Quantifying saving infinitely many lives

Suppose there is an infinite set of people, all of them worth saving, and you can save some subset of them from drowning. Can you assign a utility U(A) to each subset A of the people that represents the utility of saving the people in A subject to the following pair of reasonable conditions:

1. If A is a proper subset of B, then U(A) < U(B)

2. If A is a subset of the people, and x is one of the people not in A while I is an infinite set of people not in A, then U(A∪{x}) ≤ U(A∪I)?

The first condition says that it’s always better to add extra people to the set of people you save. The second condition says it’s always at least as good to add infinitely many people to the set of people you save as to add just one. (It would make sense to say: it’s always better to add infinitely many, but I don’t need that stronger condition.)

Theorem. For any infinite set of people, there is no real-valued utility function satisfying conditions (1) and (2), but there is a hyperreal-valued one.

It’s obvious we can’t do this with real numbers if we think of the value of saving n lives as proportional to n, since then the value of infinitely many lives will be ∞ which is not a real number. What’s mildly interesting in the result is that there is no way to scale the values of lives saved in some unequal way that preserves (1) and (2).

Proof: The hyperreal case follows from Theorem 2 here, where we let Ω = Ω′ be the set of people, G be the group of permutations of the set of people that shuffle around only finitely many people, and let U be the hyperreal probability (!) generated by the theorem. For this group is clearly locally finite, and any utility satisfying condition (1) and invariant under G will satisfy (2) (apply invariance to a permutation π be that swaps x and a member of I and does nothing else to conclude that U(A∪{x}) = U(A∪{πx}) which must be less than U(A∪I) by (1)).

The real case took me a fair amount of thought. Suppose we have a real U satisfying (1) and (2). Without loss of generality, the set of people is countably infinite, and hence can be represented by rational numbers Q. For a real number x, let D(x) be the Dedekind cut {q ∈ Q : q < x}. Fix a real number x. Choose any rational q bigger than x. Then for any real y > x we will have D(y) ∖ D(x) infinite, and by (1) and (2) we will have:

3. U(D(x)) < U(D(x)∪{q}) ≤ U(D(y)).

Let b = inf_y > xU(D(y)). It follows that U(D(x)) < b ≤ U(D(y)) for all y > x. Let f(x) be the open interval (D(x),b). Then f(x) and f(y) are disjoint and non-empty for x < y. But the collection of disjoint non-empty open intervals of the reals is always countable. (The quick argument is that we can choose a different rational in each such interval.) So f is a one-to-one function on the reals with countable range, a contradiction.

Notes: The positive part of the Theorem uses the Axiom of Choice (I think in the form of the Boolean Prime Ideal Theorem). The negative part doesn’t need the Axiom of Choice if the set of people is countable (the final parenthetical argument about intervals and rationals ostensibly uses Choice but doesn’t need it as the rationals are well-ordered); in general, the argument of the negative part uses the weak version of the Countable Axiom of Choice that says that every infinite set has a countably infinite subset.

Permanence and meaning

Consider this strong meaning-permanence thesis:

1. There being a permanent end to all humanly relevant events would render all of our present activities meaningless.

And this weak one:

2. There being a permanent end to all humanly relevant events would render some of our present activities meaningless.

Here is a quick and easy argument that both are false. Let’s imagine that we believe in a narrative N where there are humanly relevant events that are go on forever and that render some of our present activities meaningful. After all, if there is no such narrative, then it is odd to say that a permanent end to humanly relevant events renders some or all of our present activities meaningless, since these activities would necessarily be meaningless even if there were no such end.

Now, let’s imagine that we came to think that the events and experiences in N exponentially speed up with respect to objective time, in such a way that the first “year”, by human reckoning (revolutions of the earth about the sun, say), described by N takes an objective year, but the second “year” takes half a year, the third “year” takes a quarter of a year, and so on. Thus, we come to think that all the events and experineces in N take place objectively in two years. This is then followed by a clean wipe of reality, and a new creation that has no meaningful connection to any humanly relevant events. Call this story N^*. I think it makes little human difference whether reality is described by N or by N^*. In terms of subjective time, the humanly relevant events of N^* take infinitely long. The only difference is that after the humanly relevant events there are other events that are not humanly relevant. Enriching reality with these events surely does not take away meaning.

So, none of our present activities lose meaning on N^*. But on N^* there is a permanent end of humanly relevant events. Thus, (1) and (2) are both false.

