Wednesday, July 17, 2019

Distributive promises

Suppose I promise my class to grade all the weekly homework within three days. In week four, I fail and am late with grading. If the content of my promise was simply the proposition

  1. that I grade all the homework within three days,

then after week four, then no matter how speedy I am with grading the homework, proposition (1) is just plain false. And this means that my promise no longer generates any reason for me to grade the homework in weeks five and onward within three days, which seems wrong. I should, instead, apologize for failing in week four, and work even harder in the succeeding weeks.

I think this is because the promise was distributive. It wasn’t a promise to make proposition (1) true. It was a promise that for each week of homework generated a separate promissory reason to grade that week’s homework within three days.

The normative force of the promise is rather like making a separate promise for each week of class:

  1. I promise that in the first week, I will grade the homework in three days. I promise that in the second week, I will grade the homework in three days. … I promise that in the 15th week, I will grade the homework in three days.

But other cases of distributive promises aren’t as neatly handled. Suppose I promise my class:

  1. If you come to office hours, I will try to answer any question you might have about logic.

Again, this is distributive. If I refuse to answer a question out of laziness, it doesn’t let me off the hook with regard to the next question. But if I analyze this as a sequence of separate promises, then that sequence has to be infinite:

  1. I promise that if you ask me q1 at t1, I will try to answer. And if you ask me q2 at t1, I will try to answer. … And if you ask me q1 at t2, I will try to answer. …

where the list goes through all the possible questions about logic and all the possible times that fall within office hours. Have I really made an infinite number of promises? This seems implausible. Moreover, normally, we think that one cannot make a promise without knowing that one has done so. But I might not know that q8 is a question about logic or that t3 is a time within office hours (in fact, I might not even know that t3 exists—I might think that there are no intervals finer grained than a Planck time, but there might be).

Or I could make a promise to God regarding my treatment of all future as-yet-unconceived persons who have some property. Again, this is distributive: failure in one case does not excuse me from trying in other cases. But if analyzed as a collection of promises about actual future persons, we get the weirdness that what I have promised depends on what I will do. So it would have to be a collection of promises about possible future persons. And it’s not clear that this makes sense except given some controversial metaphysical assumptions, such as the existence of haecceities.

So, I think distributive promises don’t reduce to non-distributive ones.

Maybe, though, one can try to handle the cases with some sort of a doctrine of approximate truth. Perhaps when I promise a proposition, if I am no longer in a position to make the proposition true, I am required to make it as approximately true as I can? I think this kind of a principle will lead to counterintuitive results. For suppose that there is some benefit to you from having p be exactly true, while close approximations to p are harmful to you, while some way of making p very false is much better for you. Then I shouldn’t strive for a close approximation to p. (Think of cases of medicinal dosage, perhaps.)

Knowing how fast to change

Imagine two objects, M and H, where M has the intrinsic causal power of emitting some sort of a pulse once per minute and H has the intrinsic causal power of pulsing once per hour, and suppose M and H are causally separated from the rest of the universe. How do M and H “know” how quickly to pulse?

The problem seems to me to be particularly pressing on Aristotelian theories of time on which time is defined by the changes of objects. Let’s imagine that in addition to M and H there are a thousand identical clocks running in the universe, with all objects causally isolated from each other, and that there is nothing else that is changing besides what I have described. Presumably, then, the changes that define time are the changes in the positions of the clock hands. Then on our Aristotelian theory, to say that H pulses every hour just means that H pulses once per revolution of the minute hand on a typical clock, and to say that H pulses every minute means that H pulses once per revolution of the seconds hand on a typical clock.

But, first, how do M and H know about the movement of the hands of the clocks, so as to keep in sync with them, if all the objects are causally isolated?

And, second, let’s imagine this. God speeds up the clocks one by one by a factor of two: today he speeds up clock C1, tomorrow he speeds up clock C2, and so on, until eventually all the clocks have been sped up. After a week, seven clocks, C1, ..., C7, have been sped up. This doesn’t matter for the definition of time: seven clocks out of a thousand are negligible, and the time standards are set up by C8, ..., C1000. According to C1, ..., C7, M pulses once per two rotations of the seconds hand, and H once per two rotations of the minutes hand. But according to C8, ..., C1000, M pulses once per rotation of the seconds hand and H once per rotation of the minutes hand, since these rotations correspond to real minutes and real hours.

However, after 993 days, clocks C1, ..., C993 are running at the same rate and setting the time standards. The clocks C994, ..., C1000 are the outliers. So, now, M pulses once per rotation of the seconds hands and H once per rotation of the minutes hands of C1, ..., C993. And M pulses twice per rotation of the seconds hands of C994, ..., C1000, and H twice per rotation of their minutes hands. So at some point in the process of speeding up clocks C8, ..., C1000, M’s pulses go from once per two rotations of the seconds hand of C1, ..., C7 to once per rotation, and similarly for H. But how can the speeding up of clocks other than C1, ..., C7 affect the correlations between H and M when everything is causally isolated?

(Note that talk of “speeding up clock Cn” makes sense even if the clocks jointly define time. If n = 1, we can understand it as speeding it up relative to clocks C2, ..., C1000. If n > 1, we can understand it as bringing clock Cn in sync with clock Cn − 1. What may be a bit ambiguous is what “day n” means, but nothing hangs on the details of how to resolve that.)

But even without an Aristotelian theory of time it is puzzling how M and H “know” how quickly to pulse.

I think there is a nice solution that lets one keep a part of the Aristotelian theory of time: (external) time is not just the measure of change, but the measure of change in causally interconnected things. There is no common timeline between M, H and the clocks when there are no causal connections between them. This, I think, requires the rejection of any theory on which there is a metaphysically deep “objective present”.

Another move is to deny that there can be intrinsic causal powers that make reference to metric external time.

Continuous choices

Suppose at at noon, Alice is relaxed in an armchair listening to music, but at any given time she is capable of choosing to get up, walk over to the kitchen and make herself a sandwich for lunch, which it’s time for. For fifteen minutes she continues listening to the music and then gets up at 12:15. It seems that she is continually responsible for her continuing to sit until 12:15, and then she is responsible for getting up.

Here is one realistic question about what happened between 12:00 and 12:15:

  1. Did Alice make a vast number of choices, one at every moment until 12:15, to remain seated, and then at 12:15 a choice to get up?

In favor of a positive answer, it is difficult to see how she could be responsible for not getting up at a given time if she did not choose not to get up.

But a positive answer seems psychologically implausible. Indeed, it doesn’t seem like Alice would be enjoying the music if every moment she had to positively choose to stay.

Also, let’s think about what the reasons weighing in on each choice would be. On the one hand, there is a very weak reason to get up now. It’s a weak reason because getting up the next moment would be just as good hunger-wise. On the other hand, there is a very weak reason to keep sitting in order to enjoy music between this moment and the next. It’s a weak reason because the amount of music involved is very small. Choices on the basis of such very weak reasons are hard to make. These reasons would be hard to weigh. And when making choices between hard to weigh reasons, it seems that the chances of going for either option should be of the same order of magnitude. But if Alice were to make a vast number of choices between getting up and staying between, say, 12:00 and 12:10, with each choice having roughly the same order of magnitude of probability, then it was very unlikely that all these choices were choices to stay.

I find the responsibility argument pretty persuasive, though. Maybe, though, the right story that balances psychological plausibility with intuitions about responsibility is this: Alice made a small number of choices between 12:00 and 12:15. Most of these choices were a choice whether to think harder about whether to get up or just let the status quo continue “for a while”. Most of the time, she chose just to let the status quo roll on. At a time t during which the status quo was “just rolling on”, Alice’s responsibility for not getting up was derivative from her choice to stop thinking about the question. Sometimes, however, Alice decided to think harder about whether to get up. Finally, she thought harder, and got up.

Since the number of choices is smaller on this story, it doesn’t interfere as much with the enjoyment. There is some interference, but that’s realistic. And since the number of choices is smaller, the probabilities of each option can be of the same order of magnitude without this creating any problems.

Now, prescinding from the realism behind the discussion of (1), we can ask the also interesting question:

  1. Could it be that both (a) time is continuous and (b) Alice literally makes a choice to remain seated at every single moment of time between 12:00 and 12:15?

The answer, I think, is negative. For consider a choice at t. Alice would be choosing between the good of slightly more music and the good of slightly earlier relief of hunger. But how long as the “slightly more” and “slightly earlier”? Zero temporal length! For if time is continuous, and Alice is choosing at every moment, zero length of time elapses between choices. Indeed, there is no sense to the idea of “between choices”. So Alice would be choosing between zero-value goods. And that doesn’t make rational sense.

Monday, July 15, 2019

Probabilistic propensities and the Aristotelian view of time

Consider an item x with a half-life of one hour. Then over the period of an hour, it has a 50% chance of decaying, over the period of a second it only has a 0.02% chance of decaying. Imagine that x has no way of changing except by decaying, and that x is causally isolated from all outside influences. Don’t worry about Schroedinger's cat stuff: just take what I said at face value.

