Wednesday, June 13, 2018

Two open-ended cosmological argument

First argument:

  1. There are no infinite causal regresses or causal loops.

  2. Every ordinary entity has a cause.

  3. So, there is an extraordinary entity.

Second argument:

  1. There is a causal explanation why there are any ordinary entities.

  2. Causal explanations are not circular.

  3. So, there is an extraordinary entity.

Tuesday, June 12, 2018

Yet another counterexample to Nicod's Principle

Nicod’s Principle says that the claim that all Fs are Gs is confirmed by each instance.

Here’s yet another counterexample. Consider the claim:

  1. All unicorns are male.

We take this claim to be true, albeit vacuously so, since there are no unicorns.

But suppose an instance of (1), namely a male unicorn, were found. We would immediately conclude that (1) is probably false. For if there is a male unicorn, likely there is a female one as well.

The problem here is that when we learn of Sam that it is a male unicorn, we also learn that there are unicorns. And as soon as we learned that there are unicorns, that undercut the reason we had for believing (1), namely that we thought (1) was vacuously true.

Sunday, June 10, 2018

Slavery, forced marriage and unjust laws

Slavery is the ownership of one person by another. Since a person no more owns another than a thief owns the purloined goods, there has never been any slavery. But of course there have been institutions thought to be slavery: institutions in which a person was thought to be the property of another. These were not institutions of slavery in the above strict sense but forms of unjust imprisonment, kidnapping, etc.

This seems to be merely a point about words, and a mistaken one at that. “Of course, Alexander II ended serfdom in Russia while Lincoln ended slavery in the US. Words mean what they are used to mean, and to dispute historical claims like these is to be like the fusty grammarian who claims that ‘It’s me’ is bad English.”

I agree that the question of words is unimportant. But here is what is important. Institutions are defined in large part by their norms. It is a defining feature of the norms of slavery (and, with some differences, of serfdom) that one person has property-style rights over another who has onerous obligations corresponding to these rights. But in fact, nobody has such rights over another, and the supposed obligations do not obtain. The institution that the “masters” saw themselves as a part of did not in fact exist, because the rights and obligations that they took to be integral to the institution did not, and could not, in fact exist.

We can use the term “slavery” (and cognates in other languages) for that non-existent institution, just as we use the term “phlogiston” for the substance that chemists mistakenly believed in before oxygen was discovered.

But we could also use distinguish and use two terms. Maybe slaveryh is the historical form of social organization that actually (and deplorably) existed and slaveryn is the normative institution that the mastersh (and maybe some of the slavesh, as well) incorrectly thought to exist and thought to be coextensive with slaveryh.

Again, the words don’t matter, but it matters that there was a morally condemnable attempt to create a certain social institution which attempt failed because the norms that were attempted to be instituted were incapable of institution.

This is a pattern we find in many other cases. There is no such thing as a forced marriage, since the norms of love and sexuality that define marriage do not come into existence apart from the free consent of the parties. But of course over the course of history there have been morally condemnable attempts to force people—especially women—into the institution of marriage. These attempts always failed, and what the victims were forced into was a different institution, one subjecting them to such injustices as kidnapping, unjust imprisonment, rape, etc.

Thomas Aquinas, similarly, holds that there are no unjust laws. Of course, legislators may attempt to enact laws that would be unjust (or they may simply be exercising power and not even trying to legislate). But when they do so, they fail to enact laws. What they enact are mere demands masquarading as laws (philosophical anarchists think all “laws” are like that). Again, the question of words is unimportant, but what is important is the pattern: the legislator is deplorably attempting to create a social institution—a law—and failing to do so, but instead creating another institution.

The particular cases of this pattern are interesting, and so is the pattern itself. A central part of the pattern is an attempt to create an institution (or an instance of an institution) that misfires, and instead another institution is created that is widely but mistakenly thought to be the one that was the target of the attempt. But the cases of slavery, forced marriage and unjust laws also share another feature that not all the cases of misfiring do. For instance, suppose due to an honest mistake in the counting of ballots, there is a mistake as to who the mayor of a town is. The false mayor then attempts to legislate something quite just. The attempt fails, because the false mayor lacks the standing to legislate. But there need be nothing morally deplorable here, as there is in the slavery, forced marriage and unjust law cases.

Moreover, the three cases I started with are not just morally deplorable, but there seems to be an important connection between moral evil and performative misfire. Slaveryh is morally horrific, but slaveryn would be even worse, as the slavesn would be under genuine obligations to do the enforced labor required of them and not to escape. This would, as it were, make morality itself complicit with the master, and the properly formed conscience of the slave into a whip in the master’s hand. And the same holds in the other two cases: morality itself would be a tool of oppression.

There are, alas, times when morality is a tool of oppression. The duties that exist between relatives are frequently exploited by repressive regimes as a means of social control: If you are an Uyghur or Tibetan defecting to a free country and speaking out against the Chinese regime, your relatives back home will suffer, and this restricts your activity because of the duties you have to your relatives. But the kinds of cases where the wicked use morality as a lever against the righteous seem different and less direct from what would be the case if slavery, forced marriage and unjust laws had the normative force that they pretend to. It is a mere coincidental effect of duties to family when these duties make it morally impossible or difficult to stand up to a wicked regime. But it would be of the very nature of the norms induced by slavery, forced marriage and unjust laws—if these norms really came into existence—that they would oppress.

This still leaves an interesting puzzle, which different moral theories will answer differently: Why is it the case that morality does not innately oppress?

Objection: Maybe slaveryh does create norms, but not moral norms.

Response: I myself don’t think there are any non-moral norms. But in any case slaveryh does not create any kind of obligation on the slave to obey the master, whether moral or not, except in some, but not all, cases a prudential one.

Thursday, June 7, 2018

The search for new truths

I know that I have two hands. With a bit of thought, I now know a number of truths that it seems no ordinary person has ever known before:

  • I have two hands or there is a palomino painted green and pink with someone in a Darth Vader costume on its back.

  • I have two hands or the number of pigs born in 1745 is odd.

  • I have two hands or Sir Patrick Stewart will consume a prime number of calories tomorrow.

  • I have two hands or Donald Trump issued a series of anti-Klingon tweets yesterday.

And so on, ad infinitum. The search for new truths is thus really easy. I just need to search for silly propositions that no one has thought about, and disjoin them with something I know.

External time as such doesn't matter to us

Suppose a deity threatened to move us all to a universe where everything is pretty much as in our world, except that electric charges are reversed and the laws of nature are tweaked to ensure that this reverse doesn’t affect our lives. Thus, in that world, we are based not on carbon atoms, but on anti-carbon anti-atoms (they will have six anti-protons and six positrons, etc.), but the laws are tweaked so that the anti-atoms would behave just like atoms.

Assuming we can survive the shift, it seems that except for sentimental considerations (maybe when Grandma’s old wedding ring is replaced by a ring of anti-gold, it’s no longer the same ring) it would make no difference to us.

Similarly, if the deity threatened to spatially rotate the world by 180 degrees around some axis, that would make no difference to us.

What if the deity offered to rotate our world in time by 180 degrees, with causation now running temporally backwards, with us being born in the future and dying in the past, but everything being kept intact. It seems to me that this would make no difference to us.

Similarly, it seems to me that if the deity offered to rotate our four-dimensional world so that the temporal dimension and a spatial dimension were swapped, so that we would be born and die at the same time, but in different places along a spatial axis, and causation would run unidirectionally along the spatial axis, again that would make no difference to us.

I think these thought experiments suggest that external time as such is not important. What matters is how the distribution of things interacts with the causal order.

To be honest, though, I am not completely confident that any of these thought experiments make sense. It could be that any dimension along which causation runs much as causation runs along the temporal direction in our world is therefore a time dimension. But if so, then I think it's still true that it is causation, not external time as such, that matters.

I am less confident of this in the case of internal time.

Wednesday, June 6, 2018

Disembodied trees

Here’s an interesting thesis:

  1. If x has the ys among its parts, and for each z among the ys, x can survive losing z without gaining anything, then x can survive simultaneously losing all the ys without gaining anything.

There are obvious apparent counterexamples. A boat that has sufficient redundancy can survive the loss of any plank, but cannot survive losing them all. An oak tree can lose any cell but cannot lose all cells.

But counterexamples aside, wouldn’t (1) be a nice metaphysical thesis to have? Then essential parts wouldn’t be made of inessential ones. You can see all the nasty ship-of-Theseus questions that would disappear if we had (1).

I think an Aristotelian can embrace (1), and can get around the counterexamples by biting some big bullets. First, like some contemporary Aristotelians, she can deny that artifacts like boats (or bullets) exist. Second, she can say that oak trees can survive the loss of all their matter, becoming constituted by form alone, much as some philosophers say happens to human beings after death (before the resurrection). The second part seems a bigger bullet to bite, as one would need a story as to why in fact oak trees perish when they lose all their cells, even if they don’t have to. But perhaps that’s just contingently how it happens, though an all powerful being could make an oak tree survive the destruction of all its cells.

The big question here is exactly what philosophical advantages embracing (1) has.

