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


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.


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.

Wednesday, May 1, 2019

Wilde Lectures schedule

For the benefit of any readers who will be in Oxford this month, here is a schedule of my Wilde Lectures in Natural and Comparative Religion.

The Bayesian false belief pandemic

Suppose that a credence greater than 95% suffices to count as a belief, and that you are a rational agent who tossed ten fair coins but did not see the results. Then you have at least 638 false beliefs about coin toss outcomes.

To see this, for simplicity, suppose first that all the coins came up heads. Let Tn be the proposition that the nth coin is tails. Then the disjunction of five or more of the Tn has probability 96%, and so you believe every disjunction of five or more of the Tn. Each such belief is false, because all the coins will in fact come up heads. There are 638 (pairwise logically inequivalent) disjunctions of five or more of the Tn. So, you have at least 638 false beliefs here (even if we are counting up to logical equivalence).

Things are slightly more complicated if not all the coins come up heads, but exactly the same conclusion is still true: you have 638 disjunctions of five or more false single-coin-outcome beliefs.

But it seems that nothing went wrong in the coin toss situation: everything is as it should be. There is no evil present. So, it seems, reasonable false belief is not an evil.

I am not sure what to make of this conclusion, since it also seems to me that it is the telos of our beliefs to correctly represent reality, and a failure to do that seems an evil.

Perhaps the thing to say is this: the belief itself is bad, but having a bad belief isn’t always intrinsicallybad bad for the agent? This seems strange, but I think it can happen.

Consider a rather different case. I want to trigger an alarm given the presence of radiation above a certain threshold. I have a radiation sensor that has practically no chance of being triggered when the radiation is below the threshold but has a 5% independent failure rate when the radiation is above the threshold. And a 5% false negative rate is not good enough for my application. So I build a device with five independent sensors, and have the alarm be triggered if any one sensor goes off. My false negative rate goes down to 3 ⋅ 10−7. Suppose now four sensors are triggered and the fifth is not. The device is working correctly and triggers the alarm, even though one sensor has failed. The failure of the sensor is bad for the sensor but not bad for the device.

Another move is to say that there is an evil present in the false belief case, but it’s tiny.

And yet another move is to deny that one should have a belief when the credence rises above a threshold.

Tuesday, April 30, 2019

A pre-established harmony with genuine mind-world causation

Molinists have the ability to give a distinctive pre-established harmony account of how the exceptionless truth of deterministic laws of nature could be made compatible with libertarianism.

Here is the story. God considers possible worlds where dualistic agents have the causal power to miraculously contradict the physical laws in their free choices, but where outside of exercises of free will, there are elegant deterministic mathematical laws governing the world. Call such worlds Candidate Worlds.

God then narrows his consideration to Finalist Worlds, which are Candidate Worlds that are feasible—i.e., compatible with the Molinist conditionals—and where as it happens the agents’ free choices accord with the elegant deterministic mathematical laws that govern the rest of the world.

And then God wisely and prudently chooses one of the Finalist Worlds for actualization.

On this story, there are elegant deterministic mathematical laws of nature which are true even of the agents’ choices, but they are true of the agents’ choices because the agents freely chose as they did. The agents had the causal power to violate, say, the conservation of momentum, but in fact freely did not do so.

There is an ambiguity in the concept of “exceptionless laws”. “Exceptionless laws” could mean: laws that allow no exception (they are pushy laws that are so strong as to make no exception possible) and laws that in fact have no exception. The deterministic laws in this story are exceptionless in the sense of having no exception, which is why I am talking of their exceptionless truth rather than their exceptionless power.

In this story, there is a dual explanation of the agents’ choices. On the one hand, there is a standard libertarian story about the agents’ free causality. On the other hand, the laws have explanatory power, because God chose the Finalist Worlds because they are worlds where the laws have exceptionless truth.

The big difficulty with the above story is Molinism. Also, it is worth noting that it is metaphysically possible that there turn out not to be any (feasible) Finalist Worlds: in that scenario, God wouldn’t be able to create a world where there is freedom and elegant deterministic mathematical laws holding exceptionlessly. But for reasons similar to why many people think Transworld Depravity is unlikely to be true, I think it is unlikely that there would be no Finalist Worlds.

It is also interesting to note that there are two more views that could be plugged into the story that can do the same job: Thomism and compatibilism.

On Thomism, God can use primary causation to make agents freely choose as he desires. Then we can suppose that God surveys the same Candidate Worlds as on the Molinist story. Then he chooses Finalist Worlds as those Candidate Worlds where the agents’ free choices in fact do not contradict the mathematical laws. And then God uses primary causation to actualize one of the Finalist Worlds. Again, the agents have the power to contradict the laws, but freely choose not to exercise it.

Finally we have straightforward compatibilism. A dualist can just as easily be a compatibilist as a materialist. On this story, we skip the Candidate Worlds, and the Finalist Worlds are worlds with compatibilist agents, with a deterministic non-physical mental life, who have the power of contradict the physical laws of the world but who are mentally determined, in a way compatible with freedom, never to exercise such a power. And then God chooses one of the Finalist Worlds. The agents then are as free as any compatibilist agents.

The compatibilist version of this story is close to Leibniz’s pre-established harmony, except that it has real mind-world causation, which is a big improvement.

Of course, the non-theist can’t make any of these moves. And, alas, neither can I, since my mere foreknowledge view denies Molinism, Thomism (about free will) and compatibilism.

Two interaction problems

Yesterday I realized something that should have been obvious: there are two separate interaction problems for dualism.

  1. Metaphysics: How does the soul manage to cause effects in the body?

  2. Physics: Wouldn’t such causation violate the laws of physics?

I used to think of the interaction problem as just (1), and hence I thought it was spurious once one learned from Hume that all cases of causation are equally mysterious.

