Friday, April 28, 2017

Saying with possible worlds what can't be said with box and diamond

The literature contains a number of examples of a modal claim that can be made with possible worlds language but not in box-diamond language. Here is one that occurred to me that is simpler than any of the examples I’ve seen:

  • Reality could have been different.

Very simple in possible worlds language: There is a non-actual world. (Note: This doesn’t work on the version of Lewis’s modal realism that allows for duplicate worlds. All the worse for that version.) But no box-diamond statement expresses (*). One can, of course, say that there aren’t any unicorns but could be, which implies (*), but that’s not the same as saying (*).

Fun with St Petersburg

Consider any game, like St Petersburg where the expected payoff is infinite but the prizes are guaranteed to be finite. For instance, a number x is picked uniformly at random in the interval from 0 to 1 not inclusive, and your prize is 1/x.

Suppose you and I independently play this game, and we find our winnings. Now I go up to you and say: “Hey, I’ve got a deal for you: you give me your winnings plus a million dollars, and then you’ll toss a hundred coins, and if they’re all heads, you’ll get one percent of what I won.” That’s a deal you can’t rationally refuse (assuming I’m dead-set against your negotiating a better one). For the payoff for refusing is the finite winnings you have. The payoff for accepting is −1000000 + 2−100⋅0.01⋅(+∞) = +∞.


Now let’s play doubles! There are two teams: (i) I and Garibaldi, and (ii) you and Delenn. The members of each team don’t get to talk to each other during the game, but after the game each team evenly splits its winnings. This is what happens. The house calculates two payoffs using independent runs of our St Petersburg style game, w1 and w2. I am in a room with you; Garibaldi is in a room with Delenn. I and Delenn are each given w1; you and Garibaldi are each given w2. Now, by pre-arrangement with Garibaldi, I offer you the deal above: You give me a million, and then toss a hundred coins, and then you get one percent of my winnings if they’re all heads. You certainly accept. And Garibaldi offers exactly the same deal to Delenn, and she accepts. What’s the result? Well, the vast majority of the time, the Pruss and Garibaldi team ends up with all the winnings (w1 + w2 + w1 + w2 = 2w1 + 2w2), plus two million, and the you and Delenn team end up out two million. But about once in 2100 runs, the Pruss and Garibaldi team ends up with 1.99w1 + 1.99w2, plus two million, while you and Delenn end up with 0.01w1 + 0.01w2 − 2000000.

And, alas, I don’t see a way to use Causal Finitism to solve this paradox.

Thursday, April 27, 2017

Materiality and spatiality

I’ve been fond of the theory that materiality is just the occupation of space. But here is a problem for that view.

I have argued previously that we should distinguish between the internal space (or geometry) of an object and external space. Here is quartet of considerations:

  • Imagine a snake one light-year in length out in empty space arranged in a square. Then imagine that God creates a star in the middle of the square. The star instantly disturbs the geometry of space and makes the distances between parts on opposite sides of the square be different from what they previously where. But this does not make any intrinsic change to the snake until physical influence can reach the snake from the star, which will take about 1/8 of a year (the sides of the square will be 1/4 light-years, so the closest any part of the snake is to the center is 1/8 light years). The internal geometry of the snake differs from the external one.

  • We have no difficulty imagining a magical house whose inside is larger than its outside.

  • Christ in the Eucharist has very different (larger!) internal size and geometry from the external size and geometry of where he is Eucharistically located.

  • Thought experiments about time travel and the twin paradox suggest that we should distinguish internal time from external time. But space is like time.

Now, if internal and external space can come apart so much, then it is plausible that an object could have internal space or geometry in the absence of any connection to external space. Furthermore, if a material object ceased to have an occupation relation to external space but retained its internal geometry, it would surely still be material. Only a material object can be a cube. But a cubical object could remain a cube in internal geometry even after losing all relation to external space. But if so, then materiality is not the occupation of external space.

In fact, even independently of the above considerations about internal and external space, it just doesn’t seem that objects are material in virtue of a relation to something beyond them—like external space.

So, it seems, objects aren’t material in virtue of the occupation of external space. Could they be material in virtue of the occupation of internal space? Not substances! A substance does not occupy its internal space. It has that internal space, and is qualified by it, but it seems wrong to say that it is in it in the sense of occupation. (Perhaps the proper parts of material substances do occupy the substance’s internal space.) But some substances, say pigs or electrons, are material. So materiality isn’t a function of the occupation of internal space, either. And unless we find some third sort of space, we can’t say that materiality is a function of the occupation of space.

Perhaps, though, we can say this. Materiality is the possession or occupation of space. Then material substances are material by possessing internal space, and the proper parts of material substances are material by occupying the substance’s internal space. On this view, the materiality of me and my heart are analogically related—a fine Aristotelian idea.

But I have a worry. Point particles may not exist, but they seem conceivable. And they would be material. But a point particle doesn’t seem to have an internal space or geometry. I am not sure what to say. Perhaps, a point particle can be said to be material by occupying external space (in my proposed account of materiality, I didn’t specify that the space was internal). If so, then a point particle, unlike a square snake, would cease to be material if it came to be unrelated to external space. Or maybe a point particle does have an internal zero-dimensional space. It is hard to see what the spatiality of this “space” would consist in, but then we don’t have a good account of the spatiality of space anyway. (Maybe the spatiality of an internal space consists in a potentiality to be aligned with external space?) And, finally, maybe point particles that are points both externally and internally (particles that have non-trivial internal geometry but that are externally point-like aren’t a problem for the view) either aren’t material or aren’t possible.

Wednesday, April 26, 2017

Surviving furlessness and inner earlessness

If we are animals, can we survive in a disembodied state, having lost all of our bodies, retaining only soul or form?

Here is a standard thought:

  1. Metabolic processes, homeostasis, etc. are defining features of being animals.

  2. In a disembodied state, one cannot have such processes.

  3. Something that is an animal is essentially an animal.

  4. So something that is an animal cannot survive in a disembodied state.

But here’s a parody argument:

  1. Fur and mammalian inner ear bones (say) are defining features of being mammals.

  2. In a furless and internally earless state, one cannot have such structures.

  3. Something that is a mammal is essentially a mammal.

  4. So something that is a mammal cannot survive in a furless and internally earless state.

I think 5-7 are no less plausible than 1-3. But 8 is clearly false: clearly, it is metaphysically possible to become a defective mammal that is furless and internally earless.

The obvious problem with 5, or with the inferences drawn from 5, is that what is definitory of being a mammal is being such that one should to have fur and such-and-such an inner ear. The same problem afflicts 2: why not say that being such that one should have these processes and features is definitory of being a mammal.

Person is not a natural kind

  1. God is not a member of any natural kind.

  2. If person is a natural kind, then every person is a member of a natural kind.

  3. God is a person.

  4. So, person is not a natural kind.

Monday, April 24, 2017

Do God's beliefs cause their objects?

Consider this Thomistic-style doctrine:

  1. God’s believing that a contingent entity x exists is the cause of x’s existing.

Let B be God’s believing that I exist. Then, either

  1. B exists in all possible worlds


  1. B exists in all and only the worlds where I exist.

(Formally, there are other options, but they have no plausibility. For instance, it would be crazy to think B exists in some but not all the worlds where I exist, or in some but not all the worlds where I don’t exist.)

Let’s consider (3) first. This, after all, seems the more obvious option. God’s beliefs are necessarily correct, so in worlds where I don’t exist, God doesn’t believe that I exist, and hence B doesn’t exist. Then, B is a contingent being that causes my existing. Now apply the Thomistic principle to this contingent being B. It exists, so God believing that B exists is the cause of B’s existing. Let B2 be God’s believing that B exists. Since B2 causes B, B2 must be distinct from B, as causation cannot be circular. Furthermore, if (3) is the right option in respect of B and me, then an analogue for B2 and B should hold: B2 will exist in all and only the worlds where B exists. The argument repeats to generate an infinite regress of divine believings: Bn is God’s believing that Bn − 1 exists and Bn causes Bn − 1. This regress appears vicious.

So, initial appearances aside, (3) is not the way to go.

Let’s consider (2) next. Then B exists in some possible world w1 where I don’t exist. Now, at w1, God doesn’t believe that I exist, since necessarily God’s beliefs are correct. This seems to be in contradiction to the claim that B exists at w1. But it is only in contradiction if it is true at w1 that B is God’s believing that I exist. But perhaps it’s not! Perhaps (a) the believing B exists at the actual world and at w1 but with different content, or (b) B exists at w1 but isn’t a believing at w1.

Let’s think some more about (2). Let w2 be a world where only God exists (I am assuming divine simplicity; without divine simplicity, it might be that in any world where God exists, something else exists—viz., a proper part of God). Then by (2), B exists at w2. But only God exists at w2. So, God is identical to B at w2. But identity is necessary. Thus, God is actually identical to B. Moreover, what goes for B surely goes for all of God’s believings. Thus, all of God’s believings are identical with God.

It is no longer very mysterious that God’s believing that I exist is the cause of my existence. For God’s believing that I exist is identical with God, and of course God is the cause of my existence.

The difficulty, however, is with the radical content variation. The numerically same mental act B is actually a believing that I exist, while at w2 it is a believing that I don’t exist. Furthermore, if truthmaking involves entailment, we can no longer say that B truthmakes that God believes that I exist. For B can exist without God’s believing that I exist.