Monday, June 4, 2018

Distinguishing between properties

Some philosophers worry about “principles of individuation” that make two things of one kind be different from another. Suppose we share that worry. Then we should be worried about Platonism. For it is very hard to say what make two fundamental Platonic entities of the same sort different, say being positively charged from being negatively charged, or saltiness from sweetness.

However, the light-weight Platonist, who denies that predication is to be grounded in possession of universals, has a nice story to tell about the above kinds of cases. For here is a qualitative difference between saltiness and sweetness:

  • saltiness is necessarily had by all and only salty things, but

  • sweetness is not necessarily had by all and only salty things.

But for the heavy-weight Platonist to tell this story would involve circularity, for what it is for a thing to be salty will be to exemplify saltiness.

Of course, this story only works for properties that aren’t necessarily coextensive. But it’s some progress.

Saturday, June 2, 2018

Acting without existing (any more)

Thesis: It is possible for an object to be acting while it does not exist.


Imagine a rattlesnake that is ten light-years long, all stretched out. For all one hundred years of life it has been deliberately rattling its rattle. And then at the end of its hundred years, its head is destroyed, and I assume that the destruction of the head of a snake is sufficient for its death.

Rattling continues for at least about ten years even after the snake is dead, since the nerve signals the brain had sent while the snake was alive are continuing to rattle.

If this post-mortem rattle counts as the snake’s activity, the Thesis is established. But it is not clear that this ten years of post-mortem rattle is the snake’s activity.

But now consider the last year of pre-mortem rattling, call it R99 (since it starts in year 99 of the snake’s life). Whatever one says of the post-mortem rattling, clearly R99 is the snake’s activity. However, there is a reference frame—the way I set the length of the snake and the times in the story guarantees this—in which R99 occurs after the snake’s head has been destroyed, and hence occurs after the death of the snake. But R99 is the snake’s activity. Hence, there is a reference frame where an activity of the snake occurs after the snake is dead.


Obviously, only existent things can act. But while existence simpliciter is important for activity, existence-at-a-time does not have the same kind of significance. Obviously, often an actor’s action has a relationship R to some thing x that the actor itself does not have. For instance, an agent’s action may be known by me without the agent being known by me (here, R is being known and x is me).

Now, when we say that Elizabeth II exists as Queen of Canada, that is just an awkward way of saying that she has a monarchic relationship to Canada, rather than being a claim about that mysterious thing deep ontology studies: existence. I think we should think of existing-at-a-time as not really existence but simply as a particular kind of relationship—an occupation or presence relationship. It is not surprising in general that activities can stand in relationships that the agents do not. So, why can’t an activity stand in an occupation relationship to a time that the agent does not?

I think much confusion in philosophy comes from thinking of existence-at-a-time and existence-in-a-place as something special, somehow deeply ontologically different from other relations.

Wednesday, May 30, 2018

Reattachment of fingers and a new Aristotelian argument for presentism

Suppose Alice loses her finger at t1 and at t2 it is reattached. Intuitively, after t2 she has the same finger as she had before t1. But now suppose that at t3 she loses her finger again, and it is reattached again at t4. Then at t1 and t3 she is shedding the numerically same finger. Do the two sheddings result in the numerically same severed finger (which is a finger in name only)?

It seems that the answer is affirmative—if we were right in thinking the reattached finger to be the same finger as the original one. For there seems to be a symmetry between re-shedding and re-attachment as we could replace shedding by a transplant operation when a finger is moved back and forth between two people (Terry Pratchett’s Igors probably do that sort of thing for fun sometimes), after all.

But here’s something metaphysically odd. Call the finger F and the severed finger S. Then there is a major metaphysical difference between the first and the second severing. Let’s think about the difference assuming eternalism. Then the first severing causes a severed finger to exist simpliciter. But the second severing does not cause a severed finger to exist simpliciter, but only to come to exist at t3. This is puzzling. In both cases, it seems that we have the same kind of cause, namely the severing of a finger, but the first time this has an ontic effect, a new being exists, and the second time it has no ontic effect. This seems wrong: the same kind of cause should have the same kind of effect, barring something indeterministic.

Maybe we could say that the finger’s coming to exist simpliciter is overdetermined by the severings. But this is counterintuitive. It shouldn’t be possible to add overdetermination to an effect already achieved, in the way that the second severing does. (Moreover, the overdetermination view conflicts with strong origins essentialism, which I accept, and the plausible counterfactual thesis that if the second severing didn’t happen, the very same severed finger S would have come into existence at t1 as actually did. For by strong origins essentialism, if an object was overdetermined in its origination, it could not exist without being thus overdetermined. But then if the second severing didn’t happen, S wouldn’t have been overdetermined, so it couldn’t exist.)

So we have a puzzle for eternalism (and growing block, too). One could even take the above line of thought as a direct argument for presentism. Informally:

  1. After reattachment, one has the same finger F as originally.
  2. If after reattachment one has the same finger as originally, then each severing results in the same severed finger S.
  3. The first severing causes S to exist simpliciter and presently.
  4. The second severing only causes S to exist presently.
  5. Both sheddings have the same kind of effect.
  6. So, existing simpliciter must be nothing but existing presently.
  7. So, presentism is true.

What should the eternalist (or growing blocker) say? It seems to me that the best move is to deny that both sheddings result in the same severed finger. The first results in S1 and the second results in S2 and S1 ≠ S2. By symmetry between re-shedding and re-attachment, I think we have to say that the reattached finger is numerically different from the original one, and deny (1). That is counterintuitive, but it seems the least costly response.

Objection: God could ensure that the reattached finger is the same as the original.

Respose: I think so. But that would be a miraculous intervention. And the symmetry would then require a similar miraculous intervention to ensure that the severed finger after the second shedding is the same as the severed finger after the first shedding. And this makes the second shedding causally different from the first, since no such miraculous intervention was needed to modify the first shedding. And with the two sheddings being different in kind, (5) will no longer be plausible.

Sunday, May 27, 2018

The sacredness of the individual

There is a deontic prohibition on killing innocent people. But in general I think there is no similar deontic prohibition on destroying communities. For instance, there seems to be no deontic prohibition on a government dissolving a village or a city. Indeed, the reasons the state would need to have for such dissolution would have to be grave, but not outlandishly so. The state could permissibly intentionally dissolve a village or a city to end a war, but could not permissibly intentionally kill an innocent for the same end.

One might think this means that individuals are more valuable than the communities they compose. But we shouldn’t think that in general to be true, either. For instance, if a foreign invader were to threaten to dissolve a city without however killing anyone there, and the citizens could repel the invader at an expected cost of, say, six defenders’ and six attackers’ lives, it would be reasonable for the city to conscript its citizens to repel the invader. Thus the value of the shared life of the citizens is worth sacrificing some individual lives to uphold. But it is still not permissible to intentionally kill these innocent civilians.

I think it’s not that persons are more valuable than the villages and cities they compose, but rather they are sacred.

It is worth noting that where a community is sacred (two potential examples: sacramental marriages; God’s chosen people), there could very plausibly be a deontic prohibition on dissolution.

More and more I think the sacred is an ethical category, not just a theological one.

Friday, May 25, 2018

Vector display for Arduino-type boards

It's a nuisance to buy an LCD for each new Arduino project that requires a display, so I wrote an Android app that lets you use a tablet or phone as a display for an Arduino-type project. As a result, one can use a $2 board as a rudimentary oscilloscope with a phone or tablet providing the power, display and UI.

Instructions and links here.

Wednesday, May 23, 2018

Substantial change

The following seems to me to be a central tenet of classical Aristotelianism:

  1. The identity of a parcel of matter is grounded in form.

But it seems to me that matter is introduced by Aristotelianism primarily to solve the problem of distinguishing (a) one substance changing into another (or into several others) from (b) one substance perishing and a new substance coming to be. The solution seems to be that in case (a) the matter persists, but not so in case (b).

But if the identity of a parcel of matter comes from form, then it is very puzzling indeed how a parcel of matter can remain selfsame while a change of form occurs. In other words, there is a tension between (1) and the motive for the introduction of matter into the ontology.

I am inclined to hold on to (1) in some sense, but reject the idea that matter solves the problem of substantial change.

Here is my currently best deflationary solution to the problem of substantial change. Certain kinds of causal interactions are described as “transfers of qualities”. For instance, when billiard ball A strikes billiard ball B in such a way that A stops moving and B begins moving, the momentum of A is “transferred” to B. However, we certainly do not want a metaphysics of momentum transfer on which there exists an entity m that previously was in A and later the numerically same m is present in B. That would be taking the talk of “transfer” too literally. Similarly, we talk of heat transfer.

I do not have an account of quality transfer, but a rough necessary condition for it is that there is a causal interaction where A causes B to gain a property that it itself is losing. There is an obvious difference between the momentum transfer story and the case where A is miraculously stopped by God from moving while B is simultaneously and miraculously set by God in motion.