But problems (1) and (2) are pretty independent: one can have a solution to each without a solution to the other. For instance, an indeterministic physics provides a solution to (2), but says nothing about (1), while occasionalism and hylomorphism provide solutions to (1), but say little about (2).

While I think the questions are interesting, I don’t really think either poses a serious problem for interactionist dualism.

Monday, April 29, 2019

Explaining conjunctions and conjuncts

Alice is the chair of a small Department, there being only one other faculty member, Bob. Alice asks IT to run anti-virus software on all the Department faculty computers, namely her computer and Bob’s computers. IT does so. The software deletes a virus on Alice’s computer but finds none on Bob’s.

Alice’s order that anti-virus software be run on her and Bob’s computer explains why her and Bob’s computer are now virus-free by ensuring that they are both virus-free. But Alice’s order does not explain why her computer is now virus-free. Hence once can explain a conjunction without explaining every conjunct.

Van Inwagen’s famous argument against the Principle of Sufficient Reason (PSR) as well as some versions of the Cosmological Arguments from the PSR to theism depend on the idea that if something explains the conjunction of all contingent truths, then it explains every contingent truth. This in turn seems to be based on the claim that when you explain a conjunction, you explain every conjunct—something we have just seen to be false.

I think these arguments can be fixed by noting that although Alice’s order didn’t in fact explain why her computer is now virus-free, it ensured that her computer is virus-free. And perhaps one can weaken the conjunction principle to say that if p explains a conjunction, then p explains some conjuncts and the facts reported by p ensure the other conjuncts. I suspect that will be good enough for the applications (even the one I disagree with, namely van Inwagen’s).

Thursday, April 25, 2019

The analogy of being and the moving spotlight theory of time

On moving spotlight theories, eternalism is true: past, present and future things all exist. But the present is metaphysically special: you have not said all that is to be said about temporal reality if you just said what happens at which times, and how the times are related by relations like earlier-than and simultaneous-with, without having said which time is objectively present. The puzzle for moving spotlight theories is to say what makes the present special.

Here is a start of a moving spotlight theory. Start with the Thomistic insight that there are multiple ways of existing. For instance, God doesn’t exist in the same way in which we do. Now add that temporal beings have three ways of existing: existing pastly, existing presently and existing futurely. Thus, we have at least four ways of existing: divine existence as pure act, past existence, present existence and future existence. These are genuinely different forms of existence, but they are all analogous. And we further subdivide the three temporal ways of existing into substantial and accidental existence.

Moreover, interestingly, these ways of existing can occur in various combinations. For instance, I exist pastly, presently and futurely. An object in the last moment of its existence exists pastly and presently. An object in the first moment of its existence exists presently and futurely. At the first moment of the Incarnation, the Second Person of the Trinity existed as pure act, as well as both presently and futurely. Right now, the Second Person of the Trinity exists in each of these four ways of being.

So what sets out the present as special is this: an event is present provided that the substances and accidents making up the event exist in present ways of existing.

This is eternalism and not presentism, but it captures one central insight of presentism: that to exist presently is different in kind from existing pastly or futurely. It escapes the three horse argument against presentism by saying that the real horses exist analogously to each other but the unreal one does not exist at all.

Of course, this is only a start. It would be nice to be able to say something substantive about how the three temporal ways of existing differ from one another. I don’t know that this can be done, and I don’t particularly want to pursue this, since I much prefer the elegance of the B-theory of time.

Wednesday, April 24, 2019

A tale of three horses

Consider three horses: Alexander's Bucephalus, Gandalf's Shadowfax and Dawn. Here, I am using "Dawn" as the name of a horse that has come into existence just now, so that it is now the first moment of existence for Dawn. (Imagine the claims about Dawn all being made at the first moment of its existence.)

Intuitively, there is something Bucephalus and Dawn have in common with each other that they don't have in common with Shadowfax, namely reality.

The eternalist can take this at face value and say: Bucephalus and Dawn both exist, while Shadowfax does not.

But it is difficult for the presentist to say what Bucephalus and Dawn have in common which they don't share with Shadowfax. According to presentism, neither Bucephalus nor Shadowfax exist. Of course Bucephalus did exist, but on the other hand it is false that Dawn did exist: it is Dawn's first moment. So on presentism, Bucephalus and Dawn have neither existence nor past existence in common. And they don't have future existence in common either, since Bucephalus presumably has no future (unless there is a resurrection for brute animals, which we can suppose for the sake of argument there won't be). Nor do they have timeless existence in common, since none of the three is a timeless entity.

Of course, it is true that both Bucephalus and Dawn did-or-do-exist. But that's a disjunctive property, and a similarity in respect of a merely disjunctive property is not a real similarity. Perhaps the presentist can argue that it is a disjunctive property, but not a merely disjunctive one. But barring some sort of account of the similarity this seems ad hoc. We might as well say that Shadowfax and Bucephalus have this in common, that each fictionally-or-actually-exists.

Tuesday, April 23, 2019

Presentism and vagueness

If presentism is true, then vagueness about the exact moment of cessation of existence implies vagueness about existence: for if it is vague whether an object has ceased to exist at t, then at time t it was, is or will be vague whether the object exists. But it is plausible that there is vagueness about the exact moment of cessation of existence for typical organisms (horses, trees, etc.). On the other hand, vagueness about existence seems to be a more serious logical problem: it makes unrestricted quantifiers vague.

Of course, the eternalist will have a similar problem with vagueness about existence-at-t. But existence-at-t is not fundamental logical existence on eternalism, so perhaps the problem is less serious.

Perdurance, Relativity and Quantum Mechanics

It is known that perdurantists, who hold that objects persisting in time are made of infinitely thin temporal slices, have to deny that fundamental particles are simple (i.e., do not have (integral) parts). For a fundamental particle is an object persisting in time, and hence will be made of particle-slices.