Perhaps this was too quick, though. What if your life project is to fill as much of time with humanity as you can? Then on N, if there are humans always, your project is successful, But on N^*, your project is not successful, because there is infinite humanless time after the end of humanity in two objective years, and so humans occupy only an infinitesimal fraction of time.

But I think it’s mistaken to think that it should be our project to fill up time or space with humans or human events. In other words, the filling-up project is meaningless regardless of success. Take the spatial analogue. Suppose somehow we didn’t know about other galaxies (maybe there are dust clouds shielding them from our view) and we have filled up our galaxy with humans. Would we lose any real meaning in our activities if we found out that reality is richer than we thought, and contains other galaxies beyond our reach? I don’t think so.

The above argument is compatible with a modified version of (1):

3. There being a permanent end to all humanly relevant events after a finite number of events would render all of our present activities meaningless.

For we might think that the reason ordinary stories about a permanent end have a tendency to make us think our activities are meaningless does not have to do with time, but with the idea that the narrative structure for humans requires infinity.

Spatiality and temporality

Here’s an interesting thing:

1. Learning that our spatiality is an illusion need not radically change the pattern of our rational lives.

2. Learning that our temporality is an illusion would necessarily radically change the pattern of our rational lives.

To see that (1) is true, note that finding out that Berkeley’s idealism is true need not radically change our lives. It would change various things in bioethics, but the basic structure of sociality, planning for the future, and the like could still remain.

On the other hand, if our temporality were an illusion, little of what we think of as rational would make sense.

Thus, temporality is more central to our lives than spatiality, important as the latter is. It is no surprise that one of the great works of philosophy is called Being and Time rather than Being and Space.

Curiously, though, even though temporality is more central to our lives than spatiality, temporality is also much more mysterious!

Aristotle on flourishing

Aristotle thinks that the flourishing of a kind of organism is primarily defined by the excellent exercise of the distinctive functions of the kind. This works great for us: our flourishing is primarily given by the excellent exercise of rationality.

But it doesn’t, I think, work well for other organisms. Think of cats and bears. It seems plausible that their primary flourishing is found in functions that they have in common, such as growth, reproduction, sensation, hunting, feeding, etc. They do have significant distinctive features, but these distinctive features are not central constituents of their flourishing.

One might take the above observations to be evidence for the three-species view of organisms, that there are three metaphysical species: plants, brute animals, and rational animals. But I think this runs into a problem with plants. For the flourishing of a plant is presumably constituted by growth and reproduction, which plants have in common with brute and rational animals.

I think we should reject the emphasis on distinctiveness in flourishing. Instead, we should probably say that the nature of an organism also specifies a prioritization in the functions of the organisms.

An argument for the three-species view

Some contemporary Thomists have the idea that there are exactly three metaphysical species—three kinds differentiated by qualitatively different natures—of living things: plants (maybe broadly understood as non-sentient living things), mere animals, and rational animals.

Here’s a line of thought that yields two-thirds of the view, starting with a premise that most medieval Aristotelians would have accepted:

1. Our (metaphysical) species is rational animal.

2. Therefore, if there were a rational fish, it would be a member of our species.

3. And, a fortiori any rational ape would be a member of our species.

4. So, all rational fish would be the same species as all rational apes.

5. If all rational fish would be the same species as all rational apes, all non-rational fish are the same species as all non-rational apes.

6. The above generalizes from fish to all other animals.

7. So, all rational animals are the same species and all non-rational animals are the same species.

I don’t have an argument for 5, but it seems pretty plausible.

And the claim that all living non-sentients are the same species doesn’t seem implausible given 7.

I myself reject 1.

Divine timelessness and the A-theory of time

1. One can only know a proposition when it is true.

2. One can only know a proposition when one exists.

3. Thus, one can only know a proposition if it ever happens that one exists while it is true. (1 and 2)

4. If the A-theory of time is true, the proposition that it is a Wednesday is true only on Wednesdays.

5. God knows all objectively true propositions.

6. If the A-theory is true, the proposition that it is a Wednesday is objectively true. [I am posting this on a Wednesday.]

7. If the A-theory is true, God knows that it is a Wednesday. (5 and 6)

8. If the A-theory is true, God exists on a Wednesday. (3, 4 and 7)

9. If God exists on Wednesday, God exists in time.

10. So, if the A-theory is true, God exists in time. (8 and 9)

I conclude that the A-theory is false.

