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.

Scattered thoughts on self-identification

Among other things, I am a mathematician and a Wacoan. It is moderately important to my self-image, my “identity”, that I practice mathematics and that I live in Waco. But there is an important difference between the two contributions. My identifying as a mathematician also includes a certain kind of “fellow feeling” towards other mathematicians qua mathematicians, a feeling of belonging in a group, a feeling as of being part of a “we”. But while I love living in Waco, I do not actually have a similar “fellow feeling” towards other Wacoans qua Wacoans , a feeling as of being part of a “we” (perhaps I should). It’s just that I do not exemplify the civic friendship that Aristotle talks about.

An initial way of putting the distinction is this:

1. identifying with one’s possession of a quality versus identifying with being a member of the group of people who possess the quality.

This correctly highlights the fact that self-identification is hyperintensional, but it’s not quite right. Two finalists for some distinction can identify with being a member of the group of people who are finalists, and yet they need not—but can—have a “we”-type identification with this group.

It seems to me that the distinction I am after cannot be captured by egocentric facts about property possession. The “we”-type of identification is not a self-identification of oneself as having a certain quality. It seems to me that we have two different logical grammars of self-identification:

2. (a) identifying with one’s possession of a quality versus (b) identifying with the group of people who possess the quality.

I think some people go more easily from (a) to (b), and some people—including me—go less easily.

I wonder if it is possible to have (b) without (a). I don’t know, but I suspect one can. It may be that some herd animals have something like (b) without having anything like (a). So why couldn’t humans?

I think the move from (a) to (b) tends to be a good thing, as it is expressive of the good of sociality.

There are also second- and third-person analogues to (2):

3. (a) identifying a person with their possession of a quality versus (b) identify them with the group of people who possess the quality.

Regarding (b), I am reminded of Robert Nozick’s remark that people in romantic relationships want to be acknowledged as part of a “we”. In other words, people in romantic relationships want second- and third-person identification of them as part of the pair (a kind of group) of people in the particular relationship. I wonder if that’s possible without (a). Again, I am not sure.

I think 3(a) and 3(b) have a potential for being dangerous. One thinks of stereotyping here.

I think 2(a) and 2(b) also have a potential for danger, albeit a different one. The danger is that both kinds of self-identification lead to an inflexibility with respect to the quality or community. But sometimes we need to change qualities or communities, or they are changed on us. I suppose 2(a) and 2(b) are not so problematic with respect to qualities or groups that one ought to maintain oneself as having or belonging to (e.g., virtue or the Church).

Evil artifacts

Short version of my argument: Artifacts can be evil, but nothing existent can be evil, so artifacts do not exist.

Long version:

1. Paradigmatic instruments of torture are evil.

2. Nothing that exists is evil.

3. So, paradigmatic instruments of torture do not exist.

4. All non-living complex artifacts are ontologically on par.

5. Paradigmatic instruments of torture are inorganic complex artifacts.

6. So, non-living complex artifacts do not exist.

The argument for 1 is that paradigmatic instruments of torture are defined in part by their function, which function is evil.

The argument for 2 is:

7. Everything that exists is either God or created by God.

8. God is not evil.

9. Nothing created by God is evil.

10. So, nothing that exists is evil.

I think 4 is very plausible, and 5 is uncontroversial.

(My argument nihilism about artifacts is inspired by a rather different but also interesting theistic argument for the same conclusion that Trent Dougherty just sent me, but his argument did not talk of evil.)

Natural hope

One of the striking things to me about Aristotle is the pessimism. For instance, in Book IX of the Nicomachean Ethics, we’re told that vicious persons shouldn’t even love themselves, and that when one friend sufficiently outstrips another in moral excellence—whether through the one improving or the other declining—the friendship must be dropped. I do not see the virtue of hope in Aristotle, say, hope that the vicious may improve, too. For the wicked, there is just despair. (Aristotle’s odious doctrine of “natural slavery” has some similarities.)

Christianity, on the hand, professes hope to be a virtue. But the hope that Christianity talks of is a supernatural infused virtue, a virtue that comes only as a gift of God’s grace. And Aristotle, of course, is interested in the natural virtues.

But grace builds on nature. So one would expect there to be a natural counterpart to the supernatural virtue of hope. Compare how there are natural loves that are a counterpart to the supernatural virtue of charity. There should be a natural virtue of hope, too.