But what is perhaps not so well-known is that on perdurantism, the temporal slices a particle is made of will typically not be simple either, given some claims from standard interpretations of Quantum Mechanics and Special Relativity. The quick version of the argument is this: the spatial non-localizability of quantum particles requires typical temporal slices to be non-localized simples (e.g., extended simples), but this runs into relativistic problems.

Here is a detailed argument.

A perdurantist who takes Relativity seriously will say that for each inertial reference frame R and each persistent object, the object is made of R-temporal slices, where an R-temporal slice is a slice all of whose points are simultaneous according to R.

Now, suppose that p is a fundamental particle and that p is made up of a family F1 of temporal slices defined by an inertial reference frame R1. Now, particles are rarely if ever perfectly localized spatially on standard interpretations of Quantum Mechanics (Bohmianism is an exception): except perhaps right after a collapse, their position is fuzzy and wavelike. Thus, most particle-slices in F1 will not be localized at a single point. Consider one of the typical unlocalized particle-slices, call it S. Since it’s not localized, S must cover (be at least partially located at) at least two distinct spacetime points a and b. These points are simultaneous according to R1.

But for two distinct spacetime points that are simultaneous according to one frame, there will be another frame according to which they are not simultaneous. Let R2, thus, be a frame according to which a and b are not simultaneous. Let F2 be the family of temporal slices making up p according to R2. Then S is not a part (proper or improper) of any slice in F2, since S covers the points a and b of spacetime, but no member of F2 covers these two points. But:

  1. If a simple x is not a part of any member of a family F of objects, then x is not a part of any object made up of the members of that family.

Thus, if S is simple, then S is not a part of our particle p, which is absurd. Therefore, for any reference frame R and particle p, a typical R-temporal slice of p is not simple.

I think the perdurantist’s best bet is supersubstantialism, the view that particles are themselves made out of points of spacetime. But I do not think this is a satisfactory view. After all, two bosons could exist for all eternity in the same place.

Without Relativity, the problem is easily solved: particle-slices could be extended simples.

It is, I think, ironic that perdurantism would have trouble with Relativity. After all, a standard path to perdurantism is: Special Relativity → four-dimensionalism → perdurantism.

I myself accept four-dimensionalism but not perdurantism.

Perdurance, physicalism and mind

According to standard perdurantism, we are four-dimensional beings made out of three-dimensional slices, and properties such as mental ones are primarily had by the slices, and only derivatively by the four-dimensional whole.

Here are two problems with this when conjoined with widely held views.

First, mental states are intrinsic to the entity that has them primarily. But most perdurantists are physicalists. If mental states are intrinsic and had by three-dimensional slices, then it is possible to have a world with just one such three-dimensional slice with mental properties, isolated from other slices. But a single three-dimensional slice, isolated from other slices, does not have the functonal properties that the more plausible physicalist theories of mind require.

Second, it is clearly worse if someone has a constant headache for two hours than for one hour. But if time is continuous, as is widely held, then both the one-hour headache scenario and the two-hour headache scenario have the same infinite number of aching slices that are the primary bearers of the pain. But two scenarios which have the same number of primary painbearers are equally bad. Hence, a two-hour headache is no worse than a one-hour one. Which is absurd.

The perdurantist can escape this by saying that mental states are primarily had by the four-dimensional entity, and the three-dimensional slices, if they have mental states at all, have them derivatively. There are two ways of running this story. One way is that the slices have mental* states: states that aren’t mental states but that ground mental states in the four-dimensional whole. Thus, a four-dimensional entity hurts at time t just in case its slice at t hurts, but hurting isn’t a mental state, and doesn’t have the negative significance of hurting.

A second way is to say that the mental states of the four-dimensional entity reduce to ordinary physical states (positions, shapes, momenta, charges, etc.) of multiple three-dimensional slices.

Saturday, April 20, 2019

Time is not the measure of change or animals are not essentially temporal

Imagine that beings like us come into existence at the very first moment of time and they are the only contingent beings. To aid imagination, suppose we are these beings, and it is now the very first moment of time. Then, barring divine promises or other such divine moral considerations, it is possible that both (a) we won’t exist at any point of the future, and (b) it’s not the case that anything else will come into existence. Thus:

  1. It is possible that the only contingent beings there are are human-like beings and that contingent beings exist at one and only one moment.


  1. Change requires at least two moments of time.

Putting all of the above together, we get:

  1. Either (a) human-like beings can exist without time or (b) time does not require change or (c) time cannot have a beginning or (d) time cannot have an end.

I think theists are likely to deny both 3c and 3d: God can create and terminate a timeline. That leaves the theist 3a and 3b. I think both 3a and 3b are plausible moves.

Aristotle famously held that time depends on change, but he thought that time couldn’t have a beginning or an end, and thus he accepted both 3c and 3d. The argument he actually gave for 3c and 3d doesn’t work (basically, it fails to distinguish “not was” from “was not” and “not will” from “will not”), but we can now see that there actually is a plausible Aristotelian reason to accept that time can’t have a beginning or an end if we think time is the measure of change.

Why am I talking of human-like beings rather than human beings? Well, maybe, “human being” is a biological kind, and biological kinds depend on evolutionary history, so maybe it is not possible for human beings to come into existence at the first moment of time, as they wouldn’t have an evolutionary history. But beings just like humans could.

Friday, April 19, 2019

More on bilocation and movement

It is often said that the four-dimensionalist doesn’t have a good theory of movement beyond the at-at theory which holds that

  1. to move is to be at x1 at one time and at x2 at a different time, where x2 ≠ x1.

However, I am inclined to think the at-at theory is false due to an argument that my son came up with: if an object is bilocated at both x1 and x2 at one time and stays unmoved in both locations until a later time, then it is true that the object is at x1 at one time and at x2 at another time, and yet has not moved.