The above argument is similar to one that Richard Gale gives in On the Nature and Existence of God, though Gale's purpose is to provide an argument against theism.

Probably most people you know are more social than you

You might observe:

1. Most of the people I know are more social than me.

And then you might beat up on yourself, concluding:

2. I am less social than most people.

But the inference from (1) to (2) is obviously fallacious.

For whether you know a person is a function of how social you are and how social they are. Thus, the sample of people in (1) suffers from an evident sampling bias: it is skewed towards people who are more likely to be social.

How strong is this bias? Well, here is a model. There are N people. Each person has a sociality score between 0 and 1. Each person knows themselves. For each pair of distinct people, we independently decide if they know each other, with a probability equal to the average of their sociality scores. Then we calculate the fraction of people who have the property that most people they know have a higher sociality score.

Computer simulation gives us about 59% for N = 1000 or N = 1500 with sociality scores uniformly distributed from 0 to 1. I haven’t bothered to come up with a closed form solution.

So the bias isn’t that strong, but indeed most people are such that most people they know are more social than they are.

I just saw this more thorough related study.

Another infinite dice game

Suppose infinitely many people independently roll a fair die. Before they get to see the result, they will need to guess whether the die shows a six or a non-six. If they guess right, they get a cookie; if they guess wrong, an electric shock.

But here’s another part of the story. An angel has considered all possible sequences of fair die outcomes for the infinitely many people, and defined the equivalence relation ∼ on the sequences, where α ∼ β if and only if the sequences α and β differ in at most finitely many places. Furthermore, the angel has chosen a set T that contains exactly one sequence from each ∼-equivalence class. Before anybody guesses, the angel is going to look at everyone’s dice and announce the unique member α of T that is ∼-equivalent to the actual die rolls.

Consider two strategies:

1. Ignore what the angel says and say “not six” regardless.

2. Guess in accordance with the unique member α: if α says you have six, you guess “six”, and otherwise you guess “not six”.

When the two strategies disagree for a person, there is a good argument that the person should go with strategy (1). For without the information from the angel, the person should go with strategy (1). But the information received from the angel is irrelevant to each individual x, because which ∼-equivalence class the actual sequence of rolls falls into depends only on rolls other than x’s. And following strategy (1) in repeats of the game results in one getting a cookie five out of six times on average.

However, if everyone follows strategy (2), then it is guaranteed that in each game only finitely many people get a shock and everyone else gets a cookie.

This seems to be an interesting case where self-interest gets everyone to go for strategy (1), but everyone going for strategy (2) is better for the common good. There are, of course, many such games, such as Tragedy of the Commons or the Prisoner’s Dilemma, but what is weird about the present game is that there is no interaction between the players—each one’s payoff is independent of what any of the other players do.

(This is a variant of a game in my infinity book, but the difference is that the game in my infinity book only worked assuming a certain rare event happened, while this game works more generally.)

My official line on games like this is that their paradoxicality is evidence for causal finitism, which thesis rules them out.

Theism and presentism

Suppose presentism is true and truths about other times are grounded in tensed facts, such as the fact that there were once dinosaurs.

Given presentism and theism, God is in time. Suppose, as the Abrahamic religions hold, that God created all contingent things a finite amount of time ago. Before God created them, it was contingently true that God will create them. This truth would be grounded in a contingent tensed fact. Hence before God created all contingent things, there already was a contingent thing—the tensed fact that God will create. A contradiction.

So the presentist needs to have a different solution to the grounding problem than positing tensed facts. The best alternative is positing tensed properties. Thus before creation something will have to have the property of being such that God will create. There is only one candidate for that something—God. For nothing else exists before creation. So God has a contingent property, contrary to divine simplicity. Thus presentist theists need to deny divine simplicity. That’s a big price!

One solution is a restricted presentism like Feser’s on which everything that exists is either present or timeless. Then we can suppose that time begins with creation. There may be other problems there.

Growing Block and a time bias

Here’s a curious argument against Growing Block. Other things being equal, it is better to receive goods earlier in life and to receive bads later in life if Growing Block theory is true. For the earlier you receive X in life, the larger the portion of your life during which X is a part of your life. For X becomes a part of your life at its time, and on Growing Block remains a part of your life forever.

Thus, if you live to 70, and eat a chocolate cake at age 10, then for the next 60 years you are alive with a life that includes that happy event. But if you eat the cake at age 50, then it is only for 20 years that you are alive with a life that includes that happy event.