Now, a special case of quality transfer is when a causal interaction not only transfers a quality but also creates one or more new substances. For instance, suppose a gecko chased by a predator drops its tail, whose writhing confuses the predator. In doing so, the gecko transfers some of its mass, extension, color, motion and other qualities to a new substance (or aggregate of substances), a substance that comes to exist as a result of the same causal interaction.

The technical neo-Aristotelian term for the gecko’s loss of its tail is excretion. Excretion comes in two sorts. The kind of excretion in the case of the gecko’s autotomy is productive excretion, where qualities, notably including mass and extension (understood broadly to include temporal extension for aspatial temporal things), are transfered to one or more substances that are produced in the same causal interaction. Another kind of excretion is accretive excretion, where qualities are transferred to one or more substances that exist independently of this causal interaction. For instance, if an animal were to swallow a living plant, perhaps the plant in the animal’s digestive system could be accretively excreting: its qualities, notably including mass and extension, would come to be gradually lost to the plant while gained by the animal. (This is a bit more complicated in real life, I expect: I doubt the digested bits immediately become parts of the animal.)

Substantial corruption of a material substance, then, is total excretion, a causal interaction where all of a substance’s extension and mass is excreted to one or more substances. This comes in two basic varieties: substantial change where the the beneficiary substances result from the same causal interaction and accretive substantial corruption where the beneficiary substances exist independently of this causal interaction (and typically are preexistent). And one can have a combination case where some of the beneficiaries result from the interaction and some are not dependent on it.

But there is nothing metaphysically deep about substantial corruption.

Wednesday, May 16, 2018

Possibly giving a finite description of a nonmeasurable set

It is often assumed that one couldn’t finitely specify a nonmeasurable set. In this post I will argue for two theses:

  1. It is possible that someone finitely specifies a nonmeasurable set.

  2. It is possible that someone finitely specifies a nonmeasurable set and reasonably believes—and maybe even knows—that she is doing so.

Here’s the argument for (1).

Imagine we live an uncountable multiverse where the universes differ with respect to some parameter V such that every possible value of V corresponds to exactly one universe in the multiverse. (Perhaps there is some branching process which generates a universe for every possible value of V.)

Suppose that there is a non-trivial interval L of possible values of V such that all and only the universes with V in L have intelligent life. Suppose that within each universe with V in L there runs a random evolutionary process, and that the evolutionary processes in different universes are causally isolated of each other.

Finally, suppose that for each universe with V in L, the chance that the first instance of intelligent life will be warm-blooded is 1/2.

Now, I claim that for every subset W of L, the following statement is possible:

  1. The set W is in fact the set of all the values of V corresponding to universes in which the first instance of intelligent life is warm-blooded.

The reason is that if some subset W of L were not a possible option for the set of all V-values corresponding to the first instance of intelligent life being warm-blooded, then that would require some sort of an interaction or dependency between the evolutionary processes in the different universes that rules out W. But the evolutionary procesess in the different universes are causally isolated.

Now, let W be any nonmeasurable subset of L (I am assuming that there are nonmeasurable sets, say because of the Axiom of Choice). Then since (3) is possible, it follows that it is possible that the finite description “The set of values of V corresponding to universes in which the first instance of intelligent life is warm blooded” describes W, and hence describes a nonmeasurable set. It is also plainly compossible with everything above that somebody in this multiverse in fact makes use of this finite description, and hence (1) is true.

The argument for (2) is more contentious. Enrich the above assumptions with the added possibility that the people in one of the universes have figured out that they live in a multiverse such as above: one parametrized by values of V, with an interval L of intelligent-life-permitting values of V, with random and isolated evolutionary processes, and with the chance of intelligent life being warm-blooded being 1/2 conditionally on V being in L. For instance, the above claims might follow from particularly elegant and well-confirmed laws of nature.

Given that they have figured this out, they can then let “Q” be an abbreviation for “The set of all values of V corresponding to universes wehre the first instance of intelligent life is warm-blooded.” And they can ask themselves: Is Q likely to be measurable or not?

The set Q is a randomly chosen subset of L. On the standard (product measure) understanding of how to probabilistically make sense of this “random choice” of subset, the event of Q being nonmeasurable is itself nonmeasurable (see the Sawin answer here). However, intuitively we would expect Q to be nonmeasurable. Terence Tao shares this intuition (see the paragraph starting “Intuitively”). His reason for the intuition is that if Q were measurable, then by something like the Law of Large Numbers, we would expect the intersection of Q with a subinterval I of L to have a measure equal to half of the measure of I, which would be in tension with the Lebesgue Density Theorem. This reasoning may not be precisifiable mathematically, but it is intuitively compelling. One might also just have a reasonable and direct intuition that the nonmeasurability is the default among subsets, and so a “random subset” is going to be nonmeasurable.

So, the denizens of our multiverse can use these intuitions to reasonably conclude that Q is nonmeasurable. Hence, (2) is true. Can they leverage these intuitions into knowledge? That’s less clear to me, but I can’t rule it out.

Monday, May 14, 2018

Simultaneous and diachronic causation

The main problem with the idea that all causation is simultaneous is to make sense of the obvious fact of diachronic causation, as when setting an alarm in the evening causes it to go off in the morning. Here is a theory that has both simultaneity and diachronicity that bears further examination:

  • All causation between substances is simultaneous

  • There is diachronic causation within a substance.

We now have a model of how setting the alarm works, on the simplifying assumption that the alarm clock is a substance. In the evening, by simultaneous causation, I cause the clock to have a certain state. A sequence of diachronic causal interactions within the clock—accidents of the clock causing other accidents of the clock, say—then causes the alarm to go off. The alarm’s going off then, by means of simultaneous causation between substances, causes particles in the air to move, etc. In other words, the diachronicity of the causation is all internal to the substances.

An even more interesting theory would hold that:

  • All causation between substances is simultaneous

  • All causation within a substance is diachronic.

If we were willing to swallow this, then we would have a very elegant account of the internal time of a substance as constituted by the causal relations within the substance (presumably, the causal relations between the accidents of the substance).

Why are there infinitely many abstracta rather than none?

It just hit me how puzzling Platonism is. There are infinitely many abstract objects. These objects are really real, and their existence seems not to be explained by the existence of concreta, as on Aristotelianism. Why is there this infinitude of objects?

Of course, we can say that this is just a necessary fact. And maybe it’s just brute and unexplained why necessarily there is this infinitude of objects. But isn’t it puzzling?

Augustinian Platonism, on which the abstract objects are ideas in the mind of God, offers an explanation of the puzzle: the infinitely many objects exist because God thinks them. That still raises the question of why God thinks them. But maybe there is some hope that there is a story as to why God’s perfection requires him to think these infinitely many ideas, even if the story is beyond our ken.

I suppose a non-theistic Platonist could similarly hope for an explanation. My intuition is that the Augustinian’s hope is more reasonable.

Friday, May 11, 2018

Fun with desire satisfaction

Suppose that desire satisfaction as such contributes to happiness. Then it makes sense to pay a neuroscientist to induce in me as many desires as possible for obvious mathematical truths: the desire that 1+1=2, that 1+2=3, that 1+3=4, etc.

Or if desire has to be for a state of affairs in one’s control, one can pay the neuroscientist to induce in me as many desires as possible for states of affairs like: my not wearing a T-shirt that has a green numeral 1, my not wearing a T-shirt that has a green numeral 2, etc. Then by not wearing a T-shirt with any green numerals, I fulfill lots of desires.

Thursday, May 10, 2018

Provability and numerical experiments

A tempting view of mathematics is that mathematicians are discovering not facts about what is true, but about what is provable from what.

But proof is not the only way mathematicians have of getting at truth. Numerical experiment is another. For instance, while we don’t have a proof of Goldbach’s Conjecture (each even number bigger than two is the sum of two primes), it has been checked to hold for numbers up to 4 ⋅ 1018. This seems to give significant inductive evidence that Goldbach’s Conjecture is true. But it does not seem to give significant evidence that Goldbach’s Conjecture can be proved.

Here’s why. Admittedly, when we learned that that the conjecture holds for some particular number n, say 13, we also learned that the conjecture can be proved for that specific number n (e.g., 13 = 11 + 2 and 11 and 2 are prime, etc.). Inductively, then, this gives us significant evidence that for each particular number n, Goldbach’s conjecture for n is provable (to simplify notation, stipulate Goldbach’s Conjecture to hold trivially for odd n or n < 4). But one cannot move from ∀n Provable(G(n)) to Provable(∀n G(n)) (to abuse notation a little).

The issue is that the inductive evidence we have gathered strongly supports the claim that Goldbach’s Conjecture is true, but gives much less evidence for the further claim that Goldbach’s Conjecture is provable.

The argument above is a parallel to the standard argument in the philosophy of science that the success of the practice of induction is best explained by scientific realism.

Monday, May 7, 2018

Heaven and materialism: The return of the swollen head problem

Plausibly, there is a maximum information density for human brains. This means that if internal mental states supervene on the information content of brains and there is infinite eternal life, then either:

  1. Our head grows without bound to accommodate a larger and larger brain, or

  2. Our brain remains bounded in size and either (a) eventually we settle down to a single unchanging internal mental state (including experiential state) which we maintain for eternity, or (b) we eternally move between a finite number of different internal mental states (including experiential states).