It is interesting that this argument also works against the most natural tensed theory of movement, namely that:

  1. an object has moved provided that it was at x1 and is at x2, where x2 ≠ x1.

For imagine that an object was and still is bilocated between x1 and x2 and has remained entirely unmoving. Nonetheless, it was at x1 and is now at x2, and x2 ≠ x1, so according to (2) it has moved.

Thus, my son’s argument against the at-at theory does not seem to confer an advantage on the A-theory of time.

It is tempting to tweak (2) to something like this:

  1. an object has moved provided that the set of locations at which it is now present is different from a set of locations at which it was present.

But that fails. For cessation of bilocation is not movement. If an object was bilocated between two locations x1 and x2, and then ceased to exist at x2, while remaining at x1, the object nonetheless did not move, even though (3) says it did.

Furthermore, space at least could be discrete. So imagine a point particle that was bilocated at two neighboring points x1 and x2 in space. The particle then simultaneously moved from x1 to x2 and from x2 to x1. Yet the set of points occupied by the particle was the same as it is now. So (3) says it did not move, but it did move, twice over.

I suppose one can deny the possibility of bilocation. But that is a big price to pay, I think.

I suspect that any theory of change that the A-theorist comes up with that solves this problem will also solve the problem for the four-dimensionalist.

Wednesday, April 17, 2019

Aristotelians shouldn't be presentists

A foundational commitment of Aristotelian philosophy is that all facts are grounded in what substances and features intrinsic to substances, namely forms and accidents, exist. But it is possible for the past to have been different without there being any difference in what substances and features intrinsic to substances presently exist. Therefore, the Aristotelian cannot equate present existence with existence.

In other words, Aristotelians cannot escape the standard grounding arguments against presentism.

Objection 1: A theistic Aristotelian can ground facts about the past in features of God (say, God’s memories).

Response: Only if God is mutable. And there are good reasons to believe that if God exists, he is immutable.

Objection 2: Past events affect present substances in various ways.

Response: There is a possible world with laws of nature similar to ours that starts at time 0 with nothing but two material causally isolated substances A and B (and God, if theism is true) that wiggle around in indeterministic ways. A month later, substance A ceases to exist (maybe God stops sustaining its existence), and no new substances come into existence. Now, in month 2, there is only one substance B. Since the two substances were causally isolated, substance B is not affected in its intrinsic features by anything that substance A did. Thus, the facts about how substance A used to wiggle about are not grounded in the intrinsic features of material substances in month 2. (If one says that we regain grounding when we take God’s intrinsic features into account, that will take us back to Objection 1.)

One might respond that complete causal isolation is impossible. But that’s not right. For imagine that, like in our world, causal influences cannot propagate faster than at the speed of light, and A and B start off one light-year apart, and while A perishes after a month, B perishes after six months. Then B is not going to be affected by A’s wiggles.

Objection 3: But maybe there has to be some kind of a metaphysical influence whereby all present substances are affected by all past substances.

Response: This is not plausible in light of the response to Objection 2. But let’s grant it. Then I transpose my argument to the future. Obviously, future contingent events don’t normally (apart from supernatural cases, like prophecy) affect how substances presently are. Hence even if we grant the mysterious metaphysical influence of past substances on present ones, we still have a problem about the future. That problem could be solved if we embraced an open future, as Aristotle did, but we shouldn’t follow Aristotle in that.

Monday, April 15, 2019

Truth and probabilistic consistency

Suppose Alice has an inconsistent probabilistic assignment PA. Then, famously, there is a series of bets on single propositions (call these binary bets) that is a Dutch Book against Alice: i.e., Alice by her lights will accept each bet, and is guaranteed to lose money.

But now suppose Bob has a probabilistic assignment PB—perhaps a consistent one—that is strictly further from the truth than Alice’s inconsistent one in the sense that

  1. for any p, if p is false, then PB(p)≥PA(p),

  2. for any p, if p is true, then PB(p)≤PA(p), and

  3. at least one of the inequalities is strict.

Then Alice will do at least as well as Bob on every portfolio of offers of binary bets, and on some portfolios she will do strictly better than Bob. In particular, even if Bob’s probabilistic assignment is consistent, and there is a binary bet Dutch Book against Alice, Bob will fare no better than Alice with respect to that book.

Thus, if we start with a consistent assignment and then by some process move towards truth, we will do better (against binary bet portfolios) even if we lose consistency.

So why is Alice’s probabilistic assignment supposed to be rationally bad in a way that Bob’s isn’t? Well, the difference is this. A bookie can fleece Alice simply on the basis of knowing Alice’s probability assignment. But simply knowing Bob’s probability assignment won’t be enough to know which portfolio will fleece him.

However, the more I think about this, the more I lose the intuition that all this shows there is something particularly rationally problematic about Alice’s assignments just because they are inconsistent. Why should game-theoretic performance against a competitor who knows one’s credences be particularly indicative of rationality or the lack thereof? When nature offers us betting portfolios (to pursue this trail or that trail after a wounded deer in the woods, say), these portfolios are normally independent of our credences. Of course, in business and war, we have to worry about mind-reading competitors. But much of our life, we don’t.

Suppose I find myself with inconsistent credences. What should I do? Should I force them to be consistent? If I am dealing with mind-reading competitors who have no more information about the external world than I do, then I should go for consistency. But going for consistency will force me to modify some of my probabilities, and for all I know, these probabilities may get modified away from truth. And that might be more harmful.

There may be interesting trade-offs. Maybe some intellectual strategies work better against mind-reading competitors and others work better with the portfolios set by nature. We should not take doing well with respect to one selection of portfolio to be particularly informative about the nature of rationality.