But given the dark empirical facts about humanity, a habit of hope apart from grace would seem to be an irrational optimism rather than a virtue.

Perhaps, though, there is something in between irrational optimism and supernatural hope: perhaps there is room for a hope grounded in natural theology. Natural theology teaches that there is a perfectly good God. Yet there is so much that is awful in the world. But given theism there is good reason to think that the future will bring something better, and hence there is a natural justification for hope.

I am not sure I want to say that natural hope requires actual belief in God. But for that hope to be a virtue and (hence) a part of a rational state of mind, it may well require that the hoping individual be in an epistemic position to rationally believe. Thus, for natural hope to be a virtue seems to require that hopers be in a position to believe that there is a God.

Aristotle, of course, did believe in a God, or gods. But these gods were uninvolved with human affairs, and hence not a good ground for hope.

Reflecting on the above, it seems to me that to overcome the pessimism of Aristotle, one needs more than just a remote hope, but a seriously robust hope.

Calling for an explanation

If I am playing a board game and the last ten rolls of my die were 1, that calls out for an explanation. If only Jewish and Ethiopian people get Tay-Sachs disease, that calls out for an explanation.

It seems right to say that

1. a fact calls out for an explanation provided it is the sort of fact that we would expect to have an explanation, a fact whose nature is such that it "should" have an explanation, a fact such that we would be disappointed in reality in not having an explanation of.

But now consider two boring facts:

2. 44877 x 5757 = 258356889
3. Bob is wearing a shirt

These are facts that we all expect to have an explanation (e.g., the explanation of (2) is long and boring, involving many instance of the distributive law and the explanation of (3) presumably has to do with psychosocial and physical facts). They are, moreover, facts that "should" have an explanation. There would be something seriously wrong with logic itself if a complex multiplication fact had no explanation (it's certainly not a candidate for being a Goedelian unprovable truth), and with reality if people wore shirts for no reason at all.

So by (1), these would have to be facts that call out for an explanation. But I don't hear their cry. I am confident that they have explanations, but I wouldn't say that they call out for them. So it doesn't seem that (1) captures the concept of calling out for an explanation.

As I reflect on cases, it seems to me that calling out for an explanation has something to do with the intellectual desirability of having an explanation rather. Someone with a healthy level of curiosity would want to know why the last ten rolls were 1 or why only Jewish and Ethiopian people get Tay-Sachs. On the other hand, while I'm confident that there is a fine mathematical reason why 44877 x 5757 = 258356889, I have no desire to know that reason, even though I have at least a healthy degree of curiosity about mathematics.

This suggests to me an anthropocentric (and degreed) story like the following:

4. A fact calls out for an explanation to the degree that one would be intellectually unfulfilled in not knowing an explanation.

It is sometimes said that a fact's calling out for an explanation is evidence that it has an explanation. I think (4) coheres with this. That something is needed for our fulfillment is evidence that the thing is possible. For beings tend to be capable of fulfillment. (This is a kind of cosmic optimism. No doubt connected to theism, but in what direction the connection runs needs investigation.)

Generate bookmarklet dynamically from gist

Let's say you want to make some bookmarklets be available to readers of your website and you want to be able to update them conveniently without having to re-encode your javascript into a bookmarklet and edit your website html. Here's a simple method. Post the bookmarklet on gist.github.com, and then edit and use the following html/javascript code to fetch the javascript and automatically generate a bookmarklet:

<p>My bookmarklet is here: <a href="__error__" id="myBookmarklet1">My Bookmarklet</a>.</p>
<script>
var linkId = "myBookmarklet1";
var gistLink = "https://gist.githubusercontent.com/arpruss/74abc1bc95ae08e543b9b74f15a23b07/raw";
fetch(gistLink).then(function(response) {
    if (!response.ok) {
        //alert("Error fetching "+response.statusText);
    }
    else {
        response.text().then(function(text) {
            var link = document.getElementById(linkId);
            link.href = "javascript:"+encodeURIComponent("(function(){"+text+"})()");
        });
    }
}); 
</script>

For a live example, see my previous post.

Fix aspect ratio of online videos

My wife and I were watching Mr. Palfrey of Westminster on Acorn, and the aspect ratio on s2e1 was 11% off. It was really annoying me (especially before I realized it was just that one episode that was bad). So I wrote a little bookmarklet to adjust the aspect ratio of all html5 videos in a web page.