On Growing Block, this seems to be a good reason to put good things earlier in life and bad things later. But surely one does not have such a reason! So, we have evidence against Growing Block.

Two kinds of time bias

In our philosophy of time seminar, we have been thinking about time biases. Humans appear to discount future goods and bads so that a good or bad with value λ at temporal distance T in the future has effective value f(T)λ for some monotonically non-increasing function f. We might call this a relational time bias—the bias is based on the temporal relation between us-now and the goods and bads we are thinking about.

But there are also structural or non-relational time biases. Thus, as is well known, we think that a life of improvement is better to a life of deterioration, even if the total amount of good is the same. In other words, we think it’s better if the goods are rearranged in life to go closer to the end of life. Putting them closer to the end of life is also usually putting them further in the future, but the concern here is purely structural, not about how far or close the goods are to the present as such.

What is real change?

I am starting to think that it’s rather mysterious what real change—i.e., non-Cambridge change—is. (Cambridge change is illustrated by examples like: Alice became shorter than her son Bob because Bob grew.)

It is tempting to say:

1. x undergoes non-Cambridge change if and only if there is an intrinsic property that x gains or loses.

But it could well turn out that one can undergo non-Cambridge change with respect to relational, and hence non-intrinsic, properties. The radical, but I think quite possibly correct, example is that it could turn out that all creaturely properties are relational because they all involve participation in God. (Thus, to be green is to greenly participate in God.)

However, there could be less radical cases. For instance, plausibly, shape properties are constituted by relations between an object’s parts and regions of space. But an object’s changing shape is a paradigm example of a non-Cambridge change. Or it might be that a Platonism on which we have an “eye of the soul” that changingly gazes at timeless Platonic objects. It seems like the change in the eye of the soul in coming to gaze on Beauty Itself could be entirely relational and fundamental. In particular, the “gaze” might not be constituted by any non-relational features of the eye of the soul. And yet the change is not a Cambridge change.

It seems to me that this worry gives one some reason to accept this Aristotelian account:

2. x undergoes non-Cambridge change if and only if x has a passive potentiality that is actualized.

I would rather not do that—I have long tried to avoid passive potentialities—but I don’t right now know another alternative to (1). I dislike passive potentialities sufficiently that I am actually tempted to deny that there is an account of the difference between Cambridge and non-Cambridge change. But that would come at a serious cost: it would be hard to account for divine immutability.

A compositional fine-tuning argument

Assume naturalism about the human mind. Our best naturalistic account of the human mind is functionalism. But functionalism faces multiple too-many-minds problems. The most famous of these are the Chinese Room and its variants like Schwitzgebel’s consciousness of the United States argument. But a more troubling bevy of problems comes from abundant ontologies. Thus, as Dean Zimmerman noted (building on Unger), where I am there are many clouds of atoms that differ from me in an insignificant way—say, an atom in some insignificant skin cell. On functionalism, each of these clouds should have the same conscious states as I do. Or, as Johnston argued, I have many personites—temporal parts of my life that are intrinsically just like the life of a person could be. On functionalism, they will have the same conscious states as me. The clouds of atoms and personites are not just a consequence of functionalism but also of other naturalistic accounts of mind.

But why are the too-many-minds problems problems, beyond the fact that they are counterintuitive? After all, we have good reason to think that the mind is mysterious enough that the true theory will have some counterintuitive consequences.

I think the best answer is ethics. If a country has a person-level mind, then it would be a murder-suicide for the citizens to vote to dissolve the country. But it is not wrong for the citizens to vote to dissolve a country for, say, economic reasons. If the Zimmerman argument is right, then where there is a person feeling pain, there are many other beings with human-level consciousness feeling the same pain. But the number of being that coincide with a specific person rapidly increases with the size of the person—the more cells they have, the more clouds of atoms there are that differ with respect to a few insignificant atoms. Consequently, if we have a choice between relieving an equal pain in two smaller persons or one much larger person, we should always relieve the pain in the larger one, because the number of conscious atom clouds coinciding with the larger person is likely much larger than the total number of atom clouds coinciding with the smaller ones. In other words, crucial intuitions about equal treatment of people are undercut. Something similar is true on the Johnston arguments if the number of personites is finite, and if it’s infinite we have other ethical problems. On the other hand, there is no immediate serious ethical problem in saying the Chinese Room is conscious.