When being right doesn't pay

Like me, you might have naively speculated that the more truth you know, the better you’ll do in gambling scenarios. But this is mistaken, at least when taken in the strong sense that there is a guarantee of doing better (or even just as well).

For instance, suppose that Alice and Bob are betting on two coin flips. Alice has credence 1/2 for heads for each coin. Bob has credence 1 for heads for the first coin (maybe because he peeked) and credence 1/2 for the second coin. The house happens to offer Alice and Bob this bet:

  • you get $10 if the first coin is heads and you pay $16 if the second coin is heads.

And as it happens both coins are heads.

Alice calculates the expected payoff at (1/2)⋅$10 − (1/2)⋅$16 = −$3 and declines. Bob calculates the expected payoff at $10 − (1/2)⋅$16 = $2 and accepts. But of course the actual payoff on double heads is −$6, so Bob is worse off than Alice for having been right about the first coin.

Can we at least say that in the long run Bob will be better off (financially, maybe not morally) for peeking than Alice? Yes, if the house offers the same bet each time and the coins are fair and Bob accepts the bet whenever he sees the first coin to be heads. But if the house also peeks at the coins and varies the offering based on the outcome, and Bob doesn’t notice this variation, then the house can fleece Bob (e.g., the house can offer the above bet whenever both coins are heads, and in all other cases offer some tiny bet worth a penny).

So in what sense can truth be guaranteed to help? Well, if you are betting on a single proposition, you will do better (or at least no worse) the closer your credence is to the actual truth value (where 0 is falsehood and 1 is truth).

Friday, April 12, 2019

Voting and expertise

Here is something that worries me. In a democratic system, voters need to decide questions where not only is the first-order evidence regarding the questions far beyond the area of expertise of the typical voter, but it is far beyond their area of expertise to know who are the reliable experts.

Economic questions seem particularly glaring cases of this. One politician proposes to raise the minimum wage on the grounds that this will improve the earnings of the neediest members of society, and thereby on balance raise up the most vulnerable. Another proposes to keep the minimum wage fixed on the grounds that raising it will lead to greater automation or close some businesses or reduce employment hours, and thereby on balance bring down the most vulnerable. Who is right is largely an empirical question. There is no way to address it without hard data, and the analysisof the data is really difficult.

If I were voting on such an issue (as an expat Canadian, I don’t get to vote either in the US or Canada), I could to talk to colleagues in the Economics Department and try to get their expert opinion. But, frankly, even that probably wouldn’t be very reliable. These issues are ones that economists are going to be divided on, and while I know about the intellectual integrity of my colleagues in the Economics Department, it’s hard to know about their standing in the field and their knowledge of a particular question. And the vast majority of people doesn’t even know any economists personally.

This is really pessimistic. And I don’t see a solution. More education is good, of course, but the level of education that would be needed would be way higher than most people would have either the time or talent for. Maybe the one happy thought is this. When we have controverted empirical questions like that, and we need to make a decision, tossing a coin isn’t a bad way to do it. And voting is no worse than tossing a coin.

Wednesday, April 10, 2019

Natural Law and the problem of contradictory moral norms

Given a Natural Law ethic, we could imagine a type of creature whose nature is such that even under normal circumstances, it is subject to incompatible moral obligations. We see such conflicts between creatures: the flourishing of the wolf is the languishing of the sheep. But we could imagine a being which has central instances of moral flourishing that also constitute central instances of moral languishing. Perhaps the being’s nature requires both mercy of it and a strict unrelenting justice. Or perhaps it requires both impartial justice and a favoring of kin.

Given that it is much easier to come up with conflicting systems of rules than with harmonious ones, we might well expect that the natures of moral creatures would have such conflicts of characteristic virtues. Thus, given Natural Law ethics, the absence of such general moral contradictions in us is something to be explained.

Given theistic Natural Law ethics, we can give two explanations. First, we could say that divine goodness is less likely to cause such natures to be instantiated. Second, all natures are ways of participating in God. Perhaps there just are no essentially contradictory ways of participating in God, and so such natures are impossible. (Note that this is compatible with the existence of exceptional circumstances where there are contradictory moral norms.)

Along similar lines, note that the Natural Lawyer has to face the same abhorrent action objection that the Divine Command Theorist does. It seems that the Natural Lawyer has to endorse conditionals like:

  • If our nature were to command torture of the innocent, then such torture would be morally required.

But a theistic Natural Lawyer could say (parallel to what typical Divine Command Theorists do) that it is impossible for our nature to command such a thing, either because it would be contrary to God’s goodness to instantiate such a nature or because such a nature is impossible.

I am collecting ways in which Natural Law, and Aristotelian metaphysics in general, requires theism…

Natural Law and the epistemology of permissions

It is hard to know that something is permissible, because an action is permissible provided that no moral consideration is decisive against it. Thus, it seems, to know that an action is permissible requires surveying the infinite set of all possible moral considerations and checking that none of them rules out the action.

But natural law ethics provides a handy shortcut:

  1. Actions characteristic of a kind of being are permissible in relevantly normal circumstances.

Principle (1), for instance, makes it difficult to defend strong versions of antinatalism or of ethical vegetarianism by conferring a default permission status on reproduction and the eating of meat, since we are organisms (and hence characteristically reproduce in appropriate circumstances) and omnivores (and hence have a characteristic diet that includes meat).

The natural permission principle shifts the discussion from the question whether a given action type, characteristic of us humans, is generally permissible, to the question whether the circumstances at hand are relevantly normal. Thus, (1) still leaves open the possibility of an antinatalism that holds that things are so abnormally bad that it’s wrong to reproduce, or an ethical vegetarianism on which global conditions require us to forego meat.

Subscribing to principle (1) also explains the incredulous stare I see on students’ faces when I explain Andrea Dworkin’s view that heterosexual intercourse is always wrong.