We are almost sure that x will one day decay (the probability of decaying approaches one as the length of time increases).

Now imagine that everything other than x is annihilated. Since x was already isolated from all outside influences, this should not in any way affect x’s decay. Hence, we should still be almost sure that x will one day decay. Moreover, since what is outside of x did not affect x’s behavior, the propensities for decay should be unchanged by that annihilation: x has a 50% chance of decay in an hour and a 0.02% chance of decay in a second.

But this seems to mean that time is not the measure of change as Aristotle thought. For if time were the measure of change, then there would be no way to make sense of the question: “How long did it take for x to decay?”

Here is another way to make the point. On an Aristotelian theory of time, the length of time is defined by change. Now imagine that temporal reality consists of x and a bunch of analog clocks all causally isolated from x. The chances of decay of x make reference to lengths of time. Lengths of time are defined by change, and hence by the movements of the hands of the clocks. But if x is causally isolated from the clocks, its decay times should have nothing to do with the movements of the clocks. If God, say, accelerated or slows down some of the clocks, that shouldn’t affect x’s behavior in any way, since x is isolated. But an Aristotelian theory of time, it seems, such an isolation is impossible.

I think an Aristotelian can make one of two moves here.

First, perhaps the kinds of propensities that are involved in having an indeterministic half-life cannot be had by an isolated object: such objects must be causally connected to other things. No atom can be a causal island. So, even though physics doesn’t say so, the decay of an atom has a causal connection with the behavior of things outside the atom.

Second, perhaps any item that can have a half-life or another probabilistic propensity in isolation from other things has to have an internal clock—it has to have some kind of internal change—and the Aristotelian dictum that time is the measure of change should be understood in relation to internal time, not global time.

Sunday, July 14, 2019

Emotions and naturalism

On occasion, I’ve heard undergraduates suggest that naturalism faces a problem with emotions. They feel that a mere computational system would not have emotional states.

One might take this to be a special case of the problem of qualia, and I think it has some plausibility there. It is indeed hard to see how an emotionless Mary would know what it’s like to be scared or in love. Is it harder than in the case of ordinary sensory qualia, like that of red? I don’t know.

But I think it’s more interesting to take it to be a special case of the problem of intentionality or content. Emotions are at least partly constituted by intentional (quasi?) perceptual states with normative content: to be scared involves perceiving reality as containing something potentially bad for one and being in love involves perceiving someone as wonderful in some respects.

The standard materialist story about the content of perceptual states is causal: a perception of red represents an object as reflecting or emitting light roughly of a certain wavelength range because the perception is typically triggered by objects doing this. But on standard naturalist stories do not have room for normative properties to play a causal role. Post-Aristotelian scientific explanations are thought not to invoke normative features.

There is, of course, nothing here to worry an Aristotelian naturalist who believes that objects have natures that are both normative and causally explanatory.

Over the past year, I’ve been coming to appreciate the explanatory power of the Aristotelian story on which the very same thing grounds normativity and provides a causal explanation.

Saturday, July 13, 2019

Is the past changing all the time?

The past is unchangeable. But if the A-theory is true, then past events constantly objectively get older and older. That seems to be a kind of objective change. So, the A-theory is false.

Tuesday, July 9, 2019

Unreleasable promises would be useful

Alice promises Bob to impose on him some penalty should Bob do a certain wrong. Bob does the wrong, and points out to Alice that imposing the penalty is some trouble to Alice, and that Bob is happy to release Alice from the promise.

If the promisee can always release the promiser from a promise, then in a case like this Bob may be exactly right. Deterrence thus would sometimes work better if one can make a promise that the promisee cannot release one from.

Of course, the fact that a normative power would be useful does not mean that the normative power exists. I doubt one can make a promise to another that the other cannot release one from.

One might, however, be able to vow the deterrent penalty to God. Or maybe just promise it to a third party (society?) who has no incentive to release one from the promise.

Punishment is not a strict requirement of justice

There is no strict duty to reward a person who has done a supererogatory thing. Otherwise, engaging in generosity would be a way of imposing a duty on others.

But punishment is the flip side of reward. Hence, there is no strict duty to punish a person who has done a wrong.

Of course, supererogatory action makes a reward fitting, and likewise wrong action makes a punishment fitting. But in neither case is the retributive response strictly required by justice.

Tuesday, July 2, 2019

A problem for some views of a temporal God

Among those who think that God is in time, there are two views:

  1. God has existed for an infinite amount of time

  2. God came into time a finite amount of time ago when he created the world.

The second view is held by William Lane Craig. On this view, God isn’t essentially temporal: he wouldn’t have been in time if he didn’t create time or temporal beings.

It’s occurred to me that those who accept the first view have the serious problem of getting out of the time-of-creation problems: Why did God create the world when he did, instead of earlier or later? And why did he wait an infinite amount of time before creating?

St Augustine’s answer that time starts with creation doesn’t work for those who accept (1).

Supposing creation itself to be omnitemporally eternal only solves the problem with (1) if one additionally accepts a relationalist B-theory of time. For otherwise there is still the question why God’s omnitemporally eternal creation process isn’t all shifted temporally by a year forward or backward in time.

Monday, July 1, 2019

Theories of time and truth-supervenes-on-being

Truth supervenes on being is the thesis that if two worlds have the same entities, they are otherwise the same. I just realized something that should be pretty obvious. One cannot hold on to all three of the following:

  • A-theory

  • eternalism

  • truth supervenes on being.

For according to eternalism, at any two different times, the facts about what exists are the same. So if truth supervenes on being, at any two different times, all facts are the same—and in particular the facts about what time is objectively present will be the same, which contradicts A-theory.

In other words, just as the best version of presentism (that of Trenton Merricks) rejects that truth supervenes on being, so does the best version of the moving spotlight theory. Moreover, closed-future growing blockers—and, in particular, classical theist growing blockers—will also want to reject that truth supervenes on being since substantive truths about the future won’t supervene on being given growing block.

All this suggests that we are left with only two major theories of time available to those who accept that truth supervenes on being:

  • B-theoretic eternalism

  • growing block with an open future.

Presentism, change and ontology

Presentism says that only present things exist. This by itself cannot explain the nature of change.

For assume an ontology on which, necessarily, everything that exists is either a concrete substance or a necessary abstract object. Consider a world w1 where all the concrete substances exist for all time, but some of them are changing their properties, e.g., shape. Notice that the presentist, the growing blocker and the eternalist all agree about what exists at w1, since no entity comes into or out of existence on this ontology, and hence the differences between the three theories are irrelevant to w1. Yet, w1 is a world with change.

Hence presentism by itself cannot explain change.

Perhaps someone who thinks that presentism is needed to explain change should opt for a trope ontology rather than a substance-and-abstracta or substance-only ontology. For then they can say that at w1, entities—namely, tropes—come into and out of existence.

Monday, June 24, 2019

"On the same grounds"

Each of Alice and Seabiscuit is a human or a horse. But Alice is a human or a horse “on other grounds” than Seabiscuit is a human or a horse. In Alice’s case, it’s because she is a human and in Seabiscuit’s it’s because he’s a horse.

The concept of satisfying a predicate “on other grounds” is a difficult one to make precise, but I think it is potentially a useful one. For instance, one way to formulate a doctrine of analogical predication is to say that whenever the same positive predicate applies to God and a creature, the predicate applies on other grounds in the two cases.

The “on other/same grounds” operator can be used in two different ways. To see the difference, consider:

  1. Alice is Alice or a human.

  2. Bob is Alice or a human.

In one sense, these hold on the same grounds: (1) is grounded in Alice being human and (2) is grounded in Bob being human. In another sense, they hold on different grounds: for the grounds of (1) also include Alice’s being Alice while the grounds of (2) do not include Bob’s being Alice (or even Bob’s being Bob).

Stipulatively, I’ll go for the weaker sense of “on the same grounds” and the stronger sense of “on different grounds”: as long as there is at least one way of grounding “in the same way”, I will count two claims as grounded the same way. This lets me say that Christ knows that 2 + 2 = 4 on the same grounds as the Father does, namely by the divine nature, even though there is another way in which Christ knows it, which the Father does not share, namely by humanity.

Even with this clarification, it is still kind of difficult to come up with a precise account of “on other/same grounds”. For it’s not the case that the grounds are literally the same. We want to say that the claims that Bob is human and that Carl is human hold on the same grounds. But the grounding is literally different. The grounds of the former is Bob’s possession of a human nature while the grounds of the latter is Carl’s possession of a human nature. Moreover, if trope theory is correct, then the two human natures are numerically different. What we want to say is something like this: the grounds are qualitatively the same. But how exactly to account for the “qualitatively sameness” is something I don’t know.

There is a lot of room for interesting research here.

Thursday, June 20, 2019

Grace and theories of time

  1. All grace received is given through Christ’s work of salvation.
  2. Christ’s work of salvation happened in the first centuries AD and BC.
  3. One cannot give something through something that does not exist.
  4. Abraham received grace prior to the first century BC.
  5. So, Abraham’s grace was given through Christ’s work of salvation.
  6. So, it was true to say that Christ’s work of salvation exists even when it was yet in the future.
  7. So, presentism and growing block are false.