All this pushes back against (1). But now recall that I only called (1) a “Thomistic-style” doctrine, not a doctrine of St. Thomas. The main apparent source for the doctrine is Summa Theologica I.14.8. But notice some differences between what Aquinas says and (1).

The first is insignificant with respect to my arguments: Thomas talks of knowledge rather than belief. But (1) with knowing in place of believing is just as problematic. Obviously, it can’t be a necessary truth that God knows that I exist, since it’s not a necessary truth that I exist.

The second difference is this. In the Summa, Aquinas doesn’t seem to actually say that God’s knowledge that x exists is the cause of x’s existence. He just says that God’s knowledge is the cause of x’s existence. Perhaps, then, it is God’s knowledge in general, especially including knowledge such necessary truths as that x would have such-and-such nature, that is the cause of x’s existence. If so, then God’s knowledge would be a non-determining cause of things—for it could cause x but does not have it (and, indeed, in those worlds where x does not exist, it does not cause x). This fits well with what Aquinas says in Article 13, Reply 1: “So likewise things known by God are contingent on account of their proximate causes, while the knowledge of God, which is the first cause, is necessary.”

Maybe. I don’t know.

Thoughts on theistic Platonism

Platonists hold that properties exist independently of their instances. Heavy-weight Platonists add the further thesis that the characterization of objects is grounded in or explained by the instantiation of a property, at least in fundamental cases. Thus, a blade of grass is green because the blade of grass instantiates greenness (at least assuming greenness is one of the fundamental properties).

Heavy-weight Platonism has a significant attraction. After all, according to Platonism (and assuming greenness is a property),

  1. Necessarily (i) an object is green if and only if (ii) it instantiates greenness.

The necessary connection between (i) and (ii) shouldn’t just be a coincidence. Heavy-weight Platonism explains this connection by making (ii) explain or ground (i). Light-weight Platonism, which makes no claims about an explanatory connection between (i) and (ii), makes it seem like the connection is a coincidence.

Still, I think it’s worth thinking about some other ways one could explain the coincidence (1). There are three obvious formal options:

  1. (ii) explains (i)
  2. (i) explains (ii)
  3. Something else explains both (i) and (ii).

Option (2) is heavy-weight Platonism. But what about (2) and (3)? It’s worth noting that there are available theories of both sorts.

Here’s a base theory that can lead to any one of (2)–(4). Properties are conceptions in the mind of God. Furthermore, instantiation is divine classification: x’s instantiating a property P just is God classifying x under conception P. It is natural, given this base theory, to affirm (3): x’s instantiating greenness just is God’s classifying x under greenness, and God classifies x under greenness because x is green. Thus, x instantiates greenness because x is green.

But, interestingly, this base theory can give other explanatory directions. For instance, Thomists think that God’s knowledge is the cause of creation. This suggests a view like this: God’s classifying x under greenness (which on the base theory just is x’s instantiating greenness) causes x to be green. On this view, x is green because x instantiates greenness. If the “because” here involves grounding, and not just causation, this is heavy-weight Platonism, with a Thomistic underpinning. Either way, we get (2).

And here is a third option. God wills x to be green. God’s willing x to be green explains both x’s being green and God’s classifying x as green. The latter comes from God’s willing as an instance of what Anscombe calls intentional knowledge. This yields (4).

So, interestingly, a theistic conceptual Platonism can yield any one of the three options (2)–(4). I think the version that yields (3)—interestingly, not the Thomistic one—is the one that best fits with divine simplicity.

Thursday, April 20, 2017

Are we in a computer simulation?

Do we live in a computer simulation?

Here’s a quick and naive thought. We would expect most computer simulations to be of pretty poor quality and limited in scope. If we are in a simulation, the simulation we are in is of extremely high quality and of great scope. That’s not what we would expect on the simulation hypothesis. So, probably, we don’t live in a computer simulation.

But the following argument is pretty convincing: 1. If materialism is true, then probably a computer simulation of a brain can think (since the best materialist theory of mind is functionalism). 2. If a computer simulation of a brain can think, then most thinkers live inside computer simulations.

So, the argument that we don’t live in a computer simulation gives us evidence against materialism.


Suppose that somewhere in the galaxy there is a planet where there are large six-legged animals with an inner supportive structure, that evolved completely independently of any forms of life on earth and whose genetic structure is not based on DNA but another molecule. What I said seems perfectly possible. But it is impossible if animals are simply the members of the kingdom Animalia, since the six-legged animals on that planet are neither DNA-based nor genetically connected to the animalia on earth.

On the other hand, the supposition that somewhere (maybe in another universe) there is water that does not have H2O in it is an impossible one. So is the supposition that there are horses without DNA.

So the kind animal is disanalogous to the kinds water and horse. The kind water is properly identified with a chemical kind, H2O, and the kind horse is properly identified with a biological species, Equus ferus. But the kind animal does not seem to be properly identified with any biological kind.

One can have DNA-based animals and non-DNA-based animals. If the Venus fly-trap evolved the ability to move from place to place following its prey, it would be an animal, but still a member of Plantae. Animals are characterized largely functionally, albeit not purely functionally, but also in reference to the function of their embodiment—there cannot be any animals that are unembodied.

Is animal a genuine natural kind? Or is it a non-natural kind, constructed in the light of our species’ subjective interests? I don’t know. I take seriously, though, the possibility that there is an "Aristotelian" philosophical categorization that goes across biological categories.

Wednesday, April 19, 2017

How likely are you to be in a random finite subset of an infinite set?

Suppose that out of a set of infinitely many people, including you, a finite subset is chosen at random. How likely are you to be in that subset? Intuitively, not very likely. And the larger the infinity, the less likely.

But how do you pick out a finite subset at random? Here’s a natural way. First, pick out a subset at random, by flipping a fair coin for each person in the original set, and including a person in the subset if the comes up heads. Almost surely, this will generate an infinite subset (a consequence of the law of large numbers). But suppose this experiment is repeated—perhaps uncountably infinitely often—until the set picked out is finite. (This construction requires that the set of potential repetitions be well-ordered.) Or maybe you just get lucky, and to everybody’s surprise the set picked out is finite.

So now we have a method for picking out a finite subset at random (though it may take some luck). How likely are you to be in that finite subset?

Well, think about it step-by-step. Before you learned that the set picked out by the heads was finite, your probability that you were in the set was the probability that your coin landed heads, i.e., 1/2. Then you learn that the set of people for whom heads was rolled is finite. But this fact tells you nothing about your coin toss. For the claim that the set of people with heads is finite is logically equivalent to the claim that the set of people other than you with heads is finite. And the latter claim tells you nothing about your coin toss.

So, your probability needs to stay at 1/2.

Thus, the probability that a random finite subset of the infinitely many people includes you is finite. This is a little counterintuitive when the infinity is countable. And it becomes far more counterintuitive the larger this infinity gets. It is a stupendously implausible claim when that infinity is large, say ℶω.

Causal finitism blocks the story by making it impossible for you to find out that the set of people who got heads is finite.

Tuesday, April 18, 2017

A modified consciousness-causes-collapse interpretation of quantum mechanics

Here are two technical problems with consciousness causes collapse (ccc) interpretations of quantum mechanics. In both, suppose a quantum experiment with two possible outcomes, A and B, of equal probability 1/2.

1. The sleeping experimenter: The experimenter is dreamlessly asleep in the lab and the experiment is rigged to wake her up on measuring A by ringing a bell. If conscious observation causes collapse, then when A is measured, the experimenter is woken up, and collapse occurs. Presumably, this happens half the time. But what happens the other half the time? No conscious observation occurs, so no collapse occurs, so the system remains in a superposition of A and B states. But that means that when the experimenter naturally wakes up several hours later, and then collapse will happen. However, when collapse happens then, it has both A and B outcome options at equal chances. But that means that overall, there is a 75% chance of an A outcome, which is wrong.

2. Order of explanation: The experimenter is awake. On outcome A, a bell rings. On B, a red light goes on. In fact, A is observed. What caused the collapse? It wasn’t the observer’s hearing the bell, because the bell’s occurrence is explanatorily posterior to the collapse. But we said that it is conscious observation that causes the collapse. Which conscious observation was that, if it wasn’t the hearing of the bell? Note that the observer need not have been conscious prior to hearing the bell or seeing the light—the experiment can be rigged so that either the bell or the light wakes up the observer. Perhaps the cause of the collapse was the state of being about to hear a bell or see a red light, or maybe it was the disjunctive state of hearing a bell or seeing a red light. But the former is a strange kind of cause, and the second would be a weird case where the disjunction is prior to its true disjunct.

The first problem strikes me as more serious than the second—the second is a matter of strangeness, while the first yields incorrect predictions.

I’ve been thinking about a curious ccc interpretation that escapes both problems. On this interpretation, the universe branches like in Everett-style multiverse explanations, but a conscious observation in any branch causes collapse. Collapse is the termination of a bunch of branches, including perhaps the termination of the branch in which the collapse-causing observation occurred. The latter isn’t some sort of weird retroactive thing—it’s just that the branch terminates right after the observation.