Tuesday, April 9, 2019


I am not a sociopolitical philosopher and probably this post will just show my ignorance.

Here is a line of thought I used to find plausible.

Inequality is clearly not intrinsically bad: if it were, it would be worth making those who are best off be less well off even if nobody else were made better off, and that is absurd. Of course, inequality is well-known to contribute to subjective unhappiness, but if inequality is not intrinsically bad, then that contribution seems to be just a function of the vice of envy. So we don’t need to worry about inequality as such. Of course we need to worry about people not having sufficient resources to flourish, but that worry is independent of worries about inequality.

On this line of thought, we have two options:

  1. Inequality is intrinsically bad.

  2. We don’t need to worry about inequality except insofar as it contributes to other bad things (like subjective unhappiness, social unrest, etc.).

But today I realized there is a third option. There need be nothing intrinsically bad in a positive cancer test result, but it is diagnostic of a very bad thing, so we need to worry about it. The same could be true of inequality:

  1. We should worry about inequality because it is diagnostic of other bad things.

Specifically, it could be that significant inequality is a sign of a poor distribution of resources. For instance, a thousand dollars can make an enormous difference to the flourishing of someone below the poverty line but makes no noticeable difference to the flourishing of a billionaire. Thus, significant inequality could be evidence that we could significantly improve the flourishing of one while only insignificantly decreasing the flourishing of another, say by taking a thousand dollars from the richest individual and giving it to a randomly selected person below the poverty line. And thus we would have reason to worry about inequality even if inequality in and of itself wasn’t bad.

Of course, whether in fact significant inequality is evidence of a poor distribution of resources is an empirical question for the economists to figure out. My naive thought above that things would be better if a thousand dollars were moved from a rich person to a poor person assumes that nobody else would be affected. But that is, of course, not empirically clear. Such a transfer could, for instance, lead to the rich person correspondingly decreasing their charitable contributions to a local soup kitchen, or might sufficiently increase the chance of the rich person moving to a location with lower taxes to make the expected value of the transfer be negative, or might decrease incentives to hard work that produces greater benefits to society. Or not.

I am not qualified to judge the empirical question. But at least I’ve learned something from the above line of thought. While the view that inequality is intrinsically bad does seem philosophically mistaken, it is possible to be very worried about inequality without subscribing to this mistaken view.

Monday, April 8, 2019

The probability of the universe popping into existence

Consider the hypothesis that contingent reality popped into existence uncaused.

Now, either popping into existence uncaused is astronomically unlikely or not astronomically unlikely.

If it is astronomically unlikely, then we have a very strong Bayesian argument for theism. For then P(contingent reality | no God) is astronomically small while P(contingent reality | God) is at least moderately high.

If uncaused popping into existence is not astronomically unlikely, then there are two main options. The first option is that there is no meaningful probability of such an event. In that case, there is no meaningful probability of Maxwell’s Demon popping into existence for no cause at all in one’s lab. But if Maxwell’s Demon were to pop into existence in one’s lab, then one wouldn’t expect to get the predicted observations. Thus, if there is no meaningful probability of things popping into existence for no cause at all, then there is no meaningful probability of our scientific predictions, and science falls apart. That’s not acceptable.

The other option is that there is a probability, and it’s not astronomically small. But then at every moment of time, it is not astronomically unlikely that an object would causelessly pop into existence. Since there are astronomically many moments of time during a second (perhaps infinitely many, but at least equal to the number of Planck times in a second, i.e., of the order of 1043), it seems we should expect to see lots of objects pop into existence causelessly. And we don’t observe that.

There is lots of technical detail to fix in this argument.

Yet another theory of ineffability

There is a long-standing tradition of trying to explain (!) the attribute of divine ineffability. Theories that are metaphysical in flavor rule the roost:

  1. The only true assertions we can make about God are negative. (Eastern tradition)

  2. The only true assertions we can make about God are analogical. (Aquinas)

  3. The only true assertions we can make about God are non-fundamental. (Jacobs)

I want to add one more theory to the mix, one that can either be stand-alone or a complement to (1)–(3). This one is more epistemological:

  1. The only assertions we can make about God are misleading.

One can illustrate the misleadingness of true, and even literally true, statements by examples.

  • “Alice did not treat minorities as badly as Hitler” (when Alice was in fact an exemplary promoter of social justice).

  • “Bob is somewhere in this building” (when he is standing right behind you).

  • “I saw Carl in a car on I-35 this morning” (but the car was being towed by a truck).

  • “Davita passed some of her exams” (when she passed all of them).

  • “On a good day, Roger Bannister could run an 8 minute mile.”

Note that while (1)–(3) are limited to true statements, (4) does not have this restriction. After all, all false statements are misleading.

For concrete theological examples, think of how the doctrine of the Trinity shows that the doctrine of the unity of God is misleading, or the doctrine of the Incarnation shows that the doctrine of the transcendence of God is misleading. In a similar same way, when the doctrines of the Trinity and Incarnation are taught apart from the doctrines of unity and transcendence, they are misleading. But by (4) something more pessimistic is true: even when we teach Trinity and unity (or Incarnation and transcendence) together, we still mislead. I suspect that in heaven we will learn something that changes our understanding of unity and Trinity at least as much as the doctrine of the Trinity changed our understanding of unity.

Alvin Plantinga gives this counterexample to the thesis that we cannot say anything literally true of God: “God is not a bicycle.” If (4) is true, even this statement is misleading. In what way? Well, maybe it leads us to forget the intimate link between all reality and God: that all the reality in a bicycle is a participation in God.

Note that if (4) is true, then it is misleading. But that’s not a refutation.

One could also restrict (4) if one wanted to. For instance, one could restrict (4) to non-negative statements, or to non-analogical ones, or to non-fundamental ones.