Wednesday, June 19, 2019

Junia/Junias and the base rate fallacy

I think it would be useful to apply more Bayesian analyses to textual scholarship.

In Romans 16:7, Junia or Junias is described as “famous among the apostles”. Without accent marks (which were not present in the original manuscript) it is not possible to tell purely textually if it’s Junia, a woman, or Junias, a man. Moreover, “among the apostles” can mean “as being an apostle” or “to the apostles”. There seems to be, however, some reason to think that the name Junia is more common than Junias in the early Christian population, and the reading of “among” as implying membership seems more natural, and so the text gets used as support for women’s ordination.

This post is an example of how one might go about analyzing this claim in a Bayesian way. However, since I am not a Biblical scholar, I will work with some made-up numbers. A scholarly contribution would need to replace these with numbers better based in data (and I invite any reader who knows more Biblical scholarship to write such a contribution). Nonetheless, this schematic analysis will suggest that even assuming that there really were female apostles, it is more likely than not that Junia/s is one.

Let’s grant that in the early Christian population, “Junia” outnumbers “Junias” by a factor of 9:1. Let’s also generously grant that the uses of “famous among” where the individual is implied to be a member of the group outnumber the uses where the individual is merely known to the group by a factor of 9:1. One might think that this yields a probably of 0.9 × 0.9 = 0.81 that the text affirms Junia/s to be an apostle.

But that would be to commit the infamous base rate fallacy in statistical reasoning. We should think of a text that praises a Junia/s as “famous among the apostles” as like a positive medical test result for the hypothesis that the individual praised is a female apostle. The false positive rate on that test is about 0.19 given the above data. For to get a true positive, two things have to happen: we have to have Junia, probability 0.9, and we have to use “among” in the membership-implying sense, probability 0.9, with an overall probability of 0.81 assuming independence. So the false positive rate on the test is 1 − 0.81 = 0.19. In other words, of people who are not female apostles, 19 percent of them will score positive on tests like this.

But we have very good reason to think that even if there were any female apostles in the early church, they are quite rare. Our initial sample of apostles includes the 12 apostles chosen by Jesus, and then one more chosen to replace Judas, and none of these were women. Thus, we have reason to think that fewer than 1/13 of the apostles were women. So let’s assume that about 1/13 of the apostles were female. If there were any female apostles, they were unlikely to be much more common than that, since then that would probably have been more widely noted in the early Church.

Moreover, not everyone that Paul praises are apostles. “Apostle” is a very special position of authority for Paul, as is clear from the force of his emphases on his own status as one. Let’s say that apostles are the subjects of 1/3 of Pauline praises (this is something that it would be moderately easy to get a more precise number on).

Thus, the chance that a randomly chosen person that Paul praises is a female apostle even given the existence of female apostles is only about (1/13)×(1/3) or about three percent.

If we imagine Paul writing lots and lots of such praises, there will be a lot of Junia/s mentioned as “famous among the apostles”, some of whom will be male, some female, and some of whom will be apostles and some not.
All of these are the “positive test results”. Of these positive test results, the 97% percent of people praised by Paul who aren’t female apostles will contribute a proportion of 0.19 × 97%=18% of the positive test results. These will be false positives. The 3% people who are female apostles will contribute at most 3% of the positive test results. These will be true positives. In other words, among the positive test results, approximately the ratio 18:3 obtains between the false and true positives, or 6:1.

In other words, even assuming that some apostles are female, the probability that Junia/s is a female apostle is at most about 14%, once one takes into account the low base rate of women among apostles and apostles among those mentioned by Paul.

But the numbers above are made-up. Someone should re-do the analysis with real data. We need four data points:

  • Relative prevalence of Junia vs. Junias in the early Christian population.

  • Relative prevalence of the two senses of “famous among” in Greek texts of the period.

  • Reasonable bounds on the prevalence of women among apostles.

  • Prevalence of apostles among the subjects of Pauline praise.

And without such numbers and Bayesian analysis, I think scholarly discussion is apt to fall into the base rate fallacy.

Thursday, June 13, 2019

Is eternalism compatible with the actualization of potentiality?

Every so often, someone claims to me that there is a difficulty in reconciling the Aristotelian idea of the actualization of potential with eternalism, the view that past, present and future are equally real. I am puzzled by this question, because I can’t see the difficulty. On the contrary, there is a tension between presentism, the view that only present things exist, and this Aristotelian thesis:

  1. Some present events are the actualization of a no-longer present potentiality.

  2. A non-existent thing is not actualized.

  3. Therefore, some no-longer present potentialities exist.

  4. Therefore, something that is no longer present exists.

  5. Therefore, presentism is false.

One might say: Yes, the potentiality doesn’t exist, but it did exist, and it was actualized. But then:

  1. Some present potentialities are actualized in not yet present events.

  2. A non-existent thing does not actualize anything.

  3. So, there exist some not yet present things.

  4. So, presentism is false.

Of course, this is the old problem of transtemporal relations for presentism as applied to the actualization relation.

So, what about the question whether eternalists can have actualization of potentials? Here may be the problem. On eternalism plus Aristotelianism, it seems that the past unactualized potential exists even though it is now actualized. This seems to be a contradiction: how can an unactualized potential be actualized?

A first answer is that a potential is actualized at a time t provided that its actualization exists at t. Thus, the potential is unactualized at t1 but actualized at a later time t2, because its actualization exists at t2 but not at t1. But, the objector can continue, by eternalism at t1 isn’t it the case that the actualization exists? Yes: but the eternalist distinguishes:

  1. It is true at t1 that B exists.

  2. B exists at t1.

Claim (11), for spatiotemporal objects, means something like this: the three-dimensional spacetime hypersurface corresponding to t = t1 intersects B. Claim (10) means that B exists simpliciter, somewhere in spacetime (assuming it’s a spatiotemporal object). There is no contradiction in saying that the actualization doesn’t exist at t1, even though it is true at t1 that it exists simpliciter.

The second answer is that Aristotelianism does not need actualizations of unactualized potentials. Causation is the actualization of a potential. But Aristotle and Aquinas both believed in the possibility of simultaneous causation. In simultaneous causation, an event B is the actualization of a simultaneous potential A. At the time of the simultaneous causation, nobody, whether presentist or eternalist, can say that B is the actualization of unactualized potential, since then the potential would be actualized and unactualized at the same time. Thus, one can have causation, and actualization of potential, where the potential and the actualization are simultaneously real, and hence where the actualization is not of an unactualized potential. The eternalist could—but does not have to—say that transtemporal cases are like this, too: they are actualizations of a potential, but not of an unactualized potential.

Tuesday, June 11, 2019

Final and efficient causation

It is sometimes said that:

  1. One can have p explain q and q explain p when the types of explanation are different.

I think (1) is mistaken, but in this post I want to focus not on arguing against (1), but simply on arguing against one particular and fairly common form of argument for (1):

  1. In cases of Aristotelian final causation, it typically happens that y is a final cause of its own efficient cause.

  2. If y is a final cause of x, then that y occurred finally explains that x occurred.

  3. If x is an efficient cause of y, then that x occurred efficiently explains that y occurred.

  4. So, it’s possible to have p explain q and q explain p when the types of explanation are final and efficient, respectively.

I want to argue that this argument fails (bracketing the interpretive question whether Aristotle or Aquinas accepts its premises).

First, explanation is factive: if p explains q, then both p and q are true. This is because explanations provide correct answers to why questions, and a false answer isn’t correct. But final explanations are not factive. I can offer an argument in order to convince you and yet fail to convince you. (Indeed, perhaps this post is an example.) Therefore, (3) is not always true. That doesn’t show that (3) is false in the case that the argument needs. But it is plausible that an action that fails for extrinsic reasons has exactly the same explanation as a successful action. The failed action cannot be explained by its achieving its goal, since it doesn’t achieve its goal. Therefore, the successful action cannot be explained in terms of its achieving its goal, either.

Second, efficient causation is a relation between tokens. If I turn on the lights in order to alert the burglars, then my token turning-on-the-lights is the efficient cause of the token alerting-the-burglars. But final causation is not a relation between tokens. For suppose that I fail to alert the burglars, say because the burglars are blindfolded (they were challenged to rob me blind, and parsed that phrase wrong) and don’t see the lights. Then there are infinitely many possible tokens of the alerting-the-burglars type any one of which would pretty much equally well serve my goals. For instance, I could alert the burglars at 10:44:22.001, at 10:44:22.002, etc. In the case of action failure, no one of these tokens can be distinguished as “the final cause”, the token I am aiming at. Indeed, if one particular possible token a0 were the final cause, then if I happened to produce another token, say a7, my action would have been a failure—which is absurd. Thus, either all the infinitely many possible tokens serve as the final causes of the action or none of them do. It seems wrong to say that there are infinitely many final causes of the action, so none of the tokens is.