In case 2, the universe branches into an A-universe and a B-universe (or into pluralities of universes of both sorts). In the A-universe a bell is heard by the observer. In the B-universe a red light is seen by her. When this happens, collapse occurs, and there is no future to the observer after the observation of the red light, because in fact (or so case 2 was set up) it is the observation of A that won out. Or at least this is how it is when the two observations would be simultaneous. Suppose next that the bell observation would be made slightly earlier. Then as soon as the bell observation is made, the B-branch is terminated, and the red light observation is never made. On the other hand, if the light observation is timed to come first, then as soon as the light observation is made in the B-branch, this observation terminates the B-branch, and shortly afterwards the bell is heard in the remaining branch, the A-branch.

Case 1, then, works as follows. The universe branches into an A-universe, with a bell, and a silent B-universe. As soon as the bell is heard in the A-universe, the observation causes collapse, and one of the branches is terminated. If it’s the A-branch that’s terminated, then the observer heard the bell, but the future of that observation is annihilated. Instead, a couple of hours later the observer wakes up in the B-branch, and deduces that B must have been measured. If it’s the B-branch that’s terminated, on the otehr hand, then the observer’s observing of the bell has a future.

Prior to collapse, on this interpretation, we are located in multiple branches. And then our multilocation is wholly or partly resolved by collapse in favor of location in a proper subset of the branches where we were previously located. What happened to us in the other branches really did happen to us, but we never remember it, because it’s not recorded to memory.

On this interpretation, various things are observed by us which we never remember, because they have no future. This is a bit disquieting. Suppose that instead of the red light in case 2, the experimenter is poked with a red hot poker. Then if she hears the bell ring, she is relieved to have escaped the pain. But she didn’t: for if the poking is timed at or before the ringing, then the poking really did happen to her, albeit in another branch and not recorded to memory.

Fortunately for us, the futureless unremembered bad things were very brief: they only lasted for as short a period of time as was needed to establish them as phenomenologically different from the other possible outcome. So in the poked-with-a-poker branch, one only feels the pain for the briefest moment. And that’s not a big deal.

I worry a bit about quantum Zeno issues with this interpretation.

Thursday, April 13, 2017

Lying and killing

It initially seems to be a strange combination of views that (a) killing in defense of the innocent is sometimes permissible, but (b) lying is never permissible, not even in defense of the innocent. Yet that is the predominant view in the Christian tradition. Does this mean that truth is more valuable than life? That doesn't sound right, at least not in general.

I want to try a very speculative solution to this paradox, one I don't want to fully endorse as it raises some further problems. Thomas Aquinas has an interesting position on the lethal defense of the innocent: only officers of the state are permitted to kill intentionally, while private citizens may use defensive means that they foresee could be lethal only if they don't intend death.

Why the difference? Well, here is my crazy thought: perhaps all instances of permissible intentionally lethal defense of the innocent are effectively instances of the death penalty. In emergency situations, where there is an imminent threat to innocents, the state authorizes its officers to execute aggressors on the spot, without the usual legal safeguards. Every instance of permissible killing in a just war is an execution--we just don't call it that, because the emergency context makes very different procedures appropriate. Note, further, that as we learn from John Paul II's Evangelium Vitae, the death penalty is only permissible when there are no other means to the defense of society. Thus the intentionally lethal means to the defense of the innocent can only be deployed as a last resort. That is why, say, prisoners of war are not killed--there is no longer a need for an emergency execution once they are disarmed.

Suppose that this eccentric theory of lethal police and military action is correct. Then it is easy to see why there is a distinction between intentional killing and lying. Permissible intentional killing is an act of justice, an imposition of a just penalty on an aggressor. If we add Boethian idea that it is an intrinsic benefit to one to have justice done to one, then the aggressor is directly benefited by being punished. But even without that idea, the distinction between a defensive act of justice and a merely defensive act seems significant. There is a fine Kantian thought that just punishment constitutes a showing of respect to the person being punished; but a lie is innately disrespectful to the rationality of the person lied to.

Still, the puzzle remains. Why is it that the greater harm of death is appropriate punishment while the lesser harm of being lied to is not? But not every harm is appropriate as a punishment, and sometimes a lesser harm is inappropriate as punishment while a greater is appropriate. Sometimes, this is for reasons of dignity. Thus, it is a lesser harm to lose one's arms than to lose one's life, but judicial amputation is barbaric and contrary to the dignity of the criminal (it is hard to fully explain this intuitive judgment). Sometimes, the lesser harm just wouldn't fit the crime, or maybe ven any crime. Suppose a politician misused her office. Public infamy could be fitting punishment. But while the harm to reputation is greater in public infamy than in gossip, it just wouldn't be a fitting punishment to have officers of the court gossip about the politician behind her back. In fact, being gossiped about simply doesn't seem to be the right sort of harm to be a punishment--maybe it is the essential isolation of it from the consciousness of the person being gossiped about that makes it be inappropriate. I have the intuition that being lied to is pretty much like that--it is essentially isolated from the consciousness of the person being lied to (it's not a lie if they tell you they're lying to you!), and it just doesn't seem the right kind of harm to be a punishment.

The difficulty with this account is that modeling intentionally lethal police and military action as a form of the death penalty suffers from serious problems. The main one is that we have good reason to think that many enemy soldiers, even if their side is opposed to justice, are likely to be non-culpable, because they are likely to be ignorant of the fact that their side is opposed to justice. Perhaps, though, in an emergency situation--and a war is always an emergency--the evidential standards can be much lower, and so we don't need to examine culpability. Another problem is that this account will not allow the police to engage in intentionally lethal action against a clearly insane attacker. But perhaps that's the right conclusion.

Wednesday, April 12, 2017

Types of normativity

It is widely thought that our actions are governed by at least multiple types of normativity, including the moral, the prudential and the epistemic, and that each type of normativity comes along with a store of reasons and an ought. Moreover, some actions—mental ones—can simultaneously fall under all three types of normativity.

Let’s explore this hypothesis. If we make this distinction between types of normativity, we will presumably say that morality is the realm of other-concerned reasons and prudence is the realm of self-concerned reasons. Suppose that at the cost of an hour of torture, you can save me from a minor inconvenience. Then (a) you have a moral reason to save me from the inconvenience and (b) you have a prudential reason not to save me.

It seems clear that you ought to not save me from the inconvenience. But what is this ought? It isn’t moral, since you have no moral reasons not to save me. Moreover, what explains the existence of this ought seem to be prudential reasons. So it seems to be a prudential ought.

But actually it’s not so clear that this is a prudential ought. For a further part of the explanation of why you ought not save me is that the moral reasons in favor of saving me from a minor inconvenience are so very weak. So this is an ought that is explained by the presence of prudential reasons and the weakness of the opposed moral reasons. That doesn’t sound like an ought belonging to prudential normativity. It seems to be a fourth kind of ought—an overall ought.

But perhaps moving to a fourth kind of ought was too quick. Consider that it would be wrongheaded in this case to say that you morally ought to save me, even though all the relevant moral reasons favor saving me and if these were all the reasons you had, i.e., if there were no cost to saving me from inconvenience, it would be the case that you morally ought to save me. (Or so I think. Add background assumptions about our relationship as needed to make it true if you’re not sure.) So whether you morally ought to save me depends on what non-moral reasons you have. So maybe we can say that in the original case, the ought really is a prudential ought, even though its existence depends on the weakness of the opposed moral reasons.

This, however, is probably not the way to go. For it leads to a great multiplication of types of ought. Consider a situation where you have moral and prudential reasons in favor of some action A, but epistemic reasons to the contrary. We can suppose that the situation is such that the moral reasons by themselves are insufficient to make it be the case that you ought to perform A, and the prudential reasons by themselves are insufficient, but when combined they become sufficiently strong in contrast with the epistemic reasons to generate an ought. The ought which they generate, then, is neither moral nor prudential. Unless we’ve admitted the overall ought as a fourth kind, it seems we have to say that the moral and prudential reasons generate a moral-and-prudential ought. And then we immediately get two other kinds of ought in other cases: a moral-and-epistemic ought and a prudential-and-epistemic ought. So now we have six types of ought.

And the types multiply. Suppose you learn, by consulting an expert, that an action has no cost and there are either moral or prudential considerations in favor of the action, but not both. You ought to do the action. But what kind of ought is that? It’s some kind of seventh ought, a disjunctive moral-exclusive-or-prudential kind. Furthermore, there will be graded versions. There will be a mostly-moral-but-slightly-epistemic ought, and a slighty-moral-but-mostly-epistemic ought, and so on. And what if this happens? An expert tells you, correctly or not, that she has discovered there is a fourth kind of reason, beyond the moral, prudential and epistemic, and that some action A has no cost but is overwhelmingly favored by the fourth kind of reason. If you trust the expert, you ought to perform the action. But what is the ought here? Is it "unknown type ought"?

It is not plausible to think that oughts divide in any fundamental way into all these many kinds, corresponding to different kinds of normativity.

Rather, it seems, we should just say that there is a single type of ought, an overall ought. If we still want to maintain there are different kinds of reasons, we should say that there is variation in what kinds of reasons and in what proportion explain that overall ought.

But the kinds of reasons are subject to the same line of thought. You learn that some action benefits you or a stranger, but you don’t know which. Is this a moral or a prudential reason to do the action? I suppose one could say: You have a moral reason to do the action in light of the fact that the action has a chance of benefiting you, and you have a prudential reason to do the action in light of the fact that the action has a chance of benefiting a stranger. But the reason-giving force of the fact that action benefits you or a stranger is different from the reason-giving force of the facts that it has a chance of benefiting you and a chance of benefiting the stranger.