I don’t know if (4) is true.

Friday, April 5, 2019

All truths are explanatory

Let p be a true proposition. Then p explains the disjunction of p with any falsehood. Thus, all truths are explanatory.

An argument that there are no non-explanatory facts

A stronger naturalism says:

  1. Every fact is natural.

A seemingly weaker naturalism only says:

  1. Every explanatory fact is natural.

But now I will give an argument that (2) implies (1). I am suspicious of the argument but it is hard to put my finger on why it’s wrong. The argument proceeds by arguing for:

  1. Every fact is explanatory.

(Here, I take “explanatory” to go with partial, not necessarily complete, explanation.)

Here is the argument. Suppose, for a reductio, that there is a non-explanatory fact F. Now, some philosophers believe that there are non-explanatory facts. Suppose Alice is such a philosopher. Since (by assumption) there are non-explanatory facts, Alice correctly believes there are non-explanatory facts. But the obtaining of F partially explains why Alice is correct in her belief that there are non-explanatory facts. Thus, F is explanatory, which is a contradiction. Hence, there are no non-explanatory facts.

Thursday, April 4, 2019

Explanation, grounding and divine simplicity

Here is a plausible principle:

  1. If p is partly grounded in q, then p does not explain q.

But the best account of divine simplicity commits one to:

  1. That God willed horses to exist is partly grounded in there existing horses.

(For, that God willed horses is a contingent fact. By divine simplicity any contingent fact about God must be partly grounded in realities outside of God. And the only plausible candidate for the reality outside of God here is the fact that there exist horses.)


  1. That God willed horses to exist does not explain why there are horses.

This seems very counterintuitive, sufficiently counterintuitive to provide an argument against divine simplicity, or against (1).

But I think one should just accept (3). For even apart from considerations of divine simplicity, it is plausible that God’s will is so strongly efficacious that his willing something just is his making it be so:

  1. God’s willing horses to exist just is God’s causing horses to exist.

But in general, even apart from the divine case, x causing y is partly grounded in both x and y, and hence is partly grounded in y. Thus:

  1. God’s causing horses to exist is partly grounded in horses existing.

It seems to follow (there are tough issues involving the hyperintensionality of grounding) that:

  1. God’s willing horses to exist is partly grounded in horses existing.

In fact, once we understand that God’s (consequently) willing and God’s causing are the same thing, then the paradox in (3) is just very much like:

  1. My causing a boomerang to exist does not explain why the boomerang exists.

But we have good reason to accept (7). For when I made a boomerang some years back, that I caused a boomerang to exist was partly grounding in a boomerang existing. (A boomerang might not have eventuated from what I was doing. Instead, I might have been left with a broken piece of wood.) But then by (1), I have to accept (7).

What is unfortunate for me is that for a long time, in print and in speech, I’ve been happy to accept claims like:

  1. My causing a boomerang to exist explains why the boomerang exists.

  2. God’s willing horses to exist explains why horses exist.

I still find it difficult to deny (8) and (9).

Maybe I should deny (1) instead. But I don’t want to. I am strongly committed to there not being any circles of explanation, even ones involving different kinds of explanation (say, causal and grounding).

Maybe I can save the intuitions behind (8) by saying:

  1. My actuating my causal power of boomerang production explains why the boomerang exists.

(Note that my actuating that causal power does not entail a boomerang exists. A causal power can be actuated unsuccessfully.)

And maybe I can save the intuitions behind (9) with:

  1. God’s desiring that horses exist explains why horses exist.

(God’s desiring something doesn’t entail that thing’s existing, since God desires every good, and some goods are incompatible with one another.)

Wednesday, April 3, 2019

Two kinds of occasionalism

Suppose a burner is turned on, a pot is heated, and the water in the pot is boiled. On occasionalism, the heating of the pot is caused only by God, and the same is true for the boiling of the water.

But there are two ways of understanding this:

  1. God causes the water to boil because the pot is being heated. God causes the pot to be heated because the burner is on. God causes the burner to be on because….

  2. God causes the water to boil just because God causes the pot to be heated. God causes the pot to be heated just because God causes the burner to be turned on. God causes the burner to be on just because God causes…

On type 1 occasionalism, God reacts to events in the world, and one has real but non-causal explanatory connections in the world: the water boils because the burner is on. On type 2 occasionalism, there are no real explanatory connections between events in the world: they are all just the effects of God’s plan. Leibniz has type 2 occasionalism in intermonadic causation. And that’s a problem.

I am not saying that type 1 occasionalism has no problems. But at least it makes for real explanatory connections between events in the world, even if these are not causal.

Loving our neighbor as ourselves

Suppose that, as some theories of motivation hold, that all our actions are done in pursuit of our flourishing. But the Scriptures tell us that we should love our neighbor as ourselves. Therefore, all our actions should also be done in pursuit of our neighbor’s flourishing. This seems an unreasonably high standard.

There are three ways out:

  1. Deny that all our actions are done in pursuit of our flourishing.

  2. Deny the love ethic of the Old and New Testaments.

  3. Argue that the standard is not unreasonably high.

For me, (2) is not an option. I do think (1) is a serious option for independent reasons.

But I also think (3) is a very promising approach. Reasons to think that the requirement that we be pursuing our neighbor’s flourishing in all our actions is excessive are apt also to be reasons to think that Paul’s requirement that we “pray constantly” (1 Thes. 5:17) is excessive as well. But if all our actions are done in pursuit of our neighbor’s flourishing, and if we see our neighbor as in the image of God, then all our actions might be a kind of prayer, thereby fulfilling Paul’s difficult injunction. And, conversely, if we are praying always, aren’t we going to be always pursuing our neighbor’s flourishing?

We get something something similarly onerous to the requirement to pursue our neighbor’s flourishing in Kantian ethics: the requirement always to treat rational beings as ends.