Given that explanation of the failed action is the same as of the successful action, it follows that even in the successful case, none of the tokens provides the final cause.

Therefore, we should see final causation as a relation between a type, say alerting the burglars at some time or other near 10:44:22, and a token, say my particular turning on of the lights. But if so, then (2) is false, for it is false that in the successful case the same things are related by final and efficient causation: the final causation relates the outcome type with a productive token and efficient causation relates the productive token with the outcome token.

As I said, this doesn’t show that (1) is false, but it does show that efficient and final explanation do not provide a case of (1).

Acknowledgments: I am grateful to Tim Pawl for discussion of these questions.

Friday, June 7, 2019

Truly going beyond the binary in marriage?

There is an interesting sense in which standard polygamy (i.e., polygyny or polyandry) presupposes the binarity of marriage. In standard polygamy, there is one individual, A, who stands in a marriage relationship to each of a plurality of other individuals, the Bs. But the marriage relationships themselves are binary: A is married to each of the Bs, and the Bs are not married to each other (they have a different kind of relationship).

The same would be true with more complex graph theoretic structures than the simple star-shaped structure of polygyny and polyandry (with A at the center and the Bs at the periphery). If Alice is married to Bob and Carl, and Bob and Carl are each married to Davita, the quadrilateral graph-theoretic structure of this relationship is still constituted by a four binary marriage relationships.

Thus, in these kinds of cases, what we would have are not a plural marriage, but a plurality of binary marriages with overlap. This, I think, makes for more precise terminology. The moral and political questions normally considered under the head of “plural marriages” are about the possibility or morality of overlap between binary marriages.

To truly go beyond the binary would require a relationship that irreducibly contains more than two people, a relationship not constituted by pairwise relationships. I think a pretty good case can be made that even if one accepts overlapping binary marriages, as in standard polygamy, as genuine marriages (I am not sure one should), irreducibly non-binary relationships would still not be marriages (just as unary relationships wouldn't be). The structure of the relationship is just radically different.

Thursday, June 6, 2019

God and analogy

According to Aquinas, whenever we correctly say something non-negative of God, we speak analogically.

It is correct to say that Socrates is wise and God is wise. But being humanly wise and divinely wise are different—the most fundamental difference being that, by divine simplicity, God doesn’t have his wisdom, but is his wisdom. But this leads to:

  1. The predicate “is humanly wise or is divinely wise” applies literally to both Socrates and God.

And yet this disjunctive predicate is not negative, so (1) seems to provide a counterexample to Aquinas’ theory.

But this is too fast. Claim (1) only provides a counterexample to Aquinas’ theory if:

  1. Applying analogically and applying literally are incompatible.

But I think Aquinas can, and should, say that (2) is false. If he does that, then he can affirm both (1) and:

  1. The predicate “is humanly wise or is divinely wise” applies analogically to both Socrates and God.

In fact, I think Aquinas can say that the relevant kind of analogical application of predicates is a special case of literal predication.

I think that Aquinas is not really making a claim about literal and non-literal use of words when he is talking of analogical predication. Instead, I think he is making a claim about grounding, somewhat like:

  1. The predicate “is F” is used analogically between entities x and y just in case the propositions that x is F and that y is F have a relevantly different grounding structure.

On this account, disjunctive predicates like “is a human or a dog” are used analogically: for the grounding structure of the proposition that Alice is a human or a dog is that it’s grounded in Alice being a human, while the grounding structure of the proposition that Fido is a human or a dog is that it’s grounded in Fido being a dog. And similarly, “is humanly wise or is divinely wise” is used analogically, since in the case of Socrates the grounds of applicability are Socrates having wisdom and in the case of God the grounds are God being (his) wisdom.

Notice that on this story, Aquinas’ claim about analogical predication is not so much a linguistic claim as a metaphysical claim about the truth grounds.

The story makes clear why negative predicates are not used analogically: for the grounding structure of the truth that God is not a bicycle and the truth that Alice is not a bicycle is relevantly the same—both are grounded in not being arranged bicycle-wise.

So far, our reconstruction of Aquinas’ theory of predication is:

  1. A predicate that applies to God is negative or is used analogically.

But that’s not quite right. Here is one counterexample: “is not a bicycle or is both a bicycle and a non-bicycle.” This predicate is not negative but disjunctive. But it applies to God and to Socrates in the same way—by both not being bicycles.

I think the issue here is this. Just as analogical predication is a metaphysical and not linguistic notion, so negative predication is a metaphysical and not linguistic notion. We might say something like this:

  1. The predicate “is F” is used negatively of entity x just in case what grounds x being F is the non-obtaining of some state of affairs.

Thus, “is not a bicycle or is both a bicycle and non-bicycle” is used negatively of both God and Socrates, because what grounds its application in both cases are respectively the non-obtaining of the states of affairs of God being arranged bicycle-wise and of Socrates beng arranged bicycle-wise. On the other hand, the disjunctive predicate “is Athenian or not Greek” is used negatively of God and non-negatively of Socrates. Interestingly, this case shows that the disjunction in (5) is not exclusive. For “is Athenian or not Greek” is used both negatively of God and is used analogically between Socrates and God, since the structure of the grounds of application is relevantly different.

The problems haven’t all gone away. A necessary condition for “is F” to be used analogically of God and a creature is that “is F” applies to God and a creature, and hence a predicate that applies only to God cannot be used analogically. But suppose that in fact no one other than God knows whether the Continuum Hypothesis is true. Then the predicate “knows whether the Continuum Hypothesis is true” is not used analogically, since it only applies to God. But then we have a counterexample to (5).

We could try to modalize (4): a predicate is used analogically provided that it could have one ground as applied to God and another as applied to something other than God. But, again, it’s not hard to come up with a counterexample: “knows that 2 + 2 and is not a creature.” For that predicate can only apply to God.

We could also weaken (5) to merely apply to those predicates that apply (or could apply) to both God and a creature. This may seem to be an undue weakening: now one can escape from Aquinas’ doctrine of analogical predication simply by saying things that only apply (or could only apply) to God. But perhaps one can supplement the weakened (5) with:

  1. Any predicate that applies to God is built out of predicates that apply both to God and to a creature.

I am not too happy about this.

Friday, May 31, 2019

Gunk, etc.

If we think parts are explanatorily prior to wholes, then gunky objects—objects which have parts but no smallest parts—involve a vicious explanatory regress. But if one takes the Aristotelian view that wholes are prior to parts, then the regress involved in gunky objects doesn’t look vicious at all: the whole is prior to some parts, these parts are prior to others, and so on ad infinitum. It’s just like a forward causal regress: today’s state causes tomorrow, tomorrow’s causes the next day’s, and so on ad infinitum.

On the other hand, on the view that parts are explanatorily prior to wholes, upward compositional regresses are unproblematic: the head is a part of the cow, the cow is a part of the earth, the earth is a part of the solar system, the solar system is a part of the Orion arm, the Orion arm is a part of the Milky Way, the Milky Way is a part of the Local Group, and this could go on forever. The Aristotelian, on the other hand, has to halt upward regresses at substances, say, cows.

This suggests that nobody should accept an ontologically serious version of the Leibniz story on which composition goes infinitely far both downward and upward, and that it is fortunate that Leibniz doesn’t accept an ontologically serious version of that story, because only the monads and their inner states are to be taken ontologically seriously. But that's not quite right. For there is a third view, namely that parthood does not involve either direction of dependence: neither do parts depend on wholes nor do wholes depend on parts. I haven't met this view in practice, though.

Leibniz on infinite downward complexity

Leibniz famously thinks that ordinary material objects like trees and cats have parts, and these parts have parts, and so on ad infinitum. But he also thinks this is all made up of monads. Here is a tempting mental picture to have of this:

  • Monads, …, submicroscopic parts, microscopic parts, macroscopic parts, ordinary objects.

with the “…” indicating infinitely many steps.

This is not Leibniz’s picture. The quickest way to see that it’s not is that organic objects at each level immediately have primary governing monads. There isn’t an infinite sequence of steps between the cat and the cat’s primary monad. The cat’s primary monad is just that, the cat’s primary monad. The cat is made up of, say, cells. Each cell has a primary monad. Again, there isn’t an infinite sequence of steps between the cat and the primary monads of the cells: there might turn out to be just two steps.

In fact, although I haven’t come across texts of Leibniz that speak to this question, I suspect that the best way to take his view is to say that for each monad and each object partly constituted by that monad, the “compositional distance” between the monad and the object is finite. And there is a good mathematical reason for this: There are no infinite chains with two ends.

If this is right, then the right way to express Leibniz’s infinite depth of complexity idea is not that there is infinite compositional distance between an ordinary object and its monads, but rather than there is no upper bound on the compositional distance between an ordinary object and its monads. For each ordinary object o and each natural number N, there is a monad m which is more than N compositional steps away from o.