Here it is: Stretch Video.

To use it, drag it from the above link to your browser’s bookmark bar (which you can show and hide in Chrome with shift-ctrl-b). Then when you have the video on your screen, click on the bookmark and enter the horizontal and vertical stretch ratios, or the correct aspect ratio.

For full-screen video, try first resizing and then switching to full-screen (on some websites, like YouTube, there will be a one second delay before the video stretches on full-screen toggle). (On Firefox, you can also pull up bookmarks in full-screen mode with shift-ctrl-b, which helps.)

To cancel the effect, just reload your video page.

And for fun, here is a Video Rate bookmarklet (we wouldn't want to treat space very differently from time, would we?).

Public domain source code is here.

Mathematical structures, physics and Bayesian epistemology

It seems that every mathematical structure (there are some technicalities as to how to define it) could metaphysically be the correct description of fundamental physical structure. This means that making Bayesianism be the whole story about epistemology—even for idealized agents—is a hopeless endeavor. For there is no hope for an epistemologically useful probability measure over the collection of all mathematical structures unless we rule out the vast majority of structures as having zero probability.

A natural law or divine command epistemology can solve this problem by requiring us to assign zero probability to some non-actual physical structures that are metaphysically possible but that our Creator wants us to be able to rule out a priori. In other words, our Creator can make us so that we only take epistemically seriously a small subset of the possibilia. This might help with the problem of scepticism, too.

Two puzzles about pain and time

Supposing the growing block theory of time is correct and you have a choice between two options.

1. You suffer 60 minutes of pain from 10:30 pm to 11:30 pm.
2. You suffer 65 minutes of pain from 10:50 pm to 11:55 pm.

Clearly, all other things being equal, it is irrational to opt for B. But supposing growing block theory is true, there are only past and present pains, and no future pains, so why is it irrational to opt for B?

Well, maybe rationality calls on us to make future reality be better, and we have:

1. If you opt for A, then at 11:55 reality will contain 60 minutes of pain

2. If you opt for B, then at 11:55 reality will contain 65 minutes of pain.

Opting for B will make reality worse (for you) at 11:55, so it seems irrational to choose B. However, we also have facts like these:

3. If you opt for A, then at 11:30 reality will contain 60 minutes of pain.

4. If you opt for B, then at 11:30 reality will contain 55 minutes of pain.

Thus, opting for A will make reality worse at 11:30. Why should the 11:55 comparison trump the 11:30 comparison?

One answer is this: The 11:55 comparison continues forever. If you choose B, then reality tomorrow, the day after tomorrow, and so on will be worse than if you choose B, as on all these days reality will contain the 65 minutes of past pain instead of the mere 60 minutes if you choose A.

However, this answer isn’t the true explanation. For suppose time comes to an end tonight at midnight. Then it’s still just as obvious that you should opt for A instead of B. However, now, it is only during the ten minute period after 11:50 pm and before midnight that reality-on-B is worse than reality-on-A, while reality-on-A is better than reality-on-B during the whole of the 80 minute period strictly between 10:30 pm and 11:50 pm. It is mysterious why the comparison during the 10 minute period starting 11:50 pm should trump the comparison during the 80 minute period ending at 11:50 pm.

I suppose the growing blocker’s best bet is to say that later comparisons always trump earlier ones. It is mysterious why this is the case, though.

The story is also puzzling for the presentist, as I discuss here. But there is no problem for the eternalist: on B reality always contains more pain than on A.

However, there is a different puzzle where the growing blocker can tell a better story than the eternalist. Suppose you will live forever, and your choice is between:

3. You will feel pain from 10 pm to 11 pm every day starting tomorrow
4. You will feel pain from 9 am to 11 am every day starting tomorrow.

Intuitively, you should go for C rather than D. But on eternalism, on both C and D reality includes an equal infinite number of hours of pain. But on growing block, after 9 am tomorrow, reality will be worse for you if you choose D rather than C. Indeed, at every time after 9 am, on option D reality will contain at least twice as much pain for you as on option C (bracketing any pains prior to 9 am tomorrow). So it’s very intuitive that on growing block you should choose C.

