using a time-delay, you get things right. But there really is a difference between the time-delay case and Option 3. In Option 3, your administering the neutralizer kills tens of millions. But administering the time-delay neutralizer prior to the procedure doesn’t counterfactual results in the deaths of tens of millions, because had you not administered the time-delay neutralizer, you wouldn’t then administer the anaesthesia (Option 2) or you wouldn’t then perform the procedure at all (Option 1), and so tens of millions would still die.

Here is another interesting option. Suppose you could get yourself hypnotized so that as soon as the tooth is removed, you just find yourself administering the neutralizer with no choice on your part. That, I think, would be just like the time-delay neutralizer, and thus it seems permissible. But on the other hand, it seems that it is wrong to get yourself hypnotized to involuntarily do something that it would be wrong to do voluntarily, and to administer to Hitler the neutralizer after the anaesthesia is something that it would be wrong to do voluntarily. Perhaps, though, it is always wrong to get yourself hypnotized with the intention of taking away your of choice (maybe that’s a failure of respect for oneself)? Or maybe it is sometimes permissible to hypnotize yourself to involuntarily do something that it would be wrong to voluntarily do. (Here is a case that seems acceptable. You hypnotize yourself to involuntarily say: “I am now speaking involuntarily.” It would be a lie to say that voluntarily!)

Time and marriage

Consider this sequence of events:

• 2000: Alice marries Bob.

• 2010: Bob dies.

• 2020: Alice marries Carl.

• 2030: Alice and Carl invent time machine and travel to 2005 where they meet Bob.

Then, in 2005, Alice is married to Bob and Alice is married to Carl. But she is not a bigamist.

Hence, marriage is not defined by external times like 2005, but by internal times, like “the 55th year of Alice’s life”. To be a bigamist, one needs to be married to two different people at the same internal time. A marriage taken on at one internal time continues forward in the internal future.

And while we’re at it, the twin paradox shows that it is possible for two people to be married to each other and for one to have been married 10 years and the other to have been married 30 years. Again, it’s the internal time that matters for us.

Tropes of tropes

Suppose that x is F if and only if x has a trope of Fness as a part of it.

Here is a cute little problem. Suppose Jim is hurting and has a trope of pain, call it Pin. But Pin is an improper part of Pin. Thus, Pin has a trope of pain—namely itself—as a part of it, and hence Pin is hurting. Thus, wherever someone is hurting, there is something else hurting, too, namely their pain.

The standard move against “two many thinkers” moves is to say that one of them is thinking derivatively. But if we do that, then it looks like the fact that Jim is hurting is more likely to be derivative than the fact that Pin is hurting. For Jim hurts in virtue of having Pin as a part of it, while Pin hurts in virtue of having itself as a part of it, which seems a non-derivative way of hurting. But it seems wrong to say that Jim is hurting merely derivatively, so the real subject of the pain is Pin.

An easy solution is to say that x is F if and only if x has a trope of Fness as a proper part of it.

But this leads to an ugly regress. A trope is a trope, so it must have a trope of tropeness as a proper part of it. The trope of tropeness is also a trope, so it must then have another trope of tropeness as a proper part and so on. (This isn’t a problem if you allow improper parthood, as then you can arrest the regress: the trope of tropeness has itself as an improper part, and that’s it.)

One can, of course, solve the problem by saying that the trope theory only applies to substances: a substance x is F if and only if x has a trope of Fness as a proper part of it, while on the other hand, tropes can have attributes without these attributes being connected with the tropes having tropes. But that seems ad hoc.

As a believer in Aristotelian accidents and forms, which are both basically tropes, I need to face the problem, too. I have two ways out. First, maybe all tropes are causal powers. Then we can say that if “is F” predicates a power, then x is F if and only if x has a trope of Fness as a proper part. But for attribution of non-powers, we have a different story.

Second, maybe the relation between objects and their tropes is not parthood, but some other primitive relation. Some things stand in that relation to themselves (maybe, a trope of tropeness stands in that relation to itself) and others do not (Pin is not so related to itself). This multiplies primitive relations, but only if the relation of parthood is a primitive relation in the system.