For if a brain remains bounded in size, there are only finitely many information states it can have, because of the maximum information density. Neither of options 2a and 2b is satisfactory, because mental (intellectual, emotional and volitive) growth is important to human flourishing, and a single unchanging internal mental state or eternal repetition does not fit with human flourishing.

Note, too, that on both options 2a and 2b, a human being in heaven will eventually be ignorant of how long she’s been there. On option 2b, she will eventually also be ignorant of whether it is the first time, the second time, or the billionth that she is experiencing a particular internal mental state. (I am distinguishing “internal mental states” from broad mental states that may have externalist semantics.) This, too, does not fit with the image of eternal flourishing.

This is, of course, a serious problem for the Christian materialist. I assume they won’t want to embrace the growing head option 1. Probably the best bet will be to say that in the afterlife, our physics and biology changes in such a way as to remove the information density limits from the brain. It is not clear, however, that we would still count as human beings after such a radical change in how our brains function.

The above is also a problem for any materialist or supervenientist who becomes convinced—as I think we all should be—that our full flourishing requires eternal life. For the flourishing of an entity cannot involve something that is contrary to the nature of a being of that sort. But if 2a and 2b are not compatible with our flourishing, and if 1 is contrary to our nature, then our flourishing would seem to involve something contrary to our human nature.

This is a variant of the argument here, but focused on mental states rather than on memory.

Friday, May 4, 2018

Medical and spacecraft ventilators

Some thinking that to turn off a patient’s ventilator would not be to kill but “to let die”. But it seems obvious that to turn off a spacecraft’s ventilation system would be to kill the astronauts through suffocation.

Of course, there are differences between the two cases. One difference is that the medical ventilator is more intimately connected to the patient. This difference, however, would seem to make turning off the ventilator be more of a killing.

A perhaps more promising difference is that when the patient’s ventilator is turned off, the patient dies from a disease that renders unassisted breathing impossible, while the astronauts die from the turning off of the air system. Maybe there is something to this, but I am doubtful. For we can also say that just as the patient would die from a disease, the astronauts would die from the airlessness of space. It is true that one of these is a disease and the other is an environmental condition, but why should that make a difference with respect to what is a killing?

Moreover, if an engineer turns off the ventilation system on the spacecraft before an astronaut reveals that the technician’s doctoral dissertation was plagiarized, that’s murder. And similarly if a doctor turns off a ventilator before the patient reveals that the doctor cheated in medical school, that’s clearly murder, too.

Similarly, if the death penalty is ever permissible, it could in some cases be administered by disconnecting a ventilator—and it would clearly still be an execution, and hence a killing.

But what if the doctor turns off the ventilator for some reason other than to cause the patient’s death, say to prevent an electrical overload to the hospital’s system which would kill many other patients? Changing the intentions with which an act of killing is done can change whether the act is an intentional killing, whether the act is wrong and whether the act is a murder, but I do not think it changes whether the act is a killing. Thus, the doctor who turns off the ventilator for a reason other than to cause death is still killing, but not intentionally.

Nor does it make a difference with respect to killing whether the disconnection is thought of as causing or hastening death. The doctor who turns off the ventilator to prevent the doctor’s medical school cheating from coming to light could think of the activity as hastening death—making the patient die before revealing the secret. But it’s still murder, and hence it’s still killing. Similarly, the plagiarist engineer would be a murderer even if the air system on the spacecraft were failing and the astronauts would die anyway within a week.

Of course, the judgment that turning off the ventilator is killing does not imply that it is murder or even impermissible. But if we grant that it is always murder to intentionally kill the innocent, the turning off a ventilator in order to cause or hasten death is murder.

Wednesday, May 2, 2018

Time as the measure of change?

Aristotle says that time is the measure of change.

Suppose a pool of liquid changes from fragrant to putrid. We can quantify or measure such features as:

  • the spatial extent of the change

  • the value (in multiple senses) of the change

  • the probability of the change

  • the temporal extent of the change.

Obviously, when we talk of time as the measure of change, we have in mind the last of these four. But to define time as the temporal measure of change is blatantly circular. So the Aristotelian needs to non-circularly specify the sort of measurement of change that time provides. (I am not saying this can’t be done. But it is a challenge.)

Tuesday, May 1, 2018

Time and clocks

Einstein said that time is what clocks measure.

Consider an object x that travels over some path P in spacetime. How long did the travels of x take? Well, if in fact x had a clock traveling with it, we can say that the travels of x took the amount of time indicated on the clock.

But what if x had no clock with it? Surely, time still passed for x.

A natural answer:

  • the travels of x took an amount of time t if and only if a clock would have measured t had it been co-traveling with x.

That can’t be quite right. After all, perhaps x would have traveled for a different amount of time if x had a clock with it. Imagine, for instance, that x went for a one-hour morning jog, but x forgot her clock. Having forgot her clock, she ended up jogging 64 minutes. But had she had a clock with her, she would have jogged exactly 60 minutes.

That seems, though, a really uncharitable interpretation of the counterfactual. Obviously, we need to fix the spacetime path P that x takes. Thus:

  • the travels of x over path P took an amount of time t if and only if a clock would have measured t had it been co-traveling with x over the same path P.

But this is a very strange counterfactual if we think about it. Clocks have mass. Like any other massive object, they distort spacetime. The spacetime manifold would thus have been slightly different if x had a clock co-moving with it. In fact, it is quite unclear whether one can make any sense of “the same path P” in the counterfactual manifold.

We can try to control for the mass of the clock. Perhaps in the counterfactual scenario, we need to require that x lose some weight—that x plus the clock have the same mass in the counterfactual scenario as x alone had in the actual scenario. Or, more simply, perhaps we can drop x altogether from the counterfactual scenario, and suppose that P is being traveled by a clock of the same mass as x.

But we won’t be able to control for the mass of the clock if x is lighter than any clock could be. Perhaps no clock can be as light as a single electron, say.

I doubt one can fix these counterfactuals.

Perhaps, though, I was too quick to say that if x had no clock with it, time still passed for x. Ordinary material substances do have clocks in them. These clocks may not move perfectly uniformly, but they still provide a measure of length of time. Alice’s jog took 396,400 heartbeats. Bob’s education took up 3/4 of his childhood. Maybe the relevant clocks, then, are internal changes in substances. And where the substances lack such internal changes, time does not pass for them.

Monday, April 30, 2018

Avoiding double counting of culpabilities

Here’s an interesting double-counting problem for wrongdoing. Alice stands to inherit a lot of money from a rich uncle in Australia. Bob thinks he stands to inherit a lot of money from a rich uncle in New Zealand. Both of them know that it’s wrong to kill rich uncles for their inheritance, but each of them nonetheless hires a hitman with the instruction to kill the rich uncle. Both hitmen run off with the money and do nothing. But Bob in fact has no uncles—he was misinformed.

Here are some plausible observations:

  1. Alice culpably committed two wrongs: she violated her conscience and she wronged her uncle by hiring a hitman to kill him.

  2. Bob culpably committed only one of these wrongs: he violated his conscience.

  3. Bob is just as morally culpable as Alice.

Here is one way to reconcile these observations. We should distinguish between something like moral failings of the will, on the one hand, and wrongdoings, on the other. It is the moral failings of the will that result in culpability. This culpability then will qualify one or more wrongdoings. But the amount of culpability is not accounted by looking at the culpable wrongdoings, but at the moral failings of the will. A being that executes unalloyed perfect justice will look only at these failings of the will. Alice and Bob each morally failed in the same way and to the same degree (as far as the stories go), and so they are equally culpable. But, nonetheless, Alice has two culpable wrongdoings—culpable through the same moral failing of the will, which should not be double counted for purposes of just punishment.

Friday, April 27, 2018

Love and deontology

Sometimes it wrongs a person to intentionally do them what is known to be in their own best interest. If by torturing you for 60 minutes I can prevent you from being tortured in the same way for 70 minutes by someone else, it may be in your best interest that I torture you. But it is still wrong for me to torture you. Cases of this sort can be multiplied, though of course only deontologists will find any of them plausible.

(One can also analyze these cases as ones where the action is wrong because it is a violation of the agent’s own human dignity. I think the actions are violations of the agent’s own dignity, but they are violations of the agent’s dignity because they wrong the other party.)

These are cases where your action wrongs someone but causes them on balance benefit. This means that to be wronged does not entail being on balance harmed.

Here is how I think we should think of these cases. The true ethics is an ethics of love: I should love everyone. But benevolence is only one of the three fundamental aspects of love, with the other two being union and appreciation. To wrong someone is to violate one or more of the three aspects of love. If I intentionally do something that is known to be in your best interest, I do not violate the benevolence aspect of love. But I may violate one of the other two aspects. In the cases I am thinking of, like torture, the act is an affront to your human dignity, and by affronting your human dignity I am directly acting against the appropriate kind of unitive relationship between human beings—hence, I violate the unitive aspect of love.