Maybe, though, the eternalist can say that utility comparisons involving infinities just are going to be counterintuitive because infinities are innately counterintuitive, as our intuitions are designed/evolved for dealing with finite cases. Moreover, we can tell similar puzzles involving infinities without involving theories of time. For instance, suppose an infinite line of people numbered 1,2,3,…, all of whom are suffering headaches, and you have a choice whether to relieve the headache of the persons whose number is even versus the headache of the persons whose number is prime. The intuition that C is better than D seems to be exactly parallel to the intuition that it’s better to benefit the even-numbered rather than the prime-numbered. But the latter intuition is not defensible. (Imagine reordering the people so now the formerly prime-numbered are even-numbered and vice-versa. Surely such a reordering shouldn’t make any moral difference.) So perhaps we need to give up the intuition that C is better than D?

An argument for theism from certain values

Some things, such as human life, love, the arts and humor, are very valuable. An interesting question to ask is why they are so valuable?

A potential answer is that they have their value because we value (desire, prefer, etc.) them. While some things may be valuable because we value them, neither life, love, the arts nor humor seem to be such. People who fail to value these things is insensitive: they are failing to recognize the great value that is there. (In general, I suspect that nothing of high value has the value it does because we value it: our ability to make things valuable by valuing them is limited to things of low and moderate value.)

A different answer is that these things are necessarily valuable. However, while this may be true, it shifts the explanatory burden to asking why they are necessarily valuable. For simplicity, I’ll thus ignore the necessity answer.

It may be that there are things that are fundamentally valuable, whose value is self-explanatory. Perhaps life and love are like that: maybe there is no more a mystery as to why life or love is valuable than as to why 1=1. Maybe.

But the arts at least do not seem to be like this. It is puzzling why arranging a sequence of typically false sentences into a narrative can make for something with great value. It is puzzling why representing aspects of the world—either of the concrete or the abstract world—in paint on canvas can so often be valuable. The value of the arts is not self-explanatory.

Theism can provide an explanation of this puzzling value: Artistic activity reflects God’s creative activity, and God is the ultimate good. Given theism it is not surprising that the arts are of great value. There is something divine about them.

Humor is, I think, even more puzzling. Humor deflates our pretensions. Why is this so valuable? Here, I think, the theist has a nice answer: We are infinitely less than God, so deflating our pretensions puts us human beings in the right place in reality.

There is much more to be said about arts and humor. The above is meant to be very sketchy. My interest here is not to defend the specific arguments from the value of the arts and humor, but to illustrate arguments from value that appear to be a newish kind of theistic argument.

These arguments are like design arguments in that their focus is on explaining good features of the world. But while design arguments, such as the argument from beauty or the fine-tuning argument, seek an explanation of why various very good features occur, these kinds of value arguments seek an explanation of why certain features are in fact as good as they are.

The moral argument for theism is closely akin. While in the above arguments, one seeks to explain why some things have the degree of value they do, the moral argument can be put as asking for an explanation of why some things (more precisely, some actions) have the kind of value they do, namely deontic value.

Closing remarks

1. Just as in the moral case, there is a natural law story that shifts the argument’s focus without destroying the argument for theism. In the moral case, the natural law story explains why some actions are obligatory by saying that they violate the prescriptions for action in our nature. But one can still ask why there are beings with a nature with these prescriptions and not others. Why is it that, as far as we can tell, there are rational beings whose nature prescribes love for neighbor and none whose nature prescribes hatred for neighbor? Similarly, we can say that humor is highly valuable for us because our nature specifies humor as one of the things that significantly fulfills us. (Variant: Humor is highly valuable for us because it is our nature to highly value it.) But we can still ask why there are rational beings whose nature is fulfilled by the arts and humor, and, as far as we can tell, none whose nature is harmed by the arts or humor. And in both the deontic and non-deontic cases, there is a theistic answer. For instance, God creates rational beings with a nature that calls on them to laugh because any beings that he would create will be infinitely less than God and hence their sensor humor will help put them in the right place, thereby counteracting the self-aggrandizement that reflection on one’s own rationality would otherwise lead to.

2. Just as in the moral case there is a compelling argument from knowledge—theism provides a particularly attractive explanation of how we know moral truths—so too in the value cases there is a similar compelling argument.