I saw the ship of Theseus in Vancouver

An argument that motion doesn't supervene on positions at times

In yesterday’s post, I offered an argument by my son that multilocation is incompatible with the at-at theory of motion. Today, I want to offer an argument for a stronger conclusion: multilocation shows that motion does not even supervene on the positions of objects at times. In other words, there are two possible worlds with the same positions of objects at all times, in one of which there is motion and in the other there isn’t.

The argument has two versions. The first supposes that space and time are discrete, which certainly seems to be logically possible. Imagine a world w₁ where space is a two-dimensional grid, labeled with coordinates (x, y) where x and y are integers. Suppose there is only one object, a particle quadlocated at the points (0, 0), (1, 0), (0, 1) and (1, 1). These points define a square. Suppose that for all time, the particle, in all its four locations, continually moves around the square, one spatial step at a temporal step, in this pattern:

(0, 0)→(1, 0)→(1, 1)→(0, 1)→(0, 0).
Then at every moment of time the particle is located at the same four grid points. But it is also moving all the time.

But there is a very similar world, w₂, with the same grid and the same multilocated particle at the same four grid points, but where the particle doesn’t move. The positions of all the objects at all the times in w₁ and w₂ are the same, but w₁ has motion and w₂ does not.

Suppose you don’t think space and time can be discrete. Then I have another example, but it involves infinite multilocation. Imagine a world w₃ where the universe contains a circular clock face plus a particle X. None of the particles making up the clock face move. But the particle X uniformly moves clockwise around the edge of the clock face, taking 12 hours to do the full circle. Suppose, further, that X is infinitely multilocated, so that it is located at every point of the edge of the clock face. In all its locations X moves around the circle. Then at every moment of time the particle is located at the same point, and yet it is moving all the time.

Now imagine a very similar world w₄ with the same unmoving clock face and the same spacetime, but where the particle X is eternally still at every point on the edge of the clock face. Then w₃ and w₄ have the same object positions at all times, but there is motion in w₃ and not in w₄.

I think the at-at theorist’s best bet is just to deny that there is any difference between w₁ and w₂ or between w₃ and w₄. That’s a big bullet to bite, I think.

It would be nice if there were some way of adding causation to the at-at story to solve these problems. Maybe this observation would help: When the particle in w₁ moves from (0, 0) to (1, 0), maybe this has to be because something exercises a causal power to make a particle that was at (0, 0) be at (1, 0). But there is no such exercise of a causal power in w₂.

Bilocation and the at-at theory of time

I was telling my teenage children about the at-at theory of motion: an object moves if and only if it is in one location at one time and in another location at another time. And then my son asked me a really cool question: How does this fit with the possibility of being multiply located at one time?

The answer is it doesn’t. Imagine that Alice is bilocated between disjoint locations A and B, and does not move at either location between times t₁ and t₂. Nonetheless, by the at-at theory, Alice counts as moving: for at t₁ she is in location A while at t₂ she is in location B.

My response to my son was that this was the best argument I heard against the at-at theory. My son responded that the argument doesn’t work if multilocation is impossible. That’s true. But there is good reason to think bilocation is possible. First, the real presence of Christ in the Eucharist appears to require multilocation. Second, God is present everywhere, but never moves. Third, there is testimonial evidence to saints bilocating. Fourth, the argument only needs the logical possibility of bilocation. Fifth, time-travel would make it possible to stand beside oneself.

(The time-travel case is probably the least compelling, though, as an argument against the at-at theory. For the at-at theorist could say that the times in the definition of motion are internal times rather than external ones, and time travel only allows one to be in two places at one external time.)

I’ve been inclining to think the at-at theory is inadequate. Now I am pretty much convinced, but I am not sure what alternative to embrace.

One might just try to tweak the at-at theory. Perhaps we say that an object moves if and only if the set of its locations is different between times. But that isn’t right. Suppose Alice is bilocated between locations A and B at t₁, but at t₂ she ceases to bilocate, defaulting to being in location A. Then the set of locations at t₁ is {A, B} while at t₂ it is {A}. But Alice hasn’t moved: cessation of bilocation isn’t motion. Nor will it help to require that the sets of locations at the two times have the same cardinalities. For imagine that Alice is bilocated at locations A and B at t₁, and then she ceases to be located at B, defaulting to A, and walks over to location A′ at t₂. Then Alice has moved, but the sets of locations at t₁ and t₂ have different cardinalities. I don’t know that there is no tweak to the at-at theory that might do the job, but I haven’t found one.