Here’s a technical example of this. Suppose you have no evidence at all whether the action benefits you or the stranger, but it must be one or the other, to the point that no meaningful probability can be assigned to either hypothesis. (Maybe a dart is thrown at a target, and you are benefited if it hits a saturated non-measurable subset and a stranger is benefited otherwise.) That you have no meaningful probability that the action benefits you is a reason whose prudential reason-giving force is quite unclear. That you have no meaningful probability that the action benefits a stranger is a reason whose moral reason-giving force is quite unclear. But the disjunctive fact, that the action benefits you or the stranger, is a quite clear reason.

All this makes me think that reasons do not divide into discrete boxes like the moral, the prudential and the epistemic.

Tuesday, April 11, 2017

My old Right Reason posts

In case anybody is interested, I added a side-bar link to my old posts on the now-defunct Right Reason blog, from about a decade ago. I think some of the arguments I had posted there are still interesting.

GPS signals, normativity and the morality of lying

I will argue that lying is never permissible. The argument is a curious argument, maybe Kantian in flavor, which attempts to establish the conclusion without actually adverting to any explanation of what is bad about lying.

GPS satellites constantly broadcast messages that precisely specify the time at which the message is sent together with precise data as to the satellite orbit. Comparing receipt times of message from multiple GPS satellites with the positions of the satellites, a GPS receiver can calculate its position.

A part of the current design specifications of US GPS satellites is apparently that they can regionally degrade the signal in wartime in order to prevent enemies from making use of the signal (US military receivers can presumably circumvent the degradation).

Now, let’s oversimplify the situation and make up some details (the actual GPS signal specifications are here and the points I am making don’t match the actual specifications), since my point is philosophy of language, not GPS engineering. So I’m really talking about GPS satellites in another possible world.

Suppose that normally the satellite is broadcasting the time n in picoseconds up to a precision of plus or minus ten picoseconds, and suppose that currently we receive a message of n in the time field from a satellite. What does that message mean?

First of all, the message does not mean that the current time is n picoseconds. For the design specifications, I have stipulated, are that there is a precision of plus or minus ten picoseconds. Thus, what it means is something more like:

  1. The current time is n ± 10 ps, i.e., is within 10 ps of n ps.

But now suppose that it is a part of the design and operation specifications that in wartime the locally relevant satellites add a pseudorandom error of plus or minus up to a million picoseconds (remember that I’m making this up). Then what the message field means is something like:

  1. Either (a) this is a satellite that is relevant to a war region, the current time is n ± 106 ps and [extra information available to the military], or (b) the current time is n ± 10 ps.

In particular, when wartime signal degradation happens, the time field of the GPS message is (assuming the satellite is working properly) still conveying correct information—the satellite isn’t lying. For the semantic content of the time field supervenes on the norms in the design and operation specifications, and if these norms specify that wartime degradation occurs, then that possibility becomes a part of the content of the message.

Suppose lying is sometimes morally obligatory. Thus, there will be a sentence “s” and circumstances Cs in which it is both true that s and morally required to say that not s. Suppose Alice is uttering “Not s” in an assertoric way. Morality is part of Alice’s (and any other human being’s) “design and operation specifications”. Thus on the model of my analysis (2) of the semantic content of the (fictionalized) time field of the GPS message, what is being stated or asserted by Alice is not simply:

  1. Not s

but rather:

  1. Either (a) Cs obtains, or (b) not s.

But if that’s the content of Alice’s statement, then Alice is not actually lying when she says “Not s” in Cs. And the same point goes through even if Alice isn’t obligated but is merely permitted to say “Not s” in Cs. The norms in her design and operation specifications make (4) be the content of her statement rather than (3).

In other words:

  1. If lying that s is obligatory or permissible in Cs, then lying is actually impossible in Cs.

But the consequent of (5) is clearly false. Thus, the antecedent is false. And hence:

  1. Lying is never obligatory or permissible.

Note that a crucial ingredient in my GPS story is that the norms governing the degradation of GPS messages are in some way public. If these norms were secret, then the military would be making the GPS satellites do something akin to lying when they degraded their messages. But moral norms are essentially public.

Objection 1: The norms relevant to the determination of the content of a statement are not moral but linguistic norms. The moral norms require that Alice utter “Not s” in an assertoric way only when (4) obtains. But the linguistic norms require that Alice utter “Not s” in an assertoric way only when (3) obtains. And hence (3) is the content of “Not s”, not (4).

Response: This is a powerful objection. But compare the GPS case. We could try to distinguish narrowly technical norms of satellite operation from the larger norms on which GPS satellites are controlled by the US military in support of military aims. That would lead to the thought that the time field of the satellite (on my fictionalized version of the story) would mean (1). But I think it is pretty compelling that the time field of the satellite would mean (2). The meaning of the message needs to be determined according to the overall norms of design and operation, not some narrow technical subset of the specifications. Similarly, the meaning of a linguistic performance needs to be determined according to the overall norms of design and operation of the human being engaging in the performance. And it is precisely the moral norms that are such overall norms.

Second, linguistic norms are norms of voluntary behavior, since linguistic performance is a form of voluntary behavior. But a norm of voluntary behavior that conflicts with morality is null and void insofar as it conflicts, much as an illegal order is no order and an unconstitutional law is no law.

Third, on a view on which linguistic norms have the kind of independence from moral norms that the objection requires, it is difficult to specify what makes them linguistic. For we cannot simply say that they are the overall norms governing linguistic behavior. Moral norms do that, as well. A distinction like the one in the objection would make sense in the case of something where the rules are formalized. Thus, there are circumstances when the rules of chess require one to do something immoral. (For instance, suppose that a tyrant tells you she will kill an innocent unless you move a pawn forward by three squares. The rules of chess require you to refrain from doing that, but it is immoral for you to refrain from it.) But the rules of chess are simply a well-defined set of statements about what constitutes a game of chess, and it is relatively easy to tell if something is a rule of chess or not. But linguistic norms are just some among the many norms governing human behavior, and it is hard to specify which ones they are, if one can't do it by the subject matter of the norms. (I am also inclined to think that the rules of chess might not actually be norms; they are, rather, classificatory rules that specify what counts as a victory, loss, draw or forfeit; the norms governing play are moral.)

Objection 2: Content is not normatively determined.

Response: If that’s right, then my line of argument does fail. But I think a normative picture of content is the right one. In part it’s my Pittsburgh pedigree that makes me want to say that. :-)

Objection 3: Bite the bullet and say that when Alice utters “Not s”, she is in fact asserting (4) and not lying even if Cs obtains. While on this view, technically, lying is never permissible, in practice the view permits the same behaviors as a view on which lying is sometimes permissible.

Response: This just seems implausible. But I wish I had a better response.

Monday, April 10, 2017

Harmony between assertion and mind

Suppose that Gunther thinks that he believes that killing is always wrong, but in fact he believes killing is sometimes permissible. Now, Gunther asserts: “Killing is always wrong.” Is he lying?

On accounts on which to lie is to assert something that one does not believe—or maybe that one disbelieves—to be the case, Gunther has to be lying. But that seems mistaken. Lying is always a form of insincerity. But it seems that a sufficient condition for sincerity in speech is that one be trying one’s best to speak in accord with what one believes. And Gunther could well be doing that.

So maybe lying is asserting contrary to what one thinks one believes? But that seems mistaken. Someone who asserts what she knows is not lying. Suppose Agnieszka knows that caring for her friends is morally important. But her psychiatrist is incompetent and convinces her that she believes that caring for her friends is not morally important. The incompetent psychiatrist’s claims only affects Agnieszka’s second-order beliefs. So, now, Agnieszka asserts: “Caring for my friends is morally important. I wish I could get myself to believe that!” Agnieszka asserts what she knows. Hence, she isn’t lying.

Should we maybe say: To lie is to assert contrary to both what one thinks one believes and what one actually believes? But that seems really gerrymandered. And it also seems that if Agnieszka said: “Caring for my friends is not morally important”, she would be lying.

Maybe what we should do is just say that lying involves a lack of the right kind of harmony between assertion and one’s mind, and leave it as a separate task to figure out what the right kind of harmony should be? (The word “harmony” is one I’m getting from Tollefsen’s book on lying.)

Peter's denial and the ethics of lying

On views on which lying is sometimes permissible, lying to save one’s life from unjust persecution is a paradigm case of permissible lying. But Peter’s lies about his connection to Jesus—his famous three-fold denial of Jesus—fall precisely under that head. So if it is sometimes permissible to lie, it is hard to see how Peter acted wrongly.

Of course, even if lying is sometimes permissible, the purpose behind the lie can be wrong. Was that the case for Peter? I doubt it. Peter’s purpose was not to be suspected of being one of Jesus’s followers. Suppose that he chose a different means to that end, say by dressing in a non-Galilean way and affecting a non-Galilean accent. There would be nothing at all morally wrong with that—that’s presumably the sort of thing missionaries in repressive countries do all the time, without anybody (other than the repressive regime!) thinking it’s wrong.