Fundamental mereology

It is plausible that genuine relations have to bottom out in fundamental relations. E.g., being a blood relative bottoms out in immediate blood relations, which are parenthood and childhood. It would be very odd indeed to say that a is b’s relative because a is c’s relative and c is b’s relative, and then a is c’s relative because a is d’s relative and d is c’s relative, and so on ad infinitum. Similarly, as I argued in my infinity book, following Rob Koons, causation has to bottom out in immediate causation.

If this is right, then proper parthood has to bottom out in what one might call immediate parthood. And this leads to an interesting question that has, to my knowledge, not been explored much: What is the immediate parthood structure of objects?

For instance, plausibly, the big toe is a part of the body because the big toe is a part of the foot which, in turn, is a part of the body. And the foot is a part of the body because the foot is a part of the leg which, in turn, is a part of the body. But where does it stop? What are the immediate parts of the body? The head, torso and the four limbs? Or perhaps the immediate parts are the skeletal system, the muscular system, the nervous system, the lymphatic system, and so on. If we take the body as a complex whole ontologically seriously, and we think that proper parthood bottoms out in immediate parthood, then there have to be answers to such questions. And similarly, there will then be the question of what the immediate parts of the head or the nervous system are.

There is another, more reductionistic, way of thinking about parthood. The above came from the thought that parthood is generated transitively out of immediate parthood. But maybe there is a more complex grounding structure. Maybe particles are immediately parts of the body and immediately parts of the big toe. And then, say, a big toe is a part of the body not because it is a part of a bigger whole which is more immediately a part of the body, but rather a big toe is a part of the body because its immediate parts are all particles that are immediately parts of the body.

Prescinding from the view that relations need to bottom out somewhere, we should distinguish between fundamental parts and fundamental instances of parthood. One might have one without the other. Thus, one could have a story on which we are composed of immediate parts, which are composed of immediate parts, and so on ad infinitum. Then there would be fundamental instances of the parthoood relation—they obtain between a thing and its immediate parts—but no fundamental parts. Or one could have a view with fundamental parts while denying that there are any fundamental instances of parthood.

In any case, there is clearly a lot of room for research in fundamental mereology here.

Thursday, May 30, 2019

Taste and cross-cultural encounters

After visiting the British Museum yesterday, I find it rather hard to take seriously the argument for the relativity of beauty from the diversity of taste. It seems clear that just as C. S. Lewis has argued for a moral core cutting across cultures, one can argue that there is an aesthetic core across cultures.

There is, however, an interesting apparent difference between the diversity of taste and the diversity of morals. I think a cross-cultural encounter involving a difference of taste regarding the best cultural artifacts—by each culture’s own standards—should typically lead to a broadening of taste. But a cross-cultural moral encounter should not typically lead to a broadening of morals. Very often, it should lead to a narrowing of morals: for instance, one culture learning from the other that slavery sex is wrong.

Why this difference? I think it may come from a difference in quantifiers.

As Aquinas already noted (in a somewhat different way), to be morally good, an action has to be good or neutral with respect to every relevant dimension of moral evaluation. If it is good with respect to courage and kindness and generosity, but it is bad with respect to justice (Robin Hood?), then the action is plain wrong. Thus as new dimensions of moral evaluation are discovered, as can happen in cross-cultural encounter, we get a narrowing of the actions that we classify as morally good.

On the other hand, for an item to be beautiful, it only needs to be beautiful with respect to some relevant dimensions of beauty. A musical performance is still beautiful on the whole even if the orchestra is dressed in dirty rags, and a painting can be beautiful even if it reeks of oil. Thus as we discover new dimensions of beauty, we get a broadening of the pieces that we classify as beautiful.

Friday, May 24, 2019

A way forward on the normalizability problem for the Fine-Tuning Argument

The Fine-Tuning Argument claims that the life-permitting ranges of various parameters are so narrow that, absent theism, we should be surprised that the parameters fall into those ranges.

The normalizability objection is that if a parameter ξ can take any real value, then any finite life-permitting range of values of ξ counts as a “narrow range”, since every finite range is an infinitesimal portion of the full range from −∞ to ∞. Another way to put the problem is that there is no uniform probability distribution on the set of real numbers.

There is, however, a natural probability distribution on the set of real numbers that makes sense as a prior probability distribution. It is related to the Solomonoff priors, but rather different.

Start with a language L with a finite symbol set usable for describing mathematical objects. Proceed as follows. Randomly generate finite strings of symbols in L (say, by picking independently and uniformly randomly from the set of symbols in L plus an “end of string” symbol until you generate an end of string symbol). Conditionalize on the string constituting a unique description of a probability measure on the Lebesgue measurable subsets of the real numbers. If you do get a unique description of a probability measure, then choose a real number according to this distribution.

The result is a very natural probability measure PL (a countable weighted sum of probability measures on the same σ-algebra with weights adding to unity is a probability measure) on the Lebesgue measurable subsets of the real numbers.

We can now in principle evaluate the fine-tuning argument using this measure.

The problem is that this measure is hard to work with.

Note that using this measure, it is false that all narrow ranges have very small probability. For instance, consider the intuitively extremely narrow range from 101000 to 101000. Supposing that the language is a fairly standard mathematical language for describing probability distributions, we can specify a uniform distribution on the 0-length interval from 101000 to 101000 as U[101000, 101000], which is 23 characters of LaTeX, plus an end of string. Using 95 ASCII characters, plus the end of string character, PL of this interval will be at least 96−24 or something like 10−48. Yet the size of the range is zero. In other words, intuitively narrow ranges around easily describable numbers, like 101000, get disproportionately high probability.

But that is how it should be, as we learn from the fact that the exponent 2 in Newton’s law of gravitation had better have a non-zero prior, even though the interval from 2 to 2 has zero length.

Whether the Fine-Tuning Argument works with PL for a reasonable choice of L and for a particular life-permitting range of ξ is thus a hard question. But in any case, for a fixed language L where we can define a map between strings and distributions, we can now make perfectly rigorous sense of the probability of a particular range of possibilities for ξ. We have replaced a conceptual difficulty with a mathematical one. That’s progress.

Further, now that we see that there can be a reasonable fairly canonical probability on infinite sets, the intuitive answer to the normalizability problem—namely, “this range seems really narrow”—could constitute a reasonable judgment as to what answer would be returned by one’s own reasonable priors, even if these are not the same as the probabilities given above.

Oh, and this probability measure solves the tweaked problem of regularity, because it assigns non-zero probability to every describable event. I think this is even better than my modified Solomonoff distribution.

Improving on Solomonoff priors

Let’s say that we want prior probabilities for data that can be encoded as a countably infinite binary sequence. Generalized Solomonoff priors work as follows: We have a language L (in the original setting, it’ll be based on Turing machines) and we generate random descriptions in L in a canonical way (e.g., add an end-of-string symbol to L and randomly and independently generate symbols until you hit the end-of-string symbol, and then conditionalize on the string uniquely describing an infinite binary sequence). Typically the set of possible descriptions in L is countable and we get a nice well-defined probability measure on the space of all countably infinite binary sequences, which favors those sequences that are simpler in the sense of being capable of a simpler encoding.

Here is a serious problem with this method. Let N be the set of all binary sequences that cannot be uniquely described in L. Then the method assigns prior probability zero to N, even though most sequences are in N. In particular, this means that if we get an L-indescribable sequence—and most sequences generated by independent coin tosses will be like that—then no matter how much of it we observe, we will be almost sure of the false claim that the sequence is L-describable.

Here, I think, is a better solution. Use a language L that can give descriptions of subsets of the space Ω of countably infinite binary sequences. Now our (finitely additive) priors will be generated as follows. Choose a random string of symbols in L and conditionalize on the string giving a unique description of a subset. If the subset S happens to be measurable with respect to the standard (essentially Lebesgue) measure on infinite binary sequences (i.e., the coin toss measure), then randomly choose a point in S using a finitely additive extension of the standard measure to all subsets of S. If the subset S is not measurable, then randomly choose a point in S using any finitely additive measure that assigns probability zero to all singletons.

For a reasonable language L, the resulting measure gives a significant probability to an unknown binary sequence being indescribable. For Ω itself will typically be easily described, and so there will be a significant probability p that our random description of a subset will in fact describe all of Ω, and the probability that we have an indescribable sequence will be at least p.

It wouldn’t surprise me if this is in the literature.

Thursday, May 23, 2019

On a twist on too-many-thinkers arguments

One of the ways to clinch a too-many-thinkers argument (say, Merricks’ argument against perdurantism, or Olson’s argument for animalism) is to say that the view results in an odd sceptical worry: one doesn’t know which of the many thinkers one is. For instance, if both the animal and the person think, how can you know that you are the animal and not the person: it seems you should have credence 1/2 in each.

I like too-many-thinkers arguments. But I’ve been worried about this response to the sceptical clinching: When the animal and the person think words like “I am a person”, the word “I” refers to the person, even when used by the animal, and hence both think the truth. In other words, “I” means something like: the person colocated with the the thinker/speaker.

But I think I have a good response to this response. It would be a weird limitation on our language if it did not allow speaker or thinker self-reference. Even if in fact “I” means the person colocated with the the thinker/speaker, we should be able to stipulate another pronoun, “I*”, one that refers just to the thinker/speaker. And it would be absurd to think that one not be able to justifiably assert “I* am a person.”