It may seem, however, that these are cases where I have a real moral dilemma. For if I refuse to do the act, then it seems I am violating the benevolence of love. But this is mistaken. To fail to be benevolent is not to oppose benevolence. Some cases are obvious. If I fail to be benevolent to you because someone just as close to me has a greater need, I may have done something not in your best interest, but I have not violated the benevolence of love. Now, if I intentionally did to you what was not in your best interest because it was not in your best interest, then I have violated love.

Thursday, April 26, 2018

Alethic Platonism

I’ve been thinking about an interesting metaphysical thesis about arithmetic, which we might call alethic Platonism about arithmetic: there is a privileged, complete and objectively correct assignment of truth values to arithmetical sentences, not relative to a particular model or axiomatization.

Prima facie, one can be an alethic Platonist about arithmetic without being an ontological Platonist: one can be an alethic Platonist without thinking that numbers really exist. One might, for instance, be a conceptualist, or think that facts about natural numbers are hypothetical facts about sequences of dashes.

Conversely, one can be an ontological Platonist without being an alethic Platonist about arithmetic: one can, for instance, think there really are infinitely many pluralities of abstracta each of which is equally well qualified to count as “the natural numbers”, with different such candidates for “the natural numbers” disagreeing on some of the truths of arithmetic.

Alethic Platonism is, thus, orthogonal to ontological Platonism. Similar orthogonal pairs of Platonist claims can be made about sets as about naturals.

One might also call alethic Platonism “alethic absolutism”.

I suspect causal finitism commits one to alethic Platonism.

Something close to alethic Platonism about arithmetic is required if one thinks that there is a privileged, complete and objectively correct assignment of truth values to claims about what sentence can be proved from what sentence. Specifically, it seems to me that such an absolutism about proof-existence commits one to alethic Platonism about the Σ10 sentences of arithmetic.

Wednesday, April 25, 2018

We aren't just rational animals

I think some Aristotelian philosophers are inclined to think that our nature is to be rational animals, so that all rational animals would be of the same metaphysical species. Here is a problem with this. Our nature—or form or essence—specifies the norms for our structure. Our norms specify that we should be bipedal: there is something wrong with us if we are incapable of bipedality. But an intelligent squid would be a rational animal, and its norms would surely not specify that it is supposed to be bipedal. So, it seems, that the hypothetical intelligent squid would have a different nature from ours.

But that was too quick. For it could be that our nature grounds conditionals like:

  1. If you’re human, you should have two arms and two legs

  2. If you’re a squid, you should have eight arms and two tentacles.

We have some reason to think there are such conditional normative facts even if we take our metaphysical species narrowly to be something like human or even homo sapiens, since presumably our nature grounds normative conditionals about bodily structure with antecedents specifying whether we are male or female.

But there is a hitch here: if humans and intelligent squid have the same form, what makes it be the case that for me the antecedent of 1 is true while for Alice (say) the antecedent of 2 is true? I think our best story may be that it is facts about DNA, so in fact the antecedents of 1 and 2 are abbreviations for complex facts about DNA.

That might work for DNA-based animals, which are all the animals we have on earth, but it probably won’t work for all possible animals. For surely there nomically could be animals that are not based on DNA, and it is implausible that we carry in our nature the grounds for an array of conditionals for all the nomically (at least) possible genetic encoding schemes.

I suppose we could take our nature to be rational members of the Animalia, with the assumption that the kingdom Animalia necessarily includes only DNA-based organisms (but not all of them, of course). But Animalia seems a somewhat arbitrary choice of classification to tack on to rationality. It doesn’t have the exobiological generality of animal, the earthly generality of DNA-based organism, or the specificity of human.

It seems to me that

  • rational DNA-based organism, or

  • rational member of genus Homo

are better options for where to draw the lines of our metaphysical species, assuming “rationality” is the right category (as opposed to, say, St. John Paul II’s suggestion that we are fundamentally self-givers), than either rational animal or rational member of Animalia.

Tuesday, April 24, 2018

Balancing between theism and atheism

The problem of evil consists of three main parts:

  • The problem of suffering.

  • The problem of evil choices.

  • The problem of hiddenness (which is an evil at most conditionally on God’s existing).

The theist has trouble explaining why there is so much suffering. The atheist, however, has trouble explaining why there is any suffering, given that suffering presupposes consciousness, and the atheist has trouble explaining why there is any consciousness.

Of course, there are atheist-friendly naturalistic accounts of consciousness. But they all face serious difficulties. This parallels the fact that theists have theodical accounts of why God permits so much suffering, accounts that also face serious difficulties.

So, on the above, considerations of suffering are a net tie between theism and atheism.

The theist does not actually have all that much trouble explaining why there are evil choices. Libertarian free will does the job. Of course, there are some problems with libertarian accounts of free will. These problems are not, I think, nearly as serious as the problems that theists have with explaining why there is so much suffering or atheists have with explaining why there is consciousness. Moreover, there is a parallel problem for the atheist. Evil choices can only exist given free will. Prima facie the most plausible accounts of free will are libertarian agent-causal ones. But those are problematic for the atheist, who will find it difficult to explaining where libertarian agents come from. The atheist probably has to embrace a compatibilist theory, which has at least as many problems as libertarian agent-causalism.

So, considerations of evil choices look at best as a net tie for the atheist.

Finally, there is the problem of hiddenness for the theist. But while the theist has trouble explaining how we don’t all know something so important as the existence of God, the atheist has epistemological trouble of her own: she has trouble explaining how she knows that there is no God. After all, knowledge of the highly abstract facts that enter into arguments regarding the existence of God is not the sort of knowledge that seems to be accessible to evolved natural beings.

So, considerations of knowledge of the existence or non-existence of God look as a net tie.

The problem of evil, however, exhausts the powerful arguments for atheism. But the above considerations far from exhaust the powerful arguments for theism.

The above reasoning no doubt has difficulties. But I want to propose it as a strategy for settling disputes in cases where it's hard to assign probabilities. For even if it's hard to assign probabilities, we can have good intuitions that two considerations are a wash, that they provide equal evidence. And if we can line up arguments in such a way, being more careful with issues of statistical dependence than I was above, then we can come to a view as to which way some bunch of evidence points.

Monday, April 23, 2018

A tweak to the ontomystical argument

In an old paper, I argued that we do not hallucinate impossibilia: if we perceive something, the thing we perceive is possible, even if it is not actual. Consequently, if anyone has a perception—veridical or not—of a perfect being, a perfect being is possible. And mystics have such experiences. But as we know from the literature on ontological arguments, if a perfect being is possible, then a perfect being exists (this conditional goes back at least to Mersenne). So, a perfect being exists.

I now think the argument would have been better formulated in terms of what two-dimensional semanticists like Chalmers call “conceivability”:

  1. What is perceived (perhaps non-veridically) is conceivable.

  2. A perfect being is perceived (perhaps non-veridically).

  3. If a perfect being is conceivable, a perfect being is possible.

  4. A perfect being is possible.

  5. If a perfect being is possible, a perfect being exists.

  6. So, a perfect being exists.

Premise (3) follows from the fact that the notion of a perfect being is not twinearthable, so conceivability and possibility are equivalent for a perfect being (Chalmers is explicit that this is the case for God, but he concludes that God is inconceivable). Premise (1) avoids what I think is the most powerful of Ryan Byerly’s four apparent counterexamples to my original argument: the objection that one might have perceptions that are incompatible with necessary truths about natural kinds (e.g., a perception that a water molecule has three hydrogen atoms).

Friday, April 20, 2018

Non-instrumental pursuit

I pursue money instrumentally—for the sake of what it can buy—but I pursue fun non-instrumentally.

Here’s a tempting picture of the instrumental/non-instrumental difference as embodied in the money fun example:

  1. Non-instrumental pursuit is a negative concept: it is instrumental pursuit minus the instrumentality.

But (1) is mistaken for at least two reasons. The shallower reason is an observation we get from the ancients: it is possible to simultaneously pursue the same goal both instrumentally and non-instrumentally. You might have fun both non-instrumentally and in order to rest. But then lack of instrumentality is not necessary for non-instrumental pursuit.

The deeper reason is this. Suppose I am purely instrumentally pursuing money for the sake of what it can buy, but I then remove the instrumentality, either by ceasing to pursue things that can be bought or by ceasing to believe that money can buy things, without adding any new motivations to my will. Then clearly the pursuit of money rationally needs to disappear—if it remains, that is a clear case of irrationality. But if non-instrumental pursuit were simply an instrumental pursuit minus the instrumentality, then why wouldn’t the removal of the instrumentality from my pursuit of money leave me non-instrumentally and rationally pursuing money, just as I non-instrumentally and rationally pursue fun?

There is a positive element in my pursuit of fun, a positive element that would be lacking in my pursuit of money if I started with instrumental pursuit of money and took away the instrumentality and somehow (perhaps per impossibile) continued (but now irrationally) pursuing money. It is thus more accurate to talk of “pursuit of a goal for its own sake” than to talk of “non-instrumental pursuit”, as the latter suggests something negative.