Perhaps the difference in purpose is the one between (a) Peter not being thought to be one of Jesus’s followers and (b) Peter being thought to not be one of Jesus’s followers. Maybe if Peter affected non-Galilean dress, he would merely be intending (a), whereas his lies were done with the intention of (b). And maybe there is in general something wrong with intending to be thought not to be connected with Christ. Note first, however, that the defender of the permissibility of lying cannot say that the problem is with the intention to deceive. For paradigm cases of lies thought to be permissible are precisely ones where there is an intention to deceive (Nazi at the door cases, say). Second, apart from general worries about the permissibility of intentionally causing false belief, it does not seem plausible to think that it is always wrong to intend to be thought unconnected with Christ. Third, Peter need not have had intended (b): he might simply have intended (a) or he might have intended something in between—that the people he talked to would on balance have evidence that he is not connected to Christ. It does not seem that these subtle distinctions are in play in the Gospels, given that the texts do not tell us which thing Peter intended.

Maybe, though, one can argue that Matthew 10:33 (“If anyone denies me before human beings, I will deny him before my Father who is in heaven”) constitutes a special divine command, a sui generis prohibition on lying about one’s connection to Christ. That’s probably the best move for the defender of the permissibility of lying to make. I think there are some problems with this move.

First, we should limit the invocation of special divine commands that go over and beyond the natural law. We should do so both on the grounds of Ockham’s razor as well as on theological grounds. It seems that the crucial difference between the life of the Christian and Old Testament law is that the latter includes many divine commands that go over and beyond the natural law.

In fact, I like the hypothesis there are very few—and perhaps no—divine commands applicable to all Christians beyond the natural law. One might think that, say, the command to be baptized is such. But I am inclined to think not. There are consequences of baptism—grace and the forgiveness of sins. And there are consequences of refusal to be baptized—lack of the grace and the forgiveness of sins. The virtue of prudence requires of us to be baptized, but there need not be any separate divine command. There is, of course, the authority of the Church: we are to obey the elders. However, that is an instance of the authority a community has over its members for the common good of the community. (This community is a special supernatural one, of course.)

Second, the context of Matthew 10:33 is the persecution that the Church will endure. Thus if a new command is being promulgated, it seems likely to be directed at future times when the Church needs to be spreading the Gospel (hence the verse before, about acknowledging Christ before human beings). But Peter’s denial is not a part of that time. The Church has yet to be founded: the death and resurrection of Christ have not yet happened and the Holy Spirit has yet to be sent.

Of course, those of us who think all lying is wrong still have a puzzle. A lie in order to escape unjust persecution even if wrong seems to be a very minor wrong. But the Gospels do not present Peter’s denial as a minor wrong. So there is still the puzzle of where the gravity of Peter’s sin comes from. But here the task seems not to be so difficulty. It is reasonable to think of certain kinds of settings as greatly multiplying the gravity of an offense. To steal something worth less than a day’s wages is a venial sin according to reputable moral theologians. But to steal from a church a cheap mass-produced icon that is worth less than a day’s wages turns the theft into a sacrilege, a much more serious offense. The gravity is explained by the fact that it is a sacrilege, but the wrongness is explained by the fact that it is a theft—if the pastor gave one the icon, one could permissibly take it away and it would have been neither theft nor sacrilege. Similarly, pickpocketing in church is a more serious offense. Thus, I think we can say that Peter’s denial was wrong simply because it was a lie. But it was as wrong as it was because it was a lie about Peter’s affiliation with Jesus.

Friday, April 7, 2017

Aesthetic reasoning about necessary truths

We prefer more elegant theories to uglier ones. Why should we think this preference leads to truth?

This is a classic question in the philosophy of science. But I want to raise the question in connection with philosophical theories about fundamental metaphysics, fundamental ethics, philosophy of mathematics and other areas where our interest is necessary rather than contingent truth. Why should we think that the realm of necessity has the kind of aesthetic properties that would make more beautiful theories more likely to be true?

Here are two stories. The first story is that we are so constructed that we tend to find beauty in those philosophical theories that are true. It is difficult to explain why there would be such a coincidence if we are the product of naturalistic evolution, since it is unlikely that such a connection played a role in the survival of our species tens of thousands of years ago. If God exists, we can give an explanation: God gave us aesthetic preferences that guide us to truth.

The second story is that fundamental necessary reality is itself innately beautiful, and beautiful theories exhibit the beauty of their subject matter. And we recognize this beauty. It is puzzling, though: Why should fundamental necessary reality be beautiful? The best explanation of that which I can think of is again theistic: God is beauty itself, and all necessary truths are grounded in God.

Of course, one might simply reject the claim that our aesthetic preferences between theories lead to truth. But I think that would be the end of much of philosophy.

I think that in the order of knowing, aesthetics and ethics come first or close to first.

Thursday, April 6, 2017


Self-colocation is weird. An easy way to generate it is with time travel. You take a ghost or other aethereal object who time travels to meet his past self, and then walks into the space occupied by his past self--ghosts can walk into space occupied by themselves--so that he is exactly colocated with himself. If you don't like ghosts, time travel a photon--or any other boson--into the past and make it occupy the same place as itself. But time travel is controversial.

However, it occurs to me that one can get something a bit like self-colocation with an aethereal snake and no time travel. An aetherial snake can overlap itself. First, arrange the snake in spiral with two loops. Then gradually tighten the ring, so that the outer ring of the spiral overlaps the inner one, until the result looks like a single ring. Suppose that the snake exhibits no variation in cross-section. So we have a snake that is wound twice in the same volume of space. The whole snake occupies the same region as two proper parts of itself. [I'm not the only person in this room generating odd examples: Precisely as I write this, I hear our four-year-old remarking out of the blue that she wished she had two bodies, so she could be in two places at once. A minute or so later she is talking of twenty bodies.]

(The animation was generated with OpenSCAD using this simple code.)

So far it's not hard to describe this setup metaphysically: the whole overlaps two proper parts. But now imagine that our snake ghost is an extended simple. We can no longer say that the snake as a whole occupies the same region as a proper part of it does, as the snake no longer has any proper parts. But there seems to be a difference between the aethereal snake being wound twice around the loop and its being wound only once around it.

If we accept the possibility of aethereal objects that can self-overlap and extended simples, we need a way to describe the above situation. A nice way uses the concept of internal space and internal geometry. The snake's internal geometry does not change significantly as the spiral tightens. But the relationship between the internal space and the external space changes a lot, so that two different internal coordinates come to correspond to a each external coordinate. That's basically how my animation code works: there is an internal coordinate that ranges from 0 to 720 as one moves along the snake's centerline (backbone?), which is then converted to external xyz-coordinates. Initially, the map from the internal coordinate to the external one is one-to-one, but once things are completed, it becomes two-to-one (neglecting end effects).

The idea of internal and external space allows for many complex forms of self-intersection of extended simples. And all this is great for Aristotelians who are suspicious of parts of substances.

Monday, April 3, 2017

Moral failure and naturalism

Tripping while walking or acquiring an unjustified belief does not entail that we are in any way defective. It’s just not in human nature to walk steadily all the time—there is a tradeoff between perfect steadiness and the need to look for more distant dangers, or just the need to think about more important matters. Likewise, we sometimes need to acquire beliefs more quickly than checking the evidence carefully allows.

But a moral failure seems different. Acting immorally is always a defect. This tells us something interesting about nature: our nature has tradeoffs, but morality is never among the tradeoffs.

(A curiosity: If it is our nature never to act immorally, but it isn’t our nature never to trip, we would expect that tripping would be much more common than immoral activity. But it’s not like that.)

It is difficult, I think, to reconcile the special role that morality plays in us—the fact that moral failure is always a defect—with naturalism. On an evolutionary picture, we would expect tradeoffs to be everywhere in our nature. If we were meant by nature never to trip, we would expect to have an instinct that makes us always look down in front of us—but of course then we wouldn’t see distant danger, so instead we have a tradeoff where we scan the environment in all directions as well as looking down in front of us.

I have one worry about the above line of thought. Perhaps immoral activity is not always a defect. Maybe it is only a defect when isn’t innocently ignorant. Think of the extremely difficult cases that come up in medical or military ethics where one needs to act very quickly. In those cases, there just isn’t enough time to always figure out what the right solution is, and it does not seem to be necessarily a defect when the conscientious doctor or officer acts immorally, if she has given the matter as much thought and are as there was time for and innocently done what appeared right.

Maybe that’s right. It’s still surprising on a naturalistic picture of our nature and origins that it is always a defect to act knowingly immorally. We would expect our nature to exhibit tradeoffs even there.

And maybe the innocent ignorance cases aren’t a problem. Maybe in such cases, the action is to be described in terms that makes it right, like: “Performing an operation that after the due amount of investigation appeared most in keeping with the salient goods.”

Of course, some naturalists simply deny that there is any coherent concept of “defect” to be applied to us. The above line of thought may be grist for their mill. Another view might be to bite the bullet and say that we are riddled with tradeoffs through and through, and it is no defect when we occasionally act immorally. On the contrary, sometimes (say, when it causes great harm to one’s genes getting passed on) acting morally is a defect—but we should be guided by what is right or wrong, not by what is or isn’t a defect in our nature. This latter view is not, I think, very popular, but one finds it in Andrea Dworkin’s idea that “the God who doesn’t exist” (nature? evolution?) has designed us so that until recent times we could only reproduce by means that, according to Dworkin, are innately oppressive to women.

Lying in fiction?