Wednesday, May 22, 2019

Functionalism and maximalism

It is widely held that consciousness is a maximal property—a property F such that, “roughly, … large parts of an F are not themselves F.” Naturalists have used maximality, for instance, to respond to Merricks’ worry that on naturalism, if Alice is conscious, so is Alice minus a finger, as they both have a brain sufficient for consciousness (see previous link). There are also the sceptical consequences, noted by Merricks, arising from thinking our temporal parts to be consciousness.

But functionalists cannot hold to maximalism. For imagine a variant on the Chinese room experiment where the bored clerk processes Chinese characters with the essential help of exactly one stylus and one wax tablet. The functionalist is committed to the clerk plus the stylus and tablet—call that clerk-plus—being conscious, as long as the stylus and tablet are essential to the functioning of the system. But if the clerk-plus is conscious, the clerk is not by maximalism. For consciousness is a maximal property, and the clerk is a large part of the clerk-plus. But it is absurd to think that the clerk turns into a zombie as soon as he starts to process Chinese characters.

Perhaps, though, instead of consciousness being maximal, the functionalist maximalist can say that maximally specific phenomenal types of consciousness—say, feeling such and such a sort of boredom B—are maximal. The clerk feels B, but clerk-plus is, say, riveted by reading the Romance of the Three Kingdoms. There is no violation of maximality with respect to the clerk’s feeling bored, because clerk-plus isn’t bored.

That could be the case. But it could also so happen that at some moment clerk-plus feels B as well. After all, the same feeling of boredom can be induced by different things. The Romance has slow bits. It could happen that clerk-plus is stuck in a slow bit, and for a moment clerk and clerk-plus lose sight of the details and are aware of nothing but their boredom—the qualitatively same boredom. And that violates maximality for specific types of consciousness.

If maximalism is needed for a naturalist theory of mind and if functionalism is our best naturalist theory of mind, then the best naturalist theory fails.

Monday, May 20, 2019

Presentism, gappy existence and self-causation

Yesterday, at the invitation of a student, I did a Marian pilgrimage to Walsingham. If you have a chance to go, go. It’s worth it for spiritual reasons. But here I want to reflect on a metaphysics of time question, related to the experience of participating in this venerable institution.

The Walsingham pilgrimage is an institution dating back to the middle ages. It was abolished by an unecumenical king in 1538, but then eventually re-established around the 19th century.

According to presentism, between the 16th and 19th centuries, it was true that the pilgrimage does not exist. Those who caused it to be re-established, thus, caused it to exist plain and simple. But it is very strange that one could cause to exist something that already once existed—and without any time travel or backwards causation. (Given time travel, one can make something and take it into the past. In making it, then, one caused something to exist that already existed. That’s just a part of the strangeness of time travel.)

One might try to get out of this puzzle by supposing that institutions like pilgrimages do not really exist, and that nothing that exists can have gappy existence. (As stated, corruptionist presentists who believe in a resurrection are out of luck. But they can say that when God is causing the re-existence of something, it’s not so strange.)

But the puzzle remains when we consider self-preservation.

Saturday, May 18, 2019

Regularity

Plausibly—though there are some set-theoretic worries that require some care if the language is rich enough—for a fixed language, there are only countably many situations we can describe. Consequently, we only need to do Bayesian epistemology for countably many events. But this solves the problem of regularity for uncountable sample spaces. For even if there are uncountably many events, only countably many are describable and hence matter, and they form a field (i.e., are closed under finite unions and complements) and:

Proposition: For any countable field F of subsets of a set Ω, there is a countably additive probability measure P on the power set of Ω such that every event in F has non-zero probability.

Proof: Let the non-empty members of F be u1, u2, .... Let a1, a2, ... be any sequence of positive numbers adding up to 1 (e.g., an = 2n). Choose one point xn ∈ un. Let P(A)=∑nanAn where An is 1 if xn ∈ A and 0 otherwise.

Note that this proof uses the countable Axiom of Choice, but almost nobody is worried about that.

Thursday, May 16, 2019

Analogies to ectopic pregnancy

The standard Catholic view of tubal pregnancy is that it is permissible to remove the tube with the child. The idea seems to be that the danger to the mother comes from the potential rupture of the tube, and hence removal of the tube is removal of that which poses the danger, and the death of the child is a non-intended side-effect, with the action justified by double effect. I’ve always been queasy about this reasoning, but I now have two related analogies that make me feel better about this.

Case 1: There are two astronauts on a spaceship, with no oxygen left in the air. The astronauts are wearing spacesuits with oxygen tanks. The oxygen tanks are sufficient for the astronauts to survive until they get home: 50% of the oxygen can be expected to be used up before getting home. However, one of the tanks is rigged by a malefactor with an explosive device such that if more than 20% of the oxygen is used, it will explode, killing both astronauts. The astronaut wearing that particular spacesuit is unconscious and cannot be consulted. It is not feasible to disarm the bomb or to swap tanks. The conscious astronaut removes the explosive tank from the other astronaut’s space suit and throws it into space, knowing that this will result in the unconscious astronaut dying from lack of oxygen. The intention, however, is to remove the item that will dangerously rupture if it is left in place. It is not the intention to kill the other astronaut. This is true even though it is the other astronaut’s breathing that would trigger the tank’s explosion.

The proximate source of the danger is the oxygen tank. But the more distant source is the breathing. It seems very plausible that it makes a moral difference whether the conscious astronaut shoots the unconscious astronaut to stop their breathing (wrong) or removes their tank to expel the danger (right action). This seems a legitimate case of double effect reasoning.

Case 2: Much as in Case 1, but (a) there is intense radiation outside the spaceship’s shielding, so that getting pushed into space even while wearing a spacesuit on will be fatal, and (b) there is no way to separate the tank from the astronaut. Thus, the other astronaut picks up the explosive tank, and throws it far into space. The tank is connected to the unconscious astronaut, so the unconscious astronaut flies out with the tank, and is killed by radiation. The tank never explodes, because the oxygen doesn't get depleted

Again, this seems a perfectly legitimate case of double effect reasoning.

What about the alternative of removing the child from the tube, which orthodox Catholic ethicists tend to reject (unless done in the hope reattaching in the correct place)? Well, the child is connected to the tube via a placenta. The placenta is to a large degree an organ of the child. As I understand it, removal of the child from the tube would require intentionally cutting the placenta, in a way that is fatal to the child. This directly fatal intervention seems akin to slicing the astronaut to remove them from the suit. This seems harder to justify.

Monday, May 13, 2019

A tweak to regularity

Let Gp be the law of gravitation that states that F = Gm1m2/rp, for some real number p. There was a time when it was rational to believe G2. But here is a problem. When 0 < |p − 2|<10−100 (say), Gp is practically empirically indistinguishable from G2, in the sense that within the accuracy of our instruments it predicts exactly the same observations. Moreover, there are uncountably many values of p such that 0 < |p − 2|<10−100. This means that the prior probability for most (i.e., all but at most countably many) such values of p must have been 0. On the other hand, if the prior probability for G2 had been 0, then the posterior probability would have always stayed at 0 in our Bayesian updates (because the probability of our measurements conditionally on the denial of G2 never was 0, which it would have to have been to budge us from a zero prior).

So, G2 is exceptional in the sense that it has a non-zero prior probability, whereas most hypotheses Gp have zero prior probability. This embodies a radical preference for a more elegant theory.

Let N be the set of values of p such that the rational prior probability P(Gp) is non-zero. Then N contains at most countably many values of p. I conjecture that N is the set of all the real numbers that can be specifically defined in the language of mathematics (e.g., 2, 3.8, eπ and the smallest real root of z7 + 3z6 + 2z5 + 7πz3 − z + 18).

If this is right, then Bayesian regularity—the thesis that all contingent hypotheses should have non-zero probability—should be replaced by the weaker thesis that all contingent expressible hypotheses should have non-zero probability.

Note that all this doesn’t mean that we are a priori certain that the law of gravitation involves a mathematically definable exponent. We might well assign a non-zero probability to the disjunction of Gp over all non-definable p. We might even assign a moderately large non-zero probability to this disjunction.

Punishment by loss of reputation

John Stuart Mill famously wrote:

We do not call anything wrong, unless we mean to imply that a person ought to be punished in some way or other for doing it; if not by law, by the opinion of his fellow-creatures; if not by opinion, by the reproaches of his own conscience.

I have two concerns about the middle item, punishment “by the opinion of his fellow-creatures”: (1) standing and (2) due process.

1. Standing

Punishment requires the right kind of standing on the part of the punisher. Unless in some way you are under my authority or perhaps I am an aggrieved party, I do not have the standing to punish you. There are two ways of taking this worry.

First, one might take it that without standing it is literally impossible for me to punish you. It is certainly possible for me to treat you harshly, and my harshness can be a reaction to your wrongdoing, but perhaps it won’t be a punishment.