The difference here is somewhat like the difference between the concepts of an uncaused being and a self-existent being. If you take away the cause of a brick and yet keep the brick (perhaps per impossibile), you have a mere uncaused being. That’s not a self-existent being like God is said to be.

Thursday, April 19, 2018

Affronts to human dignity

Some evils are not just very bad. They are affronts to human dignity. But those evils, paradoxically, provide an argument for the existence of God. We do not know what human dignity consists in, but it isn’t just being an agent, being really smart, etc. For human dignity to play the sort of moral role it does, it needs to be something beyond the physical, something numinous, something like a divine spark. And on our best theories of what things are like if there is no God, there is nothing like that.


  1. There are affronts to human dignity.

  2. If there are affronts to human dignity, there is human dignity.

  3. If there is human dignity, there is a God.

  4. So, there is a God.

This argument is very close to the one I made here, but manages to avoid some rabbit-holes.

Wednesday, April 18, 2018

Van Inwagen on evil

Peter van Inwagen argues that because a little less evil would always serve God’s ends just as well, there is no minimum to the amount of evil needed to achieve God’s ends, and hence the arguer from evil cannot complain that God could have achieved his ends with less evil. Van Inwagen gives a nice analogy of a 10-year prison sentence: clearly, he thinks, a 10-year sentence can be just even if 10 years less a day would achieve all the purposes of the punishment just as well.

I am not convinced about either the punishment or the evil case. Perhaps the judge really shouldn’t choose a punishment where a day less would serve the purposes just as well. I imagine that if we graph the satisfaction of the purposes of punishment against the amount of punishment, we initially get an increase, then a level area, and then eventually a drop-off. Van Inwagen is thinking that the judge is choosing a punishment in the level area. But maybe instead the judge should choose a punishment in the increase area, since only then will it be the case that a lower punishment would serve the purposes of the punishment less well. The down-side of choosing the punishment in that area is that a higher punishment would serve the purposes of the punishment better. But perhaps there is a moral imperative to sacrifice the purposes of punishment to some degree, in the name of not punishing more than is necessary. Mercy is more important than retribution, etc.

Similarly, perhaps, God should choose to permit an amount of evil that sacrifices some of his ends (ends other than the minimization of evil), in order to ensure that the amount of evil that he permits is such that any decrease in the evil would result in a decrease in the satisfaction of God’s other ends. If van Inwagen is right about there not being sharp cut-offs, then this may require God to choose to permit an amount of evil such that more evil would have served God’s other ends better.

The above fits with a picture on which decrease of evil takes a certain priority over the increase of good.

Tuesday, April 17, 2018

In vitro fertilization and Artificial Intelligence

The Catholic Church teaches that it is wrong for us to intentionally reproduce by any means other than marital intercourse (though things can be done to make marital intercourse more fertile than it otherwise would be). In particular, human in vitro fertilization is wrong.

But there is clearly nothing wrong with our engaging in in vitro fertilization of plants. And I have never heard a Catholic moralist object to the in vitro fertilization of farm animals.

Suppose we met intelligent aliens. Would it be permissible for us to reproduce them in vitro? I think the question hinges on whether what is wrong with in vitro fertilization has to do with the fact that the creature that is reproduced is one of us or has to do with the fact that it is a person. I suspect it has to do with the fact that it is a person, and hence our reproducing non-human persons in vitro would be wrong, too. Otherwise, we would have the absurd situation where we might permissibly reproduce an alien in vitro, and they would permissibly reproduce a human in vitro, and then we would swap babies.

But if what is problematic is our reproducing persons in vitro, then we need to look for a relevant moral principle. I think it may have something to do with the sacredness of persons. When something is sacred, we are not surprised that there are restrictions. Sacred acts are often restricted by agent, location and time. They are something whose significance goes beyond humanity, and hence we do not have the authority to engage in them willy-nilly. It may be that the production of persons is sacred in this way, and hence we need the authority to produce persons. Our nature testifies to us that we have this authority in the context of marital intercourse. We have no data telling us that we are authorized to produce persons in any other way, and without such data we should not do it.

This would have a serious repercussion for artificial intelligence research. If we think there is a significant chance that strong AI might be possible, we should stay away from research that might well produce a software person.

The independence of the attributes in Spinoza

According to Spinoza, all of reality—namely, deus sive natura and its modes—can be independently understood under each of (at least) two attributes: thought and extension. Under the attribute of thought, we have a world of ideas, and under the attribute of extesion, we have a world of bodies. There is identity between the two worlds: each idea is about a body. We have a beautiful account of the aboutness relation: the idea is identical to the body it is about, but the idea and body are understood under different attributes.

But here is a problem. It seems that to understand an idea, one needs to understand what the idea is about. But this seems to damage the conceptual independence of the attributes of thought and extension, in that one cannot fully understand the aboutness of the ideas without understanding extension.

I am not sure what to do about this.

Monday, April 16, 2018

The Repugnant Conclusion and Strong AI

Derek Parfit’s Repugnant Conclusion says that, on standard utilitarian assumptions, if n is sufficiently large, then n lives of some minimal level of flourishing will be better any fixed size society of individuals that greatly flourish.

I’ve been thinking about the interesting things that you can get if you combine the Repugnant Conclusion argument with strong Artificial Intelligence.

Assume utilitarianism first.

Given strong Artificial Intelligence, it should be possible to make a computer system that achieves some minimal level of human-like flourishing. Once that is achieved, economies of scale become possible, and I expect it should be possible to replicate that system a vast number of times, and to do so much more cheaply per copy than the cost of supporting a single human being. Note that the replication can be done both synchronically and diachronically: we should optimize the hardware and software in such a way as to make both lots of instances of the hardware and to run as many flourishing lives per day as possible. Once the program is written, since an exact copy is being run for each instance with the same inputs, we can assure equal happiness for all.

If strong AI is possible, generating such minimally flourishing AI and making a vast number of replicates seems a more promising way to increase utility than fighting disease and poverty among humans. Indeed, it would likely be more efficient to decrease the number of humans to the minimum needed to serve the great number of duplicates. At that point, the morally best thing for humans to do will be to optimize the hardware to allow us to build more computers running the happy-ish software and to run each life in as short an amount of external time as possible, and to work to increase the amount of flourishing in the software.

Now note an interesting difference from the traditional Repugnant Conclusion. It seems not unlikely that if strong AI becomes achieved, we will be able to repeatably, safely and cheaply achieve in software not just the minimal levels of human-like flourishing, but high levels of human-like flourishing, even of forms of flourishing other than the pleasure or desire fulfillment that classical utilitarian theories talk about. We could make a piece of software that quickly and cheaply enjoys the life of a classical music afficionado, enjoying the best examples of human classical music culture, and that has no hankering for anything more. And if compatibilism is true (and it is likely that it is true if strong AI is true), then we could make a piece of software that reliably engages in acts of great moral heroism in its simulated world. We lose a bit of value from the fact that these acts only affect a simulated world, but we gain by being able to ensure that no immoral activity mars the value. If we are not certain of the correct axiology, we could hedge our bets by making a software life that is quite flourishing on any plausible axiology: say one that combines pleasure, desire satisfaction, enjoyment of the arts and virtuous activity. And then just run vast numbers of copies of that life per day.

It is plausible that, unless there is some deep spiritual component to human flourishing (of a sort that is unlikely to be there given the materialism that seems needed for strong AI to be possible), we will not only be able to more efficiently increase the sum good by running lots of copies of a happy life than by improving human life, but we will be able to more efficiently improve on the average good.

But one thing is unchanged. The conclusion is still repugnant. A picture of our highest moral imperative being the servicing of a single computer program run on as many machines as possible repeatedly as quickly possible is repugnant.

A tempting objection is to say that multiple copies of the same life count as just one. That’s easily fixed: a well-controlled amount of algorithmic variation can be introduced into lives.

Observe, too, that the above line of thought is much more practical than the original Repugnant Conclusion. The original Repugnant Conclusion is highly theoretical, in that it is difficult to imagine putting into place the kind of society that is described in it without a significant risk of utility-destroying revolution. But right now rich philanthropists could switch their resources from benefiting the human race to working to develop a happy AI (I hesitate to write this sentence, with a slight fear that someone might actually make that switch—but the likelihood of my blog having such an effect seems small). One might respond to the Repugnant Conclusion that all ethical theories give implausible answers in some hypothetical cases. But the case here is not hypothetical.

We can take the above, just as the original Repugnant Conclusion, to be a reductio ad absurdum against utilitarianism. But it seems to be more than that. Any plausible ethics has to have a consequentialist component, even if pursuit of the consequences is restricted by deontic considerations. So on many competing ethical theories, there will still be a pull to the conclusion, given the vast amount of total value, and the respectable amount of average (and median) value achieved in the repugnant proposal. And one won’t be able to resist the pull by denying the picture of value that underwrites utilitarianism, because as noted above, “deeper” values can be achieved in software, given strong AI.

I can think of three plausible ways out of the strong AI version of the Repugnant Conclusion:

  1. The correct axiology lays great stress on the value of deep differences between lives, deeper than can be reliably and safely achieved through algorithmic variation (if there is too much variation, we risk producing misery).