Exemplify: An oral word game for friends and family

For some years now, my big kids and I have occasionally played a game we call Exemplify. It works great for three people on a walk. The basic idea is that we each contribute an adjective (e.g., “slurping”, “slimy” and “absurd”, or “chunky”, “soft” and “stinky”), then we each contribute a substantive that goes nicely with all three (or as many as one can) of the adjectives (e.g., “Jabba at DQ” or “cheese”), ideally in a funny and creative way, and then we each vote which of the others’ contributions is best, with the winner being the one that has the most votes. It’s fun.

When I was inventing the game, I was influenced by Dixit and Apples to Apples.

Rules (version 1.01)

The following rules are for three or four players.

Each round goes as follows:

1. Each player independently thinks of an adjective and announces when they have thought of it. The adjective must be a single unhyphenated word of English.

2. Once each player has an adjective, all adjectives are disclosed. No player is allowed to change their adjective once the disclosures have begun.

3. Each player independently thinks of a substantive and announces once they have it. The substantive can be one to three words of English, with hyphenation counting as a word break (“horse-shaped” is two words). Proper names and acronyms that are normally usable in speech (e.g., “USA”) are allowed.

4. Once each player has a substantive, all substantives are announced. No player is allowed to change their substantive once the disclosures have begun.

5. If two or more players have the same substantive, they automatically lose the round.

6. Each player independently thinks of a vote for a substantive by one of the other players (not a duplicate that resulted in an automatic loss) and announces once they have it. The voters are recommended to use these criteria: humor, creativity, distance from the actual world (more realistic is better) or from the actual world’s works of fiction, number of adjectives matched, and brevity. There are at least two ways the substantive can go with the adjectives: either the adjectives can be expected to apply to the thing described by the substantive (Jabba at DQ can be expected to be slurping, slimy and absurd) or else the adjectives and the substantive can form a fairly natural unit (“chunky, soft and stinky cheese” seems a natural unit).

7. Once each player has a vote, all votes are announced. No player is allowed to change their vote once the disclosures have begun.

8. If one player has more votes than any other player, they get two points. In that case, the player or players in second place in the voting each get one point. If no player has more votes than any other player, then the players tied for first place in the voting each get one point. But players who have lost by dint of duplication get no points.

The game continues to a set number of points, by default 10. Each player keeps track of their scores.

Additional required rules:

1. No substantive discussion of the adjectives, substantives or votes, respectively, is permitted prior to all the players having made their decisions.

2. The adjectives and substantives cannot be disambiguated or clarified except by their spelling.

3. Players may request for repeats of adjectives and substantives as many times as they wish.

Variations:

1. If the players are not fully trusting, or in a serious competition, the adjectives, substantives or votes are secretly written out and then revealed to prevent changes in response to others. Scores are written down.

2. With two players, scoring is not possible, but one can still have some fun.

3. With four players, one can either play according to the above rules (and thus have the challenge of four adjectives), or have one of the four players omit an adjective each round, rotating which player that is in a fixed order (by default, alphabetically by bibliographic order—last name and first name). One can similarly extended to more than four players, by omitting enough players each time to reduce the number of adjectives to three or four, using a more complex rotation rule if need be.

4. For simpler score-keeping, one can award one point only to the player who got the most points (if there is such a player; otherwise, no points are awarded).

World shuffling and quantifiers

Let ψ be a non-trivial one-to-one map from all worlds to all worlds. (By non-trivial, I mean that there is a w such that ψ(w)≠w.) We now have an alternate interpretation of all sentences. Namely, if I is our “standard” method of interpreting sentences of our favorite language, we have a reinterpretation I_ψ where a sentence s reinterpreted under I_ψ is true at a world w if and only if s interpreted under I is true at ψ(w). Basically, under I_ψ, s says that s correctly describes ψ(actual world).

Under the reinterpretation I_ψ all logical relations between sentences are preserved. So, we have here a familiar Putnam-style argument that the logical relations between sentences do not determine the meanings of the sentences. And if we suppose that ψ leaves fixed the actual world, as we surely can, the argument also shows that truth plus the logical relations between sentences do not determine meanings. Moreover, can suppose that ψ is a probability preserving map. If so, then all probabilistic relations between sentences will be preserved, and hence the meanings of sentences are not determined by truth and the probabilistic and logical relations between sentences. This is all familiar ground.