I am not completely sure about this, though. For suppose you have done something wrong and a vigilante without standing has imposed harsh treatment on you in reaction to this, a harsh treatment that would have counted as maxing out retribution if the vigilante had standing, and then you fall into the hands of an authority with the standing to punish. A case can be made that at that point it is inappropriate for the authority to impose further harsh treatment, and that the best explanation is that the vigilante has already punished you. But perhaps this case isn’t right. Our law does not, I think, work this way. A judge might take into account what you suffered at the hands of the vigilante and reduce your sentence, but it does not seem that the judge would be unjust in still giving you the full sentence that the law calls for (and the vigilante then being punished if caught, too). Moreover, the intuition that “you’ve suffered enough already” may apply even in cases where you something bad happens to you as a non-punitive consequence of a crime, say if you’re a drunk driver and you crash into a wall causing yourself to be paralyzed from the neck down. So on the whole, I am dubious that it is possible to punish without standing.

The second worry about standing is that without standing, I have no right to impose the harsh treatment on you (barring special circumstances, such as your giving me permission). This is clear if in fact the previous worry about standing applies and the harsh treatment would not count as punishment—for in that case, the harsh treatment is unjustly applied, since the one relevant justification for it would be that it is a punishment, and it’s not. But even if the harsh treatment were to count as punishment, without standing an injustice has happened.

But perhaps third-parties do in fact have standing to punish. I can see two stories being told to defend this standing.

First, no man is an island, so if you wrong one person, perhaps you wrong all of society, and so third-parties have standing as aggrieved parties. I am doubtful, however, whether aggrieved parties as such do have standing to punish. My children do not have the right to punish each other for misdeeds committed against each other. Moreover, it seems implausible that there be a disjunctive story about the standing to punish, so that both authorities and aggrieved parties have standing. One might try to say that only aggrieved parties have standing to punish, and then say that authorities punish as representatives of the aggrieved community, but that seems mistaken. For authorities can also legitimately punish wrongs done against those that are not members of the aggrieved community. Parents can legitimately punish children for things that the children did against members of other families. (It is tempting to say that this is a punishment for the violation of family rules, which damages the peace of the family, but that approach does not seem pedagogically right.)

Moreover, in a Christian context, it is very dubious whether aggrieved parties have any right to punish on account of their grievance: to impose punishment on account of one’s own grievance seems to be the kind of behavior that the duty of forgiveness rules out and that is also ruled out by Romans 12:19. So a justification of punishment in terms of a standing that derives from being aggrieved is not available to Christians.

Second, perhaps random third-parties count as deputed by society to impose punishment by adverse opinion, even though they are not deputed to impose punishment by violent means. If so, then they have standing to punish on the grounds of deputed authority rather than ont he grounds of being aggrieved. This fits much better with the anti-vengeance motif of the New Testament. Perhaps some evidence of such a deputation is that truth is a defense in defamation lawsuits.

I think an implicit deputation model is the best story about punishment by adverse third-party opinion. But I am still sceptical. One reason is this. Punishment by third-party opinion can be at least as harsh on the wrongdoer as a fine or even a moderate term of imprisonment. Yet we do not think courts have a duty to routinely significantly reduce punishments for significant crimes on the grounds that the person has already been punished by public opinion, or to increase punishments on the grounds that public opinion has been silent. Thus, adverse opinion does not seem to be a properly deputed part of the punishment.

2. Due process

Punishment requires procedural justice. But public opinion rarely follows best practices there. Even though punishments through adverse opinion can be as harsh on the accused as criminal penalties, the thorough examination of evidence, with a presentation of both sides by able legal representation and a factual examination by independent peers following a “beyond reasonable doubt” standard is rarely present in the case of punishment by public opinion. And even if there are no reasonable grounds for doubt about the wrongs committed, rarely is there a serious examination of evidence about mens rea or sanity.

About the only time that public opinion is able to follow our best practices is if the public opinion comes after a proper criminal trial and is entirely conditioned on its outcome. But that is rare, and anyway isn’t the case that Mill is thinking about.

Final remarks

The above does not mean, however, that public opinion needs to be silent on wrongs done. For there are other reasons to criticize someone’s conduct besides punishment, such as:

  • protecting vulnerable others

  • leading the perpetrator to change of behavior and/or heart

  • inspiring others to resist injustice.

But if I am right, it is crucial for the sake of justice that the adverse public opinion be motivated by such goods as these rather than by retribution. And there is always the danger of self-deceit and the need for prudent choice of means (public denunciation seems less likely to lead to positive change than private admonition).

Saturday, May 11, 2019

Feeling bad about harms to our friends

Suppose something bad happens to my friend, and while I am properly motivated in the right degree to alleviate the bad, I just don’t feel bad about it (nor do I feel good about). Common sense says I am morally defective. But suppose, instead, something bad happens just to me, and I stoically (I am not making any claims about the Stoic movement by using this word, despite the etymology) bear up under it, without feeling bad, though being properly motivated to alleviate the harm. Common sense praises this rather than castigating it. Yet, aren’t friends supposed to be other selves?

So, we have a paradox generated by:

  1. The attitudes we should have towards our friends are very much like those we should have towards ourselves.

  2. It is wrong not to feel bad about harms to our friends even when we are properly motivated to fight those harms.

  3. It is not wrong to feel bad about harms to ourselves when we are properly motivated to fight those harms.

As some terminological background, feeling bad about our friends’ losses is not exactly empathy. In empathy, we feel the other’s feelings as we see things from their point of view. So, feeling bad about harms to our friends will only be empathy if our friends are themselves feeling bad about these harms. There are at least two kinds of cases where we feel bad about harms to our friends when our friends themselves do not: (a) our friends are being stoical and (b) our friends are unaware of the harms (e.g., their reputation is being harmed by gossip we witness, or our friends are being harmed by acting viciously while thinking it’s virtuous). Moreover, even when our friends are feeling bad about the harms, our feeling bad about the harms will only be a case of empathy if we feel bad because they are feeling bad. If we feel bad because of the badness of the harms, that’s different.

In fact, we don’t actually have a good word in English for feeling bad on account of a friend’s being harmed. Sympathy is perhaps a bit closer than empathy, but it has connotations that aren’t quite right. Perhaps “compassion” in the OED’s obsolete sense 1 and sense 2a is close. The reason we don’t have a good word is that normally our friends themselves do feel bad about having been harmed, and our terminology fails to distinguish whether our feeling bad is an instance of sharing in their feeling or of emotionally sharing in the harm to them. (Think of how the “passion” in “compassion” could be either the other’s negative feeling or it could be the underlying harm.) And I think we also don’t have a word for feeling bad on account of our own being harmed, our “self compassion” (we do have “self pity”, but that’s generally seen as bad), though we do have thicker words for particular species of the phenomenon, such as shame or grief. So I’ll just stick to the clunky “feeling bad on account of harm”.

When we really are dealing with empathy, i.e., when we feel bad for our friend because our friend feels bad for it, the paradox is easier to resolve. We can add a disjunct to (1) and say:

  1. The attitudes we should have towards our friends are very much like either those that we should have towards ourselves or those that our friends non-defectively have towards themselves.

This is a bit messy. I’m not happy with it. But it captures a lot of cases.

But what about the pure case of feeling bad for harms to a friend, not because the friend feels bad about it?—either because the friend doesn’t know about the harm, or the friend is being stoical, or our bad feeling is a direct reflection of the harms rather than indirectly via the other’s feeling of the harms. (Of course there will also be the special case where the feeling is the harm, as perhaps in the case of pains.) I am not sure.

I actually feel a pull to saying that especially when our friend doesn’t feel bad about the harm, we should, on their behalf. If our friend nobly does not feel the insult, we should feel it for them. And if our friend is being unjustly maligned, we should not only work to rescue their reputation, but we should feel bad.

But I am still given pause by the plausibility of (1) (even as modified to (4)) and (3). One solution would be to say that we should feel bad about harms to ourselves, that we should not be stoical about them. But I don’t want to say that the stoical attitude is always wrong. If our friends are being stoical about something, we don’t always want to criticize them for it, even mentally. Still there are cases where our friends are rightly criticizable for a stoical attitude. One case is where they should be grieving for the loss of someone they love. A more extreme case is where they should be feeling guilt for vicious action—in that case, we wouldn’t even use the fairly positive word “stoical”, but we would call their attitude “unfeeling” or something like that. In those cases, at least, it does seem like they should feel bad for the harm, and we should likewise feel bad on their behalf whether or not they do. (And, yes, this feeling may be in the neighborhood of a patronizing feeling in the case where they are not feeling the guilt they should—but the neighborhood of patronization has some places that sometimes need to be occupied.)

Still, I doubt that it is ever wrong not feel something. That would be like saying that it is wrong not to smell something. Emotions are perceptions of putative normative facts, I think. It can be defective not to smell an odor, either because one has lost one’s sense of smell or because one has failed to sniff when one should have. But the failure to smell an odor is not wrong, though it may be the consequence of doing something wrong, as when the repair person has neglected to sniff for a gas leak.