  2. There is a deontic restriction prohibiting the production of software-based persons, perhaps because it is wrong for us to have such a total influence over the life of another person or because it is wrong for us to produce persons by any process other than natural reproduction.

  3. Strong AI is impossible.

I am inclined to think all three are true. :-)

Friday, April 13, 2018

Impairment and non-human organisms

Consider a horse with three legs, a bird with one wing, an oak tree without bark, and a yeast cell unable to reproduce. There is something that all four have in common with each other, and which they also have in common with the human who has only one leg. And it seems to me to be important for an account of disability to acknowledge that which all these five organisms have in common. If the right account of disability is completely disjoined from anything that happens in non-human organisms—or even from anything that happens in non-social organisms—then there is another concept in the neighborhood that we really should also be studying in addition to disability, maybe “impairment”.

Moreover, it seems clear the thing that the five organisms in my examples have in common is bad as far as it goes, though of course it might be good for the organism on balance (the one-winged bird might be taken into a zoo, and thereby saved from a predator).

Thursday, April 12, 2018

Divine authority over us

Imagine a custody battle between Alice and Bob over their child Carl. Suppose the court finds that Alice loves Carl much more than Bob does, that Alice is much wiser than Bob, and that Alice knows Carl and his needs much better than Bob does. Moreover, it is discovered that Bob has knowingly unjustifiedly harmed Carl, while Alice has never done that. In the light of these, it is obvious that Alice is a more fitting candidate to have authority over Carl than Bob is.

But now, suppose x is some individual. Then God loves x much more than I love x, God is much wiser than I, God knows x and his needs much better than I do. Moreover, suppose that I have knowingly unjustifiedly harmed x, while God has never done that. In light of these, it should be plausible that God is a more fitting candidate to have authority over x than I am.

Suppose, however, that I am x. The above is still true. God loves me much more than I love myself; God is much wiser than I; God knows me and my needs much better than I do. And I have on a number of occasions knowingly unjustifiedly harmed myself—indeed, in typical cases when I sin, that’s what has happened—while God has never knowingly unjustifiedly harmed me. So, it seems that God is a more fitting candidate to have authority over me than I am.

I am not endorsing a general principle that if someone loves me more than I love myself, etc., then they are more fit to have authority over me. For the someone might be someone that has little intuitive standing to have authority over me—a complete stranger who inexplicably enormously cares about me might not have much authority over me. But it is prima facie plausible that God has significant authority over me, for the same sorts of reasons that my parents had authority over me when I was a child. And the above considerations suggest that God’s authority over me is likely to be greater than my own authority over myself.

If it is correct that God, if he existed, would have greater authority over me than I have over myself, then that would have significant repercussions for the problem of evil. For a part of the problem involves the question of whether it is permissible for God to allow a person to suffer horrendously even for the sake of greater (or incommensurable but proportionate) goods to them or (especially) another. But it would be permissible for me to allow myself to suffer horrendously for the sake of greater (or incommensurable but proportionate) goods for me or another. If God has greater authority over me than I have over myself, then it would likewise be permissible for God.

This does not of course solve the problem of evil. There is still the question whether allowing the sufferings people undergo has the right connection with greater (or incommensurable but proportionate) goods, and much of the literature on the problem of evil has focused on that. But it does help significantly with the deontic component of the question. (Though even with respect to the deontic aspects, there is still the question of divine intentions—it would I think be wrong even for God to intend an evil for the sake of a good. So care is still needed in theodicy to ensure that the theodicy doesn’t make God out to be intending evils for the sake of goods.)

Wednesday, April 11, 2018

A parable about sceptical theism and moral paralysis

Consider a game. The organizers place a $20 bill in one box and a $100 bill in another box. They seal the boxes. Then they put a $1 bill on top of one of the boxes, chosen at random fairly, and a $5 on top of the other box. The player of the game gets to choose a box, in which case she gets both what’s in the box and what’s on top of the box. Everyone knows that that’s how the game works.

If you are an ordinary person playing the game, you will be self-interestedly rational to choose the box with the $5 on top of it. The expected payoff for the box with the $5 on it is $65, while the expected payoff for the other box is $61, when one has no information about which box contains the $20 and which contains the $100.

If Alice is an ordinary person playing the game and she choses the box with the $1 on top of it, that’s very good reason to doubt that Alice is self-interestedly rational.

But now suppose that I am considering the hypothesis that Bob is a self-interestedly rational being who has X-ray vision that can distinguish a $20 bill from a $100 bill inside the box. Then if I see Bob choose the box with the $1 on top of it, that’s no evidence at all against the hypothesis that he is such a being, i.e., a self-interestedly rational being with X-ray vision. In repeated playings, we’ll see Bob choose the $1 box half the time and the $5 box half the time, if he is such a being, and if we didn't know that Bob has X-ray vision, we would think that Bob is indifferent to money.

Sceptical theism and the infinity of God

I’ve never been very sympathetic to sceptical theism until I thought of this line of reasoning, which isn’t really new, but I’ve just never quite put it together in this way.

There are radically different types of goods. At perhaps the highest level—call it level A—there are types of goods like the moral, the aesthetic and the epistemic. At a slightly lower level—call it level B—there are types of goods like the goods of moral rightness, praiseworthiness, autonomy, the virtue, beauty, sublimity, pleasure, truth, knowledge, understanding, etc. And there will be even lower levels.

Now, it is plausible that a perfect being, a God, would be infinitely good in infinitely many ways. He would thus infinitely exemplify infinitely many types goods at each level, either literally or by analogy. If so, then:

  1. If God exists, there are infinitely many types of good at each level.


  1. We only have concepts of a finite number of types of good at each level.


  1. There are infinitely many types of good at each level that we have no concept of.

Now, let’s think what would likely be the case if God were to create a world. From the limited theodicies we have, we know of cases where certain types of goods would justify allowing certain evils. So we wouldn't be surprised if there were evils in the world, though of course all evils would be justified, in the sense that God would have a justification for allowing them. But we would have little reason to think that God would limit his design of the world to only allowing those evils that are justified by the finite number of types of good that we have concepts of. The other types of good are still types of good. Given that there infinitely many such goods, and only finitely many of the ones we have concepts of, it would not be significantly unlikely that if God exists, a significant proportion—perhaps a majority—of the evils that have a justification would have a justification in terms of goods that we have no concept of.

And so when we observe a large proportion of evils that we can find no justification for, we observe something that is not significantly unlikely on the hypothesis that God exists. But if something is not significantly unlikely on a hypothesis, it’s not significant evidence against that hypothesis. Hence, the fact that we cannot find justifications for a significant proportion of the evils in the world is not significant evidence against the existence of God.

Sceptical theism has a tendency to undercut design arguments for the existence of God. I do not think this version of sceptical theism has that tendency, but that’s matter for another discussion (perhaps in the comments).

Bayesianism and the multitude of mathematical structures

It seems that every mathematical structure (there are some technicalities as to how to define it) could in fact 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 appendix to Bayesianism can solve this problem by requiring us to assign zero probability to some structures that are metaphysically possible but that our Creator wants us to be able to rule out a priori.

Monday, April 9, 2018

Reincarnation and theodicy

As I was teaching on the problem of evil today, I was struck by how nicely reincarnation could provide theodicies for recalcitrant cases. “Why is the fawn dying in the forest fire? Well, for all we know, it’s a reincarnation of someone who committed genocide and is undergoing the just punishment for this, a punishment whose restorative effect will only be seen in the next life.” “Why is Sam suffering with no improvement to his soul? Well, maybe the improvement will only manifest in the next life.”

Of course, I don’t believe in reincarnation. But if the problem of evil is aimed at theism in general, then it seems fair to say that for all that theism in general says, reincarnation could be true.

Here is a particular dialectical context where bringing in reincarnation could be helpful. The theist presses the fine-tuning argument. The atheist instead of embracing a multiverse (as is usual) responds with the argument from evil. The theist now says: While reincarnation may seem unlikely, it surely has at least a one in a million probability conditionally on theism; on the other hand, fine-tuning has a much, much smaller probability than one in a million conditionally on single-universe atheism. So theism wins.

Friday, April 6, 2018

Peer disagreement and models of error

You and I are epistemic peers and we calculate a 15% tip on a very expensive restaurant bill for a very large party. As shared background information, add that calculation mistakes for you and me are pretty much random rather than systematic. As I am calculating, I get a nagging feeling of lack of confidence in my calculation, which results in $435.51, and I assign a credence of 0.3 to that being the tip. You then tell me that you you’re not sure what the answer is, but that you assign a credence of 0.2 to its being $435.51.

I now think to myself. No doubt you had a similar kind of nagging lack of confidence to mine, but your confidence in the end was lower. So if all each of us had was their own individual calculation, we’d each have good reason to doubt that the tip is $435.51. But it would be unlikely that we would both make the same kind of mistake, given that our mistakes are random. So, the best explanation of why we both got $435.51 is that we didn’t make a mistake, and I now believe that $435.51 is right. (This story works better with larger numbers, as there are more possible randomly erroneous outputs, which is why the example uses a large bill.)