But here is the application that I want. Apply the above to English with its intended interpretation. This results in a language English^* that is syntactically and logically just like English but where the intended interpretation is weird. The homophones of the English existential and universal quantifiers in English^* behave logically in the same way, but they are not in fact the familiar quantifiers. Hence quantifiers are not defined by their logical relations. I’ve been looking for a simple argument to show this, and this is about as simple as can be.

Existential quantifiers aren't defined by their logic

Start with a first order language L describing the concrete objects of our world and expand L to a language L^* by adding a new name “obump”. Given an interpretation I of L in a model M, create a model M^* such that:

• The domain of M^* is the domain of M with one more object, o, in its domain.

• The non-unary relations of M^* are the same as those of M, except that I(=) is replaced by a new relation J = I(=)∪{(o, o)}.

• The unary relations of M^* are all and only the relations R^* for R a unary relation of M, where R^* = R ∪ {o} if R is equal to I(F) either for a physical predicate F of L such that I(trump)∈I(F) or for a mental predicate F of L such that I(obama)∈I(F) and R^* = R otherwise.

Define the interpretation I^* of L^* in M^* as follows: I^*(a)=I(a) for any name other than obump, I^*(obump)=o, I^*(F)=(I(F))^* for a unary F, and I^*(F)=I(F) for any non-unary F.

We can now give a semantics for L^*: If I_w is the intended interpretation of L in a world w, then the intended interpretation of L^* in w is given by I_w^*. We can define validity for L in an analogous way.

The symbols ∃ and ∀ of L^* have the same logic as the same symbols of L. But the ∃ of L^* is not really an existential quantifier. For if it were, then it would be true that there exists an entity that has all the mental properties of Obama and all the physical properties of Trump, which is false. Thus, logic is not sufficient to make a symbol be an existential quantifier.

Physical and psychological pain

In English, we have a category “pain” which we subdivide into the “physical” and the “psychological”. But this taxonomy is misleading.

Consider the experiences of eating some intensely distasteful food—once as a kid I added chocolate chips to my tomato soup and it was awful—or of smelling a really nasty odor. These sensations are not pains. But, phenomenologically, the difference between these unpleasantness experiences and the physical pains does not seem greater than the difference between some of the psychological pains and the physical pains.

Reflection on the phenomenology does not, I think, reveal any good reason to classify physical pains and psychological pains in one natural category and the experiences of nasty taste or smell in another.

Nor does there seem to be any good reason to classify this way when one thinks of what the representational content of the experiences is. Physical pains seem to represent our body as damaged. Psychological pains seem to represent complex external states of affairs as bad, particularly in relation to ourselves. And bad taste seems to represent a food as bad for us. There is a common core in all these cases, and there does not seem to be a tighter common core to the physical and psychological pains taken as a unit.

Thus it seems to me that having a category of pain that includes physical and psychological pains but excludes the other unpleasant experiences I mentioned is like having a biological category of bovinoequines that comprises cows and horses but excludes donkeys. It’s just not a natural taxonomy, and unnatural taxonomies can mislead one in reflection.

I propose that the natural category here is the unpleasant, under which fall most physical pains, most psychological pains and a large host of other experiences. But there seem to be such things as pleasant or at least not unpleasant pains.)

One can have suffering without pain—I suffered when I had the soup with cholocate chips, but it didn’t hurt (except my pride in my culinary ideas). One can have pain without suffering. So the tie between pain and suffering is not very tight. But perhaps there is a tighter connection between suffering and the unpleasant. I now have two options that are worth exploring, both quite simple:

• suffering is unpleasantness

• suffering is significant unpleasantness.

We can talk of physical pains and psychological pains, but we need to be careful not to be misled by the repetition of the word “pain” into thinking there is a natural category that includes just these two subcategories of pains but excludes the others.

How do we divide up the unpleasant? One way is to base things on the representational content. Maybe all of the unpleasant represents a state of affairs as bad, but we can subdivide the bads. Here are some potentially natural subdivisions of bads:

• to self vs. not to self (more precisely: qua to self vs. not qua to self)

• non-instrumental vs. instrumental

• intrinsic vs. relational

• actual vs. potential

• past vs. present vs. future

• bodily vs. mental.

We get something a little bit like the English category of “pain” if we consider unpleasantness that represents non-instrumental intrinsic actual present bad to self. But not quite: many psychological pains are backward looking, and some are complex experiences that include components of representing bads to others.