Instead, I think the thing to say is that there is a good in feeling bad about harms to a friend—or to ourselves. The good is the good of correct perception of the normative state of affairs. A good always generates reasons, and the good is to be pursued absent countervailing reasons. But there can be countervailing reasons. When I injure my shoulder, my pain is a correct perception of my body’s injured state. Nonetheless, because that pain is unpleasant (or fill in whatever the right story about why we rightly avoid pain), I take an ibuprofen. I have reason to feel the pain, namely because the pain is a correct way of seeing the world, but I also have reason not to feel the pain, namely because it hurts.

Similarly, if someone has insulted me, I have reason to feel bad, because feeling bad is a correct reflection of the normative state of affairs. But I also have reason not to feel bad, because feeling bad is unpleasant. So it can be reasonable not to feel bad. Loving my friend as myself does not require me to make greater sacrifices for my friend than I would make for myself, though it is sometimes supererogatory to do so (and sometimes foolish, as when the sacrifice is excessive given the goods gained). So if I don’t have an obligation to sacrifice my equanimity to in order to feel bad for the insult to me, it seems that I don’t have an obligation to sacrifice it in order to feel bad for the insult to my friend. But that sounds wrong, doesn’t it?

So where does the asymmetry come from? Here is a suggestion. In typical cases where our friend feels bad for the harm, our feeling does not actually match the intensity of our friend’s, and this is not a defect in friendship. So the unpleasantness of feeling bad for oneself is worse than in the case of feeling bad for one’s friend. Thus, more equanimity is sacrificed for the sake of our feelings correctly reflecting reality when it is our own case, and hence the argument that if I don’t have an obligation to make the sacrifice for myself, I don’t have an obligation to make the sacrifice for my friend is fallacious, as the sacrifices are not the same. Furthermore, to be honest, there is a pleasure in feeling bad for a friend. The OED entry for “compassion” cites this psychological insight from a sermon by Mozley (1876): “Compassion … gives the person who feels it pleasure even in the very act of ministering to and succouring pain.” I haven’t read the rest of the sermon, but I think this is not any perverse wallowing or the like. The “compassion” is an exercise of the virtue of friendship, and there is an Aristotelian pleasure in exercising a virtue. And this is much more present when it is one’s friend one is serving. Thus, once again, the sacrifice tends to be less when one feels bad for one’s friend than when one feels bad for oneself, and hence the reason that one has to feel bad for one’s friend is less often outbalanced by the reason not to than in one’s own case.

Nonetheless, the reason to feel bad for one’s friend can be outbalanced by reasons to the contrary. Correct perceptual reflection of reality is not the only good to be pursued—not even the only good in the friendship.

Friday, May 10, 2019

Closure views of modality

Logical-closure views of modality have this form:

  1. There is a collection C of special truths.

  2. A proposition is necessary if and only if it is provable from C.

For instance, C could be truths directly grounded in the essences of things.

By Goedel Second Incompleteness considerations like those here, we can show that the only way a view of modality like this could work is if C includes at least one truth that provably entails an undecidable statement of arithmetic.

This is not a problem if C includes all mathematical truths, as it does on Sider’s view.

Anti-S5

Suppose narrowly logical necessity LL is provability from some recursive consistent set of axioms and narrowly logical possibility ML is consistency with that set of axioms. Then Goedel’s Second Incompleteness Theorem implies the following weird anti-S5 axiom:

  • LLMLp for every statement p.

In particular, the S5 axiom MLp → LLMLp holds only in the trivial case where MLp is false.

For suppose we have LLMLp. Then MLp has a proof. But MLp is equivalent to ∼LLp. However, we can show that ∼LLp implies the consistency of the axioms: for if the axioms are not consistent, then by explosion they prove p and hence LLp holds. Thus, if LLLLp, then ∼LLp can be proved, and hence consistency can be proved, contrary to Second Incompleteness.

The anti-S5 axiom is equivalent to the axiom:

  • MLLLp.

In particular, every absurdity—even 0≠0—could be necessary.

I wonder if there is any other modality satisfying anti-S5.

An infinite chain can't have two ends

Say that a chain C is a collection of nodes with the following properties:

  1. Each node is connected to at most two other nodes.

  2. If x is connected to y then y is connected to x (symmetry).

  3. C is globally connected in the sense that for any proper subset S of C, there is a node in S and a node outside of S that are connected to each other.

(This is a different sense of “chain” from the one in Zorn’s Lemma.)

Fun fact: Every infinite chain has at most one endpoint, where an endpoint is a node that is connected to only one other node.

I.e., one cannot join two nodes with an infinite chain.

Corollary: We cannot join two events by an infinite chain of instances of immediate causation.

I've occasionally wondered if there is a useful generalization of transitive closure to allow for infinite chains, and to my intuition the fact above suggests that there isn't.

An argument for animals in heaven

In quick outline, here’s a valid argument:

  1. There are plants in heaven.

  2. If there are plants in heaven, there are non-human animals in heaven.

  3. So, there are non-human animals in heaven.

Let me expand on the argument.

Humans in heaven (i.e., on the New Earth, after resurrection) will have both supernatural and natural fulfillment. The natural fulfillment of humans requires an appropriate environment. That environment requires plants. A heavenly city with no trees or grass or flowers just wouldn’t be heavenly for us. This is fitting as humans were made for a garden. The fall turned the garden into a field of hard labor for survival, but all will be restored, and so there will be a garden again.

But plants, of the sort that form the natural environment of humans, require an ecosystem that includes non-human animals. There need to be pollinators in the air and worms in the ground. And how eerily quiet a garden would be with no birds chirping, how unnatural for humans.

This does not mean that there will be a resurrection of animals. Just as a plant can be perfect without living forever, a non-rational animal can be perfect without living forever. One may, however, worry that we will form attachments to non-human animals and would be saddened by their death. There are three responses. First, perhaps some non-human organisms could live forever, namely particular ones which are important to humans: say, a bonsai or a companion dog. Second, perhaps we wouldn’t form these attachments, maybe because no animals would be tame. Third, it might be that we would all transcend time to the extent that (a) our memory would not fade and (b) we would all have the correct view of time, i.e., eternalism, so that we would be constantly aware that our beloved animal exists simpliciter, albeit in the past.

Thursday, May 9, 2019

Yet another bundle theory of objects

I will offer a bundle theory with one primitive symmetric relationship. Moreover, the primitive relationship is essential to pairs. I don’t like bundle theories, but this one seems to offer a nice and elegant solution to the bundling problem.

Here goes. The fundamental entities are tropes. The primitive symmetric relationship is partnership. As stated above, this is essential to pairs: if x and y are partners in one world, they are partners in all worlds in which both exist. If x and y are tropes that exist and are partners, then we say they are coinstantiated.

Say that two possible tropes, existing in worlds w1 and w2 respectively, are immediate partners provided that there is a possible world where they both exist and are partners. Then derivative partnerhood is defined to be the transitive closure of immediate partnerhood.

The bundles in any fixed world are in one-to-one correspondence with the maximal non-empty pluralities of pairwise-partnered tropes, and each bundle is said to have each of the tropes that makes up the corresponding plurality. We have an account of transworld identity: a bundle in w1 is transworld identical with a bundle in w2 just in case some trope in the first bundle is a derivative partner of some trope in the second bundle. (This is a four-dimensionalist version. If we want a three dimensionalist one, then replace worlds throughout with world-time pairs instead.) So we have predication (or as good as a trope theorist is going to have) and identity. That seems enough for a reductive story about objects.

We can even have ersatz objects if we have the ability to form large transworld sets of possible tropes: just let an ersatz object be a maximal set of pairwise derivately partnered tropes. An ersatz object then is said to ersatz-exist at a world w iff some trope that is a member of the ersatz object exists at w. We can then count objects by counting the ersatz objects.

This story is compatible with all our standard modal intuitions without any counterpart theoretic cheats.

Of course, the partnership relationship is mysterious. But it is essential to pairs, so at least it doesn’t introduce any contingent brute facts. And every story in the neighborhood has something mysterious about it.

There are two very serious problems, however:

  1. On this story we don’t really exist. All that really exist are the tropes.

  2. This story is incompatible with transsubstantiation—as we would expect of a story on which there is no substance.

So what’s the point of this post? Well, I think it is nice to develop a really good version of an opposing theory, so as to be able to focus one’s critique on what really matters.

Wednesday, May 8, 2019

A ray of Newtonian particles

Imagine a Newtonian universe consisting of an infinite number of equal masses equidistantly arranged at rest along a ray pointing to the right. Each mass other than first will experience a smaller gravitational force to the left and a greater (but still finite, as it turns out) gravitational force to the right. As a result, the whole ray of masses will shift to the right, but getting compressed as the masses further out will experience less of a disparity between the left-ward and right-ward forces. There is something intuitively bizarre about a whole collection of particles starting to move in one direction under the influence of their mutual gravitational forces. It sure looks like a violation of conservation of momentum. Not that such oddities should surprise us in infinitary Newtonian scenarios.