It seems that fiction can't lie because, well, it's fiction. But suppose you are reading a novel, and it says: "A woman wearing a woolen cloak entered the room." A chapter later, you learn there was no woman, but a wizard created an illusion. Weren't you lied to by the author?

In those cases where the narrator is a character, at most the narrator lied. But what if the narration is by an impersonal omniscient narrator? Certainly, at the least there is temporary deceit about the world of the fiction, and the deceit is created within the context of a literary style where the reader expects truth about the world of the fiction.

But lying requires assertion. Could we say that statements of an impersonal omniscient narrator are assertions about the world of the fiction? That would seem to be going too far.

Friday, March 31, 2017

Fictional characters and the ontological argument

This argument is valid:

  1. If God exists in any way, he exists in the supreme way of existing.
  2. If God does not exist in the supreme way of existing, God exists as a fictional character.
  3. So, God exists in the supreme way of existing.

Star Trek cookie cutters for First Contact Day

In honor of First Contact Day, my big kids wanted to make Starfleet insigna and Vulcan IDIC cookies. So I generated some 3D printable cookie cutters (Starfleet; Vulcan).

Wednesday, March 29, 2017

Yet another odd double effect case

Alice has just fed a poison to Bob. Bob hasn’t died yet. He is standing, by coincidence, on the edge of a cliff, and soon will die of the poison, unless he gets an antidote. Carl is there and has a syringe full of the antidote. Carl injects Bob with the antidote, but this startles Bob and Bob falls off the cliff to his death.

Question 1: Did Alice murder Bob?

Answer: I think not. Here’s an argument. Bob dies as a side-effect of injection with the antidote. But it could just as well have been Carl who slipped and fell while injecting Bob instead of Bob falling. And surely then we shouldn’t say that Alice murdered Carl—though she did wrongfully cause his death.

Question 2: Suppose that Carl was Alice’s friend and foresaw that Bob would fall off the cliff to his death if injected with the antidote, but reasoned: “I am saving Alice from being a murderer.” Could one legitimately make this double-effect analysis? “Carl is intending that Alice not be a murderer. His means to that is giving Bob an antidote to the poison. A foreseen side-effect of Carl’s action is Bob’s death, but this side-effect is not intended either as an end or as a means. And given that Bob would have died anyway, the side-effect is not disproportionate to the good of saving Alice from being a murderer.”

Answer: I think the proportionality condition is not met. Sure, Carl makes Alice not be a murderer. But Alice is still an attempted murderer—which is just as culpable as being an actual murderer—and her malfeasance still causes Bob’s death, so she still has that death on her conscience. Granted, she isn’t a murderer any more (if I am right about Question 1), but the bad of Carl’s accidentally killing Bob seems disproportionate to the relatively minor good achieved here.

It’s interesting when it is the proportionality condition in double effect that ends up being crucial.

Leprechauns and fairies

Why aren’t multiverse—or large universe—hypotheses that imply that there very likely exist fairies and leprechauns dismissed as mere sceptical hypotheses?

Tuesday, March 28, 2017

More remarks on Aristotelian set theory

If we have an Aristotelian picture of abstracta, we should expect that what mathematical objects exist differs between possible worlds.

For the Aristotelian, abstract objects are abstractions from concrete things. So we shouldn’t expect the same full panoply of sets regardless of what concrete things there are. For instance, suppose that the universe contains exactly three point particles, A, B and C. Then we can immediately abstract from these particle positions distance ratios like AB : BC, AC : AB and AC : BC. These ratios are then represented by real numbers. So we are going to have these real numbers. More sophisticated abstractive processes may well generate other real numbers: for instance, we will have a real number representing the ratio of the height of the triangle drawn from A to the base BC. And given a real number, we might be able to use purely abstract processes to generate further real numbers: given a and b, we may generate a + b and ab, say. But there is no reason to think that these abstract processes will generate the same collection of real numbers regardless of what the three particle positions we start with are.

So, what real numbers exist should vary between possible worlds. But every real number defines a subset of the natural numbers (just write the real number in binary, and let the nth bit decide if n is in the subset or not). If the real numbers vary between possible worlds, so do the subsets of the natural numbers. In particular, we should expect that in different possible worlds, a different set counts as ``the power set’’ of the natural numbers.

Furthermore, what bijections there are between sets will vary between possible worlds. Thus, if we see the question of whether two sets have the same count of members as having the same answer in every world where the two sets exist, we cannot take the standard Cantorian account of the size of a set. Instead, we may want to generate the concept of sameness of size from bijections in different worlds. Thus, we may try to say that two sets A and B are the same size at level 0 provided that there is a bijection between A and B. Then we say that A and B are the same size at level n provided that possibly there is a set C that is the same size as A at level p and the same size as B at level q and n ≥ 1 + p + q. Finally, we say that A and B are the same size simpliciter provided that they are the same size at some finite level. This is complicated, and I haven’t checked under what assumptions it generates a transitive relation (it’s plausibly reflexive and symmetric).

Anyway, the point is this: It is an interesting and not easy philosophical project to work out the set-theoretic consequences of Aristotelianism. This could make a good dissertation.

Elections as hiring decisions

People tend to think of elections for high office as sui generis rather than as what they are: hiring decisions, for a particularly onerous but important job.

Once we see elections for high office as hiring decisions, some things become a bit puzzling.

  1. It is often seen as important that a candidate for high office have a strong and sincere personal commitment to a platform. But why? Suppose I hire a lawyer to represent my interests. It might be nice if the lawyer had a strong and sincere personal commitment to the things I want the lawyer to represent me in respect of, but it is not at all necessary. What is needed is that the lawyer further my interests, and do so along rough lines that I may sketch, in a professional and effective way. The lawyer does not need to think that it would be better for the world if I get what I want—she may simply think that it is good to have in place a legal system where almost everyone gets able legal representation for the furtherance of their interests, and that what I want isn’t so bad as to make it immoral for her to represent me. One can even imagine a lawyer who specializes in representing a particular kind of interest without actually sharing that interest, but holding that nonetheless it is important that an interest of that sort should be represented.

  2. There is an interest in the personal life of candidates that would be seen as creepy and likely illegal in most other hiring decisions.

Of course, these kinds of things might be appropriate in light of the specific features of high political office. But they shouldn’t be taken for granted.

Monday, March 27, 2017

Voting for Schmitler

Three people are running for election in Germany: Hitler, Schmitler and Bonhoeffer. Bonhoeffer promises just policies but has no chance of being elected. Hitler promises to kill 50% of minorities. Schmitler promises to kill 80% of minorities. You might think that at this point I will raise the difficult question whether it is permissible, all other things being equal, to vote for Hitler. But I won’t raise exactly that question.

Instead, I want to expand on the above scenario in a different way. Schmitler is incompetent and won’t manage to do more than a quarter of the evils he promises, unlike Hitler who is going to exactly what he promises. So, whom should you vote for? Bonhoeffer who has just policies but won’t be elected? Hitler whose policies are less bad than Schmitler’s, but who will do exactly what he promises? Or Schmitler whose policies are much worse than Hitler’s, but who will do much less bad than Hitler?

There is a good utilitarian case for voting for Schmitler. Here’s an argument for this case. Suppose the elections are occurring in the middle of World War II. It seems that a very reasonable thing for Allied spies to do is to ensure that incompetent people run Nazi Germany. One means to that goal is stuffing ballot boxes with votes for Schmitler. And while typically one shouldn’t stuff ballot boxes, this seems to be a case where the stuffing of ballot boxes would be permissible. So, Allied spies, we suppose, are stuffing ballot boxes in favor of Schmitler. Helga is a German resister to Nazism, working for the Allies. She is an excellent prestidigitator and is going to the voting booth with a sleeve full of Schmitler ballots, in order to stuff the box surreptitiously. If the Allied spies are doing the right thing, Helga is doing the right thing.

Now, if Helga can permissibly stuff the ballot box in favor of Schmitler, then she could permissibly do this: put in a vote for Bonhoeffer (or Hitler), then surreptitiously remove that ballot and replace it with a fake ballot in favor of Schmitler. But if that’s permissible for her, then it would be very strange if she wasn’t permitted simply to vote for Schmitler.

So, it seems, it is permissible to vote for Schmitler on the grounds that he is incompetent, despite the fact that his policies are significantly worse than Hitler’s. But if this is permissible, then it would be a fortiori permissible to vote for Schmitler if he promised to kill 5% of minorities, and this would seem to be permissible even if Schmitler were as competent as Hitler. So, we have an argument that it is permissible to vote for a candidate whose policies represent a lesser evil. Of course, one should never endorse an evil, even a lesser one. So, it follows that voting for a candidate is not endorsement of the candidate’s policies.

I am not wholly convinced by the above argument. I feel a certain pull to the strange view that while it would be permissible for Helga to replace her real Bonhoeffer vote with a Schmitler fake ballot, it would not be permissible for her to vote for Schmitler. After all, strange circumstances make for strange conclusions.

Friday, March 24, 2017

Authorless books

I've been imagining a strange scenario. I come across a text that I know for sure was generated by an entirely random process--say, the proverbial monkeys at the typewriter. I look at it. Mirabile dictu, it's coherent and reads just like a literary masterpiece--let's say it's just like something Tolstoy would have written had he written one more novel at the peak of his creative powers.