"Commitment": Phenomenology at the rock wall

If you watch people rock climbing enough (in my case, only in the gym, as I have seen disturbing outdoor climbing safety numbers, while gym climbing safety numbers are excellent), you will hear a climber get advised to “commit” more. The context is usually a dynamic move for a hold, one where the climber’s momentum is essential to getting into position to secure the hold, with the paradigm example being a literal jump. The main physiological brunt of the advice to “commit” is to put greater focused effort into jumping higher, reaching further, grabbing more strongly, etc. But the phenomenological brunt of the advice is to will more strongly, with greater, well, commitment. And sometimes when one misses a move, one feels the miss as due to a lack of commitment, a failure to will strongly enough.

While once I heard someone at the gym say “Commit like you’re married to it”, the notion of commitment here seems quite different from the ordinary notion tied to relationships and long-term projects. The most obvious difference is that of time. In the ordinary case, a central component of commitment is a willingness to stick to something for an extended period of time. The climber’s “commitment” lasts at most a second or two. This results in what seems to be a qualitatively different phenomenology, but it could still be that the difference is quantitative, much as living through a week and living through a second only feels qualitatively different.

But there seems to be a more obviously qualitative difference. The rock-climbing sense of “commit” is essentially occurrent: there is an actual expending of effort. But the ordinary sense is largely dispositional: one would expend the effort if it were called for. Moreover, the rock-climbing sense of the word is typically tied to near-maximal effort, while in the ordinary sense one counts as committed to a project as long as one is willing to expend a reasonable amount of effort. In other words, when it would be unreasonable to expend a certain degree of effort, in the ordinary sense of the word one is not falling short of commitment: the employee unwilling to sacrifice a marriage to the job is not short on commitment to the job. The rock-climbing sense of commitment is not tied to reasonableness: a climber who holds back on a move out of a reasonable judgment that near-maximal effort would be too likely to result in an injury is failing to commit on the move—and typically is doing the right thing under the circumstances (of course in both sense of the word “commit”, there are times when failure to commit is the right thing to do).

Finally, the ordinary sense of divides into normative and non-normative commitment. Normative commitment is a kind of promise—implicit perhaps—while non-normative commitment is an actual dispositional state. Each can exist without the other (though it is typically vicious when the normative exists without the dispositional). In the climbing case, normally the normative component is missing: one hasn’t done anything promise-like.

Here is a puzzle. Bracket the cases where one holds back to avoid an over-use or impact injury (I would guess, without actually looking up the medical data, that when one is expanding more effort, one is more tense and injury is likely to be worse). One also understands why someone might fail to commit to a job or a relationship, in either the normative or the non-normative sense: a better thing might come one’s way. But when one is in the middle of a strenous climbing move, one typically isn’t thinking that one might have something better one could do with this second of one’s time. So: Why would someone fail to commit?

My phenomenology answers in two ways. First and foremost, fear of failure. This is rationally puzzling. One knows that a failure to commit to a climbing move increases the probability of failure. So at first sight, it seems like someone who goes to a dog show out of a fear of dogs (which is different from the understandable case of someone who goes to a dog show because of a fear of dogs, e.g., in order to fight the fear or in order to have a scary experience). But I think there is actually something potentially rational here. There are two senses of failure. One sense is external: one is failing to meet some outside standard. The second sense is internal to action: one is failing to do what one is trying to do. The two can be at cross-purposes: if I have decided to throw a table tennis match, my gaining a point can be a failure in the action-internal sense but is a success in the external sense.

In climbing, outside of competitive settings, it is the action-internal sense that tends to be more salient: we set our own goals, and what constitutes them as our goals is our willing of them. Is my goal to climb this route, to see how hard it is, or just to get some exercise? It’s all in what I am trying to do.

But in the action-internal sense, generally the badness of a failure increases with the degree to which one is trying. If I am not trying very hard, my failure is not very bad in the action-internal sense. (Of course, in some cases, my failure to try very hard might bad in some external sense, even a moral one—but it might not be.) So by trying less hard, one is minimizing the badness of a failure. There is a complex rational calculus here, whether or not one takes into account risk averseness. It is easy to see how one might decide, correctly or not, that giving significantly less than one’s greatest effort is the best option (and this is true even without risk averseness).

The secondary, but also interesting, reason that my phenomenology gives for a refusal to commit is that effort can be hard and unpleasant.