One family of difficult cases, both for the flourishing requirement and the Kantian one, lies in everyday businesslike interactions. To use an example of Parfit, you’re buying coffee. It seems that all that is relevant about the barista is that they are supplying coffee. How can you not treat them as a mere means? How can you be pursuing their flourishing? Well, a useful reflection is that we flourish in large part by promoting the wellbeing of others. The barista’s professional activity is a part of their flourishing as a social animal. In courteously buying coffee, one is doing one’s part in an interaction that constitutes a part of that flourishing. Of course, it would be very odd, and likely to lead to pride (“Look at how great I am: I am enabling his flourishing”), if one were to be explicitly thinking about this each time one buys coffee. But courteously making opportunities for others to exercise their professional skills can be a habitual background intention in one’s actions. Similarly, when I when I bite into a delicious sandwich, my intention to get some enjoyment is not something that I need to think about, but it structures the activity (e.g., it explains why I don’t at the same time pinch myself hard).

A different kind of difficult case is given by activity which adversely impacts the flourishing of others. Morality sometimes requires such actions. Less well qualified applicants need to be turned down and trolleys need to be redirected towards more sparsely occupied tracks. Here I think three things can be done to abide by the flourishing requirement. The first is that one not intend a bad effect on flourishing. One doesn’t turn down the less well qualified applicants in order to negatively impact their flourishing. The second is that while declining the applicants or redirecting the trolley, one should be taking their flourishing into account, by thinking about any creative ways to decrease the negative impact on flourishing. Even if no creative ways are found (but isn’t prayer always an option?), the action is chosen as part of a pursuit of the flourishing of those who are harmed by it—but not of course as part of the pursuit of only their flourishing. The third is that there is a kind of harm to one if one is benefited immorally. To a morally sensitive person, it feels bad to get a job that another applicant is was better qualified for, and it would surely feel awful to have five people die because the trolley operator refused to redirect the trolley away from them for one’s sake. These feelings reflect reality. No human is an island, and when our flourishing is at the expense of those who deserve flourishing more, that is bad for us—even if we don’t know about it. It may not be on balance bad for us, but still it is a bad thing. And so the person who turns down the less qualified candidate or redirects the trolley prevents this bad thing from happening, and this is a positive impact on flourishing.

Monday, April 1, 2019

The infinite disvalue strategy for modeling deontological constraints

An standard way to handle deontological constraints is to simply specify an infinite disvalue for breaking the constraints. Thus, you shouldn’t kill an innocent person to save ten innocents, because the disvalue of your murdering the one is infinitely greater than the finite value of the lives of the ten.

A standard response to this is to imagine cases where one deontological violation prevents multiple similar deontological violations. That cannot be handled by disvalue, since the multiple violations should have greater cumulative disvalue than the single violation. However, such cases may seem contrived.

But I just realized recently that they need not be contrived. In fact, the standard strategic bombing of civilian targets cases may be like that. These cases—which were probably exemplified by the bombings of Hiroshima, Nagasaki and Dresden—are usually described as cases where it is expected (or at least hoped) that the deaths of the innocents will persuade the enemy to surrender and stop a greater number of deaths.

However, in cases—like the World War II cases—where one is fighting an unjust aggressor, killings performed by the enemy (whether the victims are civilians or military personnel) are typically murders. Thus such cases may very well be cases where a smaller number of murders—committed by means of bombing—by one’s side prevents a greater number of murders committed by the other side. Thus, we have historical cases, or at least cases very close to historical cases, where a smaller number of immoral acts is thought to prevent a greater number of immoral acts of the same kind. And hence we have uncontrived cases where the disvalue strategy for modeling deontological constraints fails.

Molinism and Thomism and control over others

  1. It is not possible for a creature to exercise complete control over another person’s (non-derivatively) free action.

  2. If Molinism is true, it is possible for a creature to exercise complete control over another person’s (non-derivatively) free action.

  3. So, Molinism is false.

For, if Molinism is true, there will be a possible situation where God reveals to Alice that if she were to make a request of Bob while wearing blue gloves, Bob would acquiesce to the request, but if she were to make the request while wearing red gloves, Bob would turn down the request. In such a case, by controlling which gloves she wears, Alice could exercise complete control over whether Bob acquiesces to the request.

Interestingly the same argument works against Thomism. For on Thomism, God can use primary causation to determine Bob to freely acquiesce in the request and God can use primary causation to determine Bob to freely refuse the request. God could then promise Alice that he would hear her prayers as to whether Bob agrees or refuses, and then with her prayers, Alice would have complete control over Bob's decision.

The argument doesn't work against mere foreknowledge views, open theist views or compatibilist views. On mere foreknowledge and open theism, the analogue of (2) is false, while on compatibilism, (1) is not plausible.

[Thesis:] April Fool's Philosophy Post Generator

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The thesis that [thesis] has not received much of a defense[literature type]. But here is an argument for it:

  1. This argument is valid.

  2. Therefore, [thesis].

Let's see why this argument is not only valid but sound.

First, let’s see that it’s valid. Suppose for a reductio that it is invalid. But whether an argument is valid or not cannot be a contingent matter. Thus if, the argument is invalid, it is necessarily invalid. But if it is necessarily invalid, then necessarily its first premise is false (since the premise says that the argument is valid). But any argument which has a necessarily false premise is automatically valid. (An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. This is trivially satisfied if it is impossible for a premise to be true.) But that would contradict the assumption that it’s invalid. So, the argument must be valid.

But if the argument (1)–(2) is valid, it’s also automatically sound. For a valid argument is sound provided its premises are true. But the only premise of the argument is (1), the statement that the argument is valid. If the argument is valid, then that premise is true, and so the argument is sound.

But the conclusion of a sound argument is true. Therefore, [thesis].