I think reading this random text could be a disquieting experience. I could read it shallowly, the way one reads some novels for mere entertainment. And in that context, it would work just as well as shallowly reading a real novel. But of course with a masterpiece, one wants to read it more deeply. In doing so, one draws connections between different parts of the texts ("Oh! So that's what that foreshadowed!" or "Ah, so that's why she did that!"), between the content and the mode of expression ("Look at all these short words describing the rapidity of the march"), between what is overtly the text and other texts, ideas, historical events and persons, etc. Drawing such connections, whether explicitly or just as a barely conscious sensation of something there--is a part of the enjoyment of reading a literary masterpiece, when done in moderation. But in our random text, all connections are merely coincidental. Nothing is there on purpose, not even unconsciously. When we read a literary giant like a Plato or a Tolstoy, when we see a compelling connection, we have good reason to think the author meant it to be there, and that sensing the connection is a part of a good reading of the text. But in the random text, there will be no such thing as a good reading or a misreading. And that would have to be disquieting. There is a sense in which we would be inventing all the connections. Reading would be more like creating than like discovering. I suppose death-of-author people think that's already the case with normal novels. But I don't think so. Real connections differ from chance ones.

At the same time, I think that in practice if I were reading this text which is just like a literary masterpiece, I'd end up suspending my disbelief about the author, and just delight in the connections and subtleties, even if they are merely apparent.

But maybe in a world with God there is no true randomness. So maybe the hypothesis of a book where nothing is intended is impossible?

Wednesday, March 22, 2017

More on life

God is alive, angels are alive, people are alive, dogs are alive, worms are alive and trees are alive. What is it that makes them all be alive, while the Milky Way, the Sun, Etna, a car, a Roomba, and an electron are not? I raised a version of this question recently, and since then have had discussions about it with a number of our graduate students, most extensively with Alli Thornton and Hilary Yancey, to whom I am very grateful.

We could say that they are all alive in an analogical sense. But that doesn’t solve the problem, but simply puts a constraint on the shape of a solution. For to solve the problem, we still have to say something about how this particular analogy works.

Here is the best answer I have right now, but it still has some difficulties I will discuss:

  • A living thing is one that can act in pursuit of its own ends.

This indeed covers God, angels, people, dogs, worms and trees. Moreover, it produces a gradation of life in respect of the degree and quality with which the thing can act in pursuit of its own ends and the degree of ownership the thing has over its ends. For instance, God is omnipotent and perfectly rational, and he is his own end, so he is most fully alive. All the living creatures, on the other hand, have ultimate ends imposed on them by their nature, to the realization of which end their activity are ordered. However, angels and people additionally make a rational choice of ways to realize their ultimate ends, adopting which ways involves setting themselves intermediate ends. Higher non-human animals like dogs do something that approximates this. Moreover, angels, people and dogs have a wide variety of ways of pursuing that end. On the other hand, trees only pursue a limited variety of ends with a limited variety of means.

A bonus of this definition is that we get the conclusion, which seems intuitively correct, that anything that thinks is alive. For thinking is an end-directed activity—it is directed at action and/or truth. So if we ever make an artificial intelligence system that really thinks, it will be alive.

The Milky Way, the Sun, Mount Etna, a car and a Roomba do not pursue their own ends, I think, if only because they are not substances, and only substances own their ends.

But electrons… This is what troubles me. I think that the fundamental constituents of physical reality, be they particles or fields, are substances. And I think all substances have a teleology, and hence have an end. The distinction I would like to be able to make, however, is between activity in pursuit of an end and teleological activity more generally. Electrons in their characteristic activity are acting teleologically. But their action is not in pursuit of an end. Rather their end is simply to engage in this very activity and nothing more. The activity is teleological, but it does not pursue a telos.

But what if it turns out that electrons do genuinely act in pursuit of an end? Then, perhaps, we will have learned that electrons are a very primitive form of life.

What about God, given divine simplicity, though? God = God’s telos = God’s activity. Well, I think that even if God’s activity is identical with God’s telos, one can make a conceptual distinction that allows one to say that God acts for the sake of that telos, a distinction that perhaps is not there in the case of the electron.

As you can see, I am still not very happy with the account. But it’s the best I have right now.

If naturalism is true, there is an infinite afterlife

  1. Deontology is true.
  2. A finite being could not have the kind of dignity that deontology ascribes to human beings.
  3. So, human beings are infinite. (1-2)
  4. If human beings are infinite, they are infinite synchronically or diachronically.
  5. If naturalism is true, human beings are finite synchronically.
  6. If there is no infinite afterlife, human beings are finite diachronically.
  7. So, either naturalism is not true or there is an infinite afterlife. (3-6)
  8. So, if naturalism is true, there is an infinite afterlife. (this is a material conditional following from 7)
Of course, there are also arguments that if naturalism is true, there is no afterlife, and if these are sound, then together we get an argument that naturalism is not true.

Tuesday, March 21, 2017

Eternal life and the crucible of character theodicy

Consider the crucible of character theodicy, that we are permitted by God to meet with great evils in order to form a character with virtues like courage and sacrificial love whose significant exercise requires significant evils.

I take it that it’s clear that forming such a character is worthwhile. But there are at least three problems with this theodicy:

  1. While such character formation is valuable, is it valuable enough to justify our suffering great evils? Wouldn’t it have been better if God just gave us the virtues directly, rather than having us pay a great price?

  2. Even if it is valuable enough to justify our suffering great evils, wouldn’t it be better if we suffered fewer or lesser ones?

  3. What about those who suffer and develop a vicious character?

I think these three problems can be overcome if we think about heavenly life as an infinite value multiplier.

Ad 1: There is clearly some additional value to having virtues that were formed through significantly free exercises of them rather than having had these virtues imposed on one. In heaven, on infinitely many days one has and enjoys the value of having virtues. But if one has formed these virtues through significantly free exercise, then on infinitely many days one also has and enjoys the additional value of having virtues that were thus formed. That’s an infinite additional increment. So as long as the disvalue of the sufferings in this life was finite—which surely it was—it’s worth it.

Ad 2: The greater the sufferings that one endured courageously and the greater the sacrifices one made in love, the more fully one owns the resulting courage and love. For in more extreme exercises of these virtues, one has a greater opportunity to abandon the path of virtue, and one’s presence on that path is more truly one’s own. And this deeper ownership over one’s virtue—bearing in mind, of course, that all one has is a participation of God, and that grace is deeply involved—adds an additional value of virtue-ownership throughout an infinite number of future days. Hence, it adds an infinite amount of value, which is surely worth it.

Ad 3: This is probably the most serious worry. Start with this thought. God is choosing whether to snatch Judas up to heaven in the first moment of his existence, imposing on him a perfectly virtuous character, or to give Judas the opportunity to freely develop and own that character. A toy model for this an extended utility calculation. On the first option, we have an expected utility of

  • V(eternal unowned virtue),

where V is value. On the second option, we have an expected utility of

  • pV(eternal owned virtue) + (1 − p)V(Judas chooses vice)

where p is the probability that Judas would come through the crucible well. (Of course, this line of thought requires rejecting theological compatibilism and Molinism.) Here, V(eternal unowned virtue) and V(eternal owned virtue) are each infinite and positive. Plausibly, V(Judas chooses vice) is negative. Is it infinite? That’s not clear. One might think that on orthodox Christian views of hell, it is both negative and infinite. But that need not be the case. It could be that the suffering and vice in hell actually decreases from day to day, so that the total amount of suffering and vice over eternity is actually finite (think of how 1 + 1/2 + 1/4 + ... = 2).

If V(Judas chooses vice), the argument still isn’t over, but I will assume that V(Judas chooses vice) is finite—we could just build that into the theodicy. In that case, we can basically neglect V(Judas chooses vice)—when the other quantities are infinite, a finite subtraction is only going to be a tie-breaker.

So now the question is whether V(eternal unowned virtue) is bigger than or equal to pV(eternal owned virtue). And here it seems very reasonable simply to make a sceptical theist move. We don’t know what was Judas’ probability of coming through the crucible well. We don’t know exactly how V(eternal owned virtue) compares to V(eternal virtue). It could be that a day with owned value is three times as valuable as a day with unowned virtue. If so, then as long as p > 1/3, God’s giving Judas the opportunity for freely choosing virtue was worthwhile.

There are many objections, of course, that one can make. Here’s one that particularly comes to my mind: Wouldn’t it be better for God to first give people the opportunity to freely choose a virtuous character, but then if they refuse to do so, to impose that character on them? After all, at least some infants go to heaven after death. But they haven’t developed a virtuous character through the described kind of crucible. And so it seems that God imposes on them a virtuous character.

There are two things I’m inclined to say to this. First, there is a relevant difference between the case of imposing virtue on an infant and imposing virtue on someone who has chosen against virtue. Second, those who choose virtue own their virtue more fully if they had the possibility of not having that virtue at all.

Monday, March 20, 2017

Three levels of sex/gender

The biological understanding of male and female is something like this. Some species reproduce sexually. Some species that reproduce sexually exhibit a consistent difference in size between the two gametes that come together in sexual reproduction. In those species, the producer of the larger gamete is called “female” and the producer of the smaller gamete is called “male”. We can thus draw a distinction between a species having sexes, namely having respective producers of two different kinds of gametes, each of which is needed for sexual reproduction, and the species having male and female sexes.