Hence, your lower reported credence of 0.2 not only did not push me down from my credence of 0.3, but it pushed me all the way up into the belief range.

Here’s the moral of the story: When faced with disagreement, instead of moving closer to the other person’s credence, we should formulate (perhaps implicitly) a model of the sources of error, and apply standard methods of reasoning based on that model and the evidence of the other’s credence. In the case at hand, the model was that error tends to be random, and hence it is very unlikely that an error would result in the particular number that was reported.

Thursday, April 5, 2018

Defeaters and the death penalty

I want to argue that one can at least somewhat reasonably hold this paradoxical thesis:

  • The best retributive justice arguments in favor of the death penalty are sound and there are no cases where the death penalty is permissible.

Here is one way in which one could hold the thesis: One could simply think that nobody commits the sorts of crimes that call for the death penalty. For instance, one could hold that nobody commits murder, etc. But it’s pretty hard to be reasonable in thinking that: one would have to deny vast amounts of data. A little less crazily, one could think that the mens rea conditions for the crimes that call for the death penalty are so strict that nobody actually meets them. Perhaps every murderer is innocent by reason of insanity. That’s an improvement over the vast amount of denial that would be involved in saying there are no murders, but it’s still really implausible.

But now notice that the best retributive justice arguments in favor of the death penalty had better not establish that there are crimes such that it is absolutely morally required that one execute the criminal. First, no matter how great the crime, there are circumstances which could morally require us to let the criminal go. If aliens were to come and threaten to destroy all life on earth with the exception of a mass murderer, we would surely have to just leave the mass murderer to divine justice. Second, if the arguments in favor of the death penalty are to be plausible, they had better be compatible with the possibility of clemency.

Thus, the most the best of the arguments can be expected to establish is that there are crimes which generate strong moral reasons of justice to execute the criminal, but the reasons had better be defeasible. One could, however, think that there defeaters occur in all actual cases. Of course, some stories about defeaters are unlikely to be reasonable: one is not likely to reasonably hold that aliens will destroy all of us if we execute someone.

But there could be defeaters that could be more reasonably believed in. Here are some such things that one could believe:

  • God commanded us to show a clemency to criminals that in fact precludes the death penalty.

  • Criminals being executed are helpless, and killing helpless people—even justly—causes a harm to the killer’s soul that is a defeater for the reasons for the death penalty.

  • We are all guilty of offenses that deserve the death penalty—say, mortal sins—and executing someone when one oneself deserves the death penalty is harmful to one’s character in a way that is a defeater for the reasons for the death penalty.

(I myself am open to the possibility that the first of these could actually be the case in New Testament times.)

Wednesday, April 4, 2018

Group impairment and Aristotelianism

Aristotelians have a metaphysical ground for claims about what is normal and abnormal in an individual: the form of a substance grounds the development of individuals in a teleological ways and specifies what the substance should be like. Thus a one-eyed owl is impaired—while it is an owl, it falls short of the specification in its form.

But there is another set of normalcy claims that are harder to ground in form: claims about the proportions of characteristics in a population. Sex ratios are perhaps the most prevalent example: if all the foals born over the next twenty years were, say, male, then that would be disastrous for the horse as a species. And yet it seems that each individual foal could still be a perfect instance of its kind, since both a male and a female can be a perfect instance of horsehood. Caste in social insects is another example: it would be disastrous for a bee hive if all the females developed into workers, even though each one could be a perfect bee.

The two cases are different. The sex of a horse is genetically determined, while social insect caste is largely or wholly environmental. Still, both are similar in that the species not only has norms as to what individuals should be like but also what the distribution of types of individuals should be. There is not only the possibility of individual but of group impairment. But what is the metaphysics behind these norms?

Infamously, Aristotle interpreters differ on whether forms are individual or common: whether two members of the same species have a merely exactly similar or a numerically identical form. Here is a place where taking forms to be common would help: for then the form could not only dictate the variation between the parts of each organism’s body but also the variation between the organisms in the species. But taking forms to be common would be ethically disastrous, because it would mean that all humans have the same soul, since the soul is the form of the human being.

Here’s my best solution to the puzzle. The form specifies the conditions of the flourishing of an individual. But these conditions can be social in addition to individual. Thus, a perfectly healthy and well-nourished male foal would not be flourishing if it lacks a society with potential future mates. And while each worker bee can internally be a fulfilled worker bee, it is not flourishing if its work does not in fact help support a queen. These social conditions for flourishing are constitutive. It’s not that the lack of a queen will cause the worker bee to die sooner (though for all I know, it might), but that the lack of a queen is constitutive of the worker bee being poorly off.

Once we see that there can be constitutive social conditions for flourishing, it is natural to think that there will be constitutive environmental conditions for flourishing. And this could be the start of an Aristotelian philosophy of ecology.

A multiple-realizability problem for computational theories of mind

Consider a computational theory of mind overlaid on a reductive physicalist ontology. Here’s I think how the story would have to work. We need a mapping between physical system (PS) and an abstract model of computation (AMC), because on a computational theory of mind, thoughts need to be defined in terms of the functioning of an AMC associated with a PS. But there are infinitely many mappings between PSs and AMCs. If thought is defined by computation and yet if we are to avoid a hyper-panpsychism on which every physical system thinks infinitely many thoughts, we need to heavily restrict the mappings between PSs and AMCs. I know of only one promising strategy of mapping restriction, and that is to require that if we specify the PSs using a truly fundamental language—one whose primitives are “structural” in Sider’s sense—the mapping can be sufficiently briefly described.

If we were dealing with infinite PSs and infinite AMCs, there would be a nice non-arbitrary way to do this: we could require that the mapping description be finite (assuming the language has expressive resources like recursion). But with finite PSs and AMCs, that will still generate hyper-panpsychism, since there will be infintely many finite AMCs that can be assigned to a given PS.

This means that not only we have to restrict the mapping description to a finite description, but to a short finite description. Once we do that, we will specify that a PS x thinks the thoughts that are associated with an AMC y if and only if the mapping between x and y is short. One obvious problem here is the seeming arbitrariness of whatever threshold of shortness we have.

But there is another interesting problem. This approach will violate the multiple realizability intuition that leads many people to computational theories of mind. For imagine a reductive physicalist world w* which is just like ours at the macroscopic level, and even at the atomic level, but whose microscopic reduction goes a number of extra levels down, with the reductions being quite complex. Thus, although in our world facts about electrons may be fundamental, in w* these facts are far from fundamental, being reducible to facts about much more fundamental things and reducible in a complex way. Multiple realizability intuitions lead one to think that macroscopic entities in a world like w* that behave just like humans down to the atomic level could think like we do. But if the reduction from the atomic level to the fundamental level in w* is sufficiently complicated, then the brain to human-like AMC mapping in w* will fail to meet the brevity condition, and hence the beings won’t think, or at least not like we do.

The problem is that it is really hard to both avoid hyper-panpsychism and allow for multiple realizability intuitions while staying within the confines of a reductive physicalist computational theory of mind. A dualist, of course, has no such difficulty: a soul can be attached to w*’s human-like organisms with no more difficulty than it can to our world’s human organisms.

Suppose the computationalist denies that multiple realizability extends to worlds like w*. Then there is a new and interesting feature of fine-tuning in our world that calls out for explanation: our world’s fundamental level is sufficiently easily mapped to a neural level to allow the neural level to count as engaging in thoughtful computation.

Tuesday, April 3, 2018

Divine command and natural law epistemology

I am impressed by the idea that other kinds of beings from humans can appropriately have different doxastic practices from ours, in light of:

  1. a different environment which makes different practices truth-conductive, and

  2. different proper goals for their doxastic practices (e.g., a difference of emphasis on explanation versus prediction; a difference in what subject matter is more important).

Option (a) is captured by reliabilism, but reliabilism does not by itself do much to help with (b), and suffers from an insuperable reference class problem.

I know of two epistemological theories that nicely capture the differences between epistemic practices in the light of both (a) and (b):

  • divine command epistemology: a doxastic practice is required just in case God commands it (variant: commands it in light of truth-based goods)

  • natural law epistemology: a doxastic practice is required just in case it is natural to its practitioner (variant: natural and ordered towards truth-based goods).

Both of these theories have an interesting meta-theoretic consequence: they make particularly weird thought experiments less useful in epistemology. For God’s reasons for requiring a doxastic practice may well be linked to our typical way of life, and a practice that is natural in one ecological niche may have unfortunate consequences outside that niche. (That’s sad for me, since making up weird thought experiments is something I particularly enjoy!)

(Note, however, that both of these theories have nothing to say on the question of knowledge. That’s a feature, not a bug. I think we don’t need a concept of (propositional) knowledge, just as we don’t need a concept of baldness. Anything worth saying using the language of “knowledge” or “baldness” can be more precisely said without it—one can talk of degrees of belief and justification, amount of scalp coverage, etc.—and while it’s an amusing question how exactly to analyze knowledge or baldness, it’s just that.)