Let me speak vaguely but heuristically. Human reproduction has a deep ethical and theological significance because it produces persons. Moreover, humans normally reproduce sexually (the exception of course being twinning). So it’s unsurprising if the existence of two sexes among humans has intrinsic ethical and theological significance. But the difference between male and female seems to have no intrinsic ethical or theological significance. It matters that there are two reproductive kinds, but that one of the two kinds produces a larger gamete than the other has no intrinsic ethical or theological significance.

But of course even though what defines the difference between male and female humans is the difference in gamete size, the actual differences between male and female humans are not in fact limited to differences of gamete size. Those humans that produce smaller gametes produce more of them, while those humans that produce larger gametes produce fewer of them and gestate offspring. Humans have “primary sex characteristics” that support differing ways of reproductive functioning.

Here is a thought experiment. Imagine earth* where there are humans*. To a cursory external examination, humans* live, look and behave just like humans, and have the same kind of sexual differentiation. One sex produces lots of gametes and the other relatively few. The sex that produces fewer gametes gestates offspring for nine months, has mammary-type glands that nourish offspring after gestation, is a little smaller on average, etc. But on earth*, it also turns out that the the sex that produces relatively few gametes produces the smaller gametes. (There may be evolutionary reasons why this is unlikely. But unlikely is not impossible.) Thus, on earth* male humans* fill the same biological roles as female humans do on earth, except at a near-microscopic level where the sizes of gametes become visible.

Now overlay on this the social level. This could go in multiple ways. It is easiest to imagine that on earth*, male humans* have the same social positions, and suffer from the same sorts of discrimination, as female humans do on earth. But it could in principle be reversed: it could be that the social position of male and female humans* is like that of male and female humans, respectively. Or it could be nullified: there could be no significant differences in social position.

This suggests that there are three levels to sex/gender:

  • The definitionally fundamental distinction between male and female in terms of gamete size.

  • Other biological differences—particularly with respect to reproductive functioning.

  • The social distinctions.

The first two tend to be lumped together as “sex” or “biological sex”, while the last gets called “gender”. But there really are three distinct levels. We might roughly call them: “biological gametic sex”, “biological functional sex” and “social gender”. Thus, among humans*, the connection between biological functional sex and biological gametic sex is the reverse of how it is among humans. So we now have three different senses of terms like “man”, “woman”, “male” and “female”.

Friday, March 17, 2017

Some paradoxes of reference

  • one plus the biggest integer that can be expressed in English in fewer than fifty words
  • one; two; three; one plus the biggest integer mentioned in this list
  • one; two; three; one plus the last integer mentioned in this list
  • one plus the last integer mentioned in this list; two; three; one plus the first integer mentioned in this list
  • one plus this integer
  • one; two; three; the biggest integer mentioned in this list
  • one; two; three; the last integer mentioned in this list
  • the last integer mentioned in this list; two; three; the first integer mentioned in this list
  • this integer
  • the square of this integer

Wednesday, March 15, 2017


One of the things that most strengthens my faith is compelling accounts of heavenly happiness. I think there are at least two reasons why such accounts tend to strengthen faith. First, a compelling account of heavenly happiness rebuts the "sounds like fairy tale" objection to Christian faith. Second, a compelling account of heavenly happiness resonates with us in a way that gives us evidence that we are meant for a different kind of life than the one we have hear. I wish there were more sermons on heaven. And we philosophers also should work more on giving good accounts of what heaven might be like.

Tuesday, March 14, 2017

Disjunctive victimization?

Alice, Bob and Carl are suffering from a deadly disease. Alice possesses one dose of a medication necessary and sufficient to cure the disease. She has four relevant options. First there are:

  1. Use the medication on herself.
  2. Use the medication on Bob.
  3. Use the medication on Carl.

Option 1 is permissible. Options 2 and 3 are supererogatory. But what Alice actually does is:

  1. Destroy the medication.

Alice clearly did something wicked by failing to use the medication to save a life. But how do we describe this wicked deed?

It seems that Alice’s action was a fatal negligence of a duty towards herself, and a fatal negligence of a duty towards Bob and a fatal negligence of a duty towards Carl. But that makes it sound like three counts of fatal negligence, which is triple-counting the wrongful act.

I suppose what we can say is something like this: Alice neglected to use the medication to save a life. Whom did she act against? Maybe each of: herself, Bob and Carl. But we shouldn’t look at the action as the violation of three duties, but only of one duty, to use the medication to save herself, Bob or Carl. So she violated a single duty, to the tune of a single life, but that single duty was one she owed to three people.

Question 1: Does it follow that one can have a duty to a group which does not reduce to a duty to each member? For Alice surely doesn’t owe Bob that she save herself, Bob or Carl, and she doesn’t owe Bob that she save Bob, since she can permissibly save herself or Carl.

Answer: I don’t know. Maybe we can say:

  • Alice owes herself that if she doesn’t use the medication to save Bob or Carl, she use it to save herself
  • Alice owes Bob that if she doesn’t use the medication to save herself or Carl, she use it to save Bob
  • Alice owes Carl that if she doesn’t use the medication to save herself or Bob, she use it to save Carl.

And so Alice wrongs each of herself, Bob and Carl. A problem with this solution, however, is that it seems to triple counting Alice’s wrongdoing, by making it seem like she fatally wronged each of three people—but she is only responsible for a single death. Maybe, though, we can say that the duty to the three reduces to the three individual duties, but that the culpabilities don’t sum?

Question 2: Does the case provide an argument that one can wrong oneself? My above description of the case as one one where Alice owes it to herself, Bob and Carl that she save herself, Bob or Carl presupposes duties to herself. What can someone who thinks there are no duties to self say?

Answer: I don’t know. Maybe she can say: Alice owes Bob and Carl that she save herself, Bob or Carl. But it would be a little weird to think that by saving herself, Alice would be fulfilling a duty to Bob and Carl.

Final remarks: I am far from clear how to morally describe the case. I think the neatest description is one where a group is non-reducibly victimized, and where there are duties to self. But that may not be the only admissible description.

Instantaneous Newtonian gravitational causation at a distance?

It’s widely thought that Newtonian gravity, when causally interpreted, involves instantaneous causation at a distance. But I think this is technically not right.

Suppose we have two masses m1 and m2 with distance r apart at time t1. The location of m2 at t1 causes m1 to accelerate at t1 towards m2 of magnitude Gm2/r2. And this sure looks like instantaneous causation at a distance.

But this isn’t an instance of instantaneous causation. For facts about what m1’s acceleration is at t1 are not facts about how the mass is instantaneously at t1, but facts about how the mass is at t1 and at times shortly before and after t1: acceleration is the rate of change of velocity over time. Suppose that a poison ingested at t1 caused Smith to be dead at all subsequent times. That wouldn’t be a case of instantaneous causation, even though we could say: “The poison caused t1 to be the last moment of Smith’s life.” For the statement that t1 is the last moment of Smith’s life isn’t a statement about what the world is instantaneously like at t1, but is a conjunctive statement that at t1 he’s alive (that part isn’t caused by the poison) and that at times after t1 he’s dead (that part is caused by the poison, but not instantaneously). Similarly, m1’s velocity (and position) at times after t1 is caused by m2’s location at t1, but m1’s velocity (or position) at t1 itself is inot.

Let’s call cases where a cause at t1 causes an effect at interval of times starting at, but not including, t1 a case of almost instantaneous causation. In the gravitational case, what I have described so far is only almost instantaneous causation. Of course, people balking at instantaneous action at a distance are apt to balk at almost instantaneous action at a distance, but the two are different.

The above is pretty much the whole story about instantaneous Newtonian causation if one is not a realist about forces. But if one is a realist about forces, then things will be a bit more complicated. For m2’s location at t1 causes a force on m1 at t1, which complicates the causal story. On the bare story above, we had m2’s location causing an acceleration of m1. When we add realism about forces, we have an intermediate step: m2’s location causes a force on m1, which force then causes an acceleration of m1. (There might even be further complications depending on the details of the realism about forces: we may have component forces causing a net force.) Now, when the force-at-t1 causes an acceleration-at-t1, this is, for the reasons given above, a case of almost instantaneous causation. But the causing of the force-at-t1 by the location-at-t1 of m2 is a case of genuinely instantaneous causation.

But is it a case of causation at a distance? It seems to be: after all, the best candidate for where the force on m1 is located is that it is located where m1 is, namely at distance r from m2. (There are two less plausible candidates: the force acting on m1 is located at m2, and almost instantaneously pulls on m1; or it’s bilocated between the two locations; in any case, those candidates won’t improve the case for instantaneous action at a distance.) But here is another problem. The force on m1 is not produced by m2. It is produced by m1 and m2 together. After all, the Newtonian force law is Gm1m2/r2. (It is only when we divide the force by m1 to get the acceleration that m1 disappears.) Rather than m2 pulling on m1, we have m1 and m2 pulling each other together. Thus, m2 instantaneously partially causes the force on m1 at a distance. But the full causation, where m1 and m2 cause the force on m1, is not causation at a distance, because m2 is at the location of that force.

In summary, the common thought that Newtonian gravitation involves instantaneous causation at a distance is wrong:

  • If forces are admitted as genuine causal intermediates (“realism about forces”), then we have almost instantaneous causation of acceleration by force (moreover, not at a distance), and instantaneous partial causation of force at a distance.

  • Absent force realism, we have almost instantaneous causation at a distance.