Given functionalism, I think there is only one way to block the ethically problematic too-many-minds cases: deny that the alleged entities exist. There are no countries. There is only one human-shaped cloud of atoms where I am. There are no personites. But we better not go all the way to blocking all complex objects—we will get other ethical problems if we conclude with the early Unger that humans don’t exist. In other words:

1. If functionalism and ethical realism are true, restricted composition is true.

Restricted composition says that some but not all (proper) pluralities of atoms compose a whole. Note that (1) also applies to some other naturalistic theories than functionalism.

But it’s not enough that restricted composition be true. What we need is a carefully fine-tuned restricted composition. If we restrict composition too much, there will be no humans—and that’s ethically unacceptable. If we don’t restrict composition enough, there will be too many minds of an ethically problematic sort. In other words, restricted composition must be fine-tuned to fit with human ethics.

That’s difficult to do. For instance, van Inwagen’s life-account—that a plurality composes a whole if and only if it has a life together—has the problem that clouds of atoms that differ from me insignificantly have a life together just as I do.

Given naturalism, I think any restricted composition account that fits with ethics will involve seemingly arbitrary choices. Thus, one might start with van Inwagen’s account, but have an incredibly fine-grained account of what counts as “a life together” such that only one of the clouds of atoms nearly coinciding with me has a life together—namely, the cloud constituting me. But such a fine-grained account will have a ton of free parameters, and will be an implausible candidate for a metaphysically necessary account of restricted composition. Thus, the account will not only be fine-tuned but will likely be contingent.

How do we explain the fine-tuning of restricted composition for ethics? It’s hard to see how to do it other than by supposing that fundamental reality is value-driven. There are two main value-driven theories of fundamental reality: theism and axiarchism, where the latter is something like the view that reality must be for the best. Thus we have an argument for theism or axiarchism. And axiarchism, as Rescher noted, plausibly implies theism, since it’s for the best that there be a perfect being. So, either way, we get theism.

We can also run this argument in a Bayesian way. Assume naturalism about the earth ecosystem as a background belief, and assume as part of the background that the physical simples are arranged as they are. On atheism, it is extremely unlikely that composition is fine-tuned for ethics. On theism, it is at least moderately likely. So, we have significant evidence for theism.

Objection: God can’t control which cloud of atoms composes a whole, because whatever is the answer, the answer is metaphysically necessary.

Response: First, as noted above, it is likely that any ethically fine-tuned restricted composition theory has a bunch of parameters that appear contingent, and hence is likely contigent. Second, God is creator and has power over being itself. It seems quite plausible that where there is a bunch of particles God can lend his power to create an entity composed of the particles. Third, if God exists, likely modality itself is grounded in God—all reality necessarily reflects the goodness of God. But if so, then divine goodness may help to explain surprisingly good features of necessary truths, such as a fine-tuned but necessary theory of composition. Fourth, we don’t need to be certain of any of the above. All we need is that one of these stories is an order of magnitude more likely on theism than the fine-tuning of restricted composition is given naturalism (where the probabilities are all epistemic).

If my argument succeeds, it yields a dilemma:

2. Either naturalism about humans is false or God exists.

One may ask whether some variant of the above fine-tuning argument applies if naturalism about humans is true. I expect it does, but the exact shape of the bump under the rug will be different for different non-naturalistic stories. For instance, on Cartesian theories, there will be the question of why there is exactly one soul per human body. On strong emergence, we can ask why consciousness arises in exactly one of the human-shaped clouds of atoms where I am.

Avoiding temporal parts of elementary particles

It would be appealing to be able to hold on to all of the following:

1. Four-dimensionalism.

2. Elementary particles are simples.

3. There is only kind of parthood and it is timeless parthood.

4. Uniqueness of fusions: a plurality of parts composes at most one thing.

But (1)–(4) have a problem in cases where one object is transformed into another object made of the same elementary particles. For instance, perhaps, an oak tree dies and then an angel meticulously gathers together all the elementary particles the oak ever has and makes a pine out of them, which he shortly destroys before it can gain any new particles. Then the elementary particles of the oak seem to compose the pine, contrary to (4).

One common solution for four-dimensionalists is to deny (2). Elementary particles have temporal parts, and you can’t make the old temporal parts of the oak’s particles live again in the pine. But there are problems with this solution. First, you might believe in a patchwork principle which should allow the old temporal parts to get re-used again. Second, it is intuitive to think that elementary particles are parts of the oak. But on the temporal part solution, this violates the transitivity of parthood, since the elementary particles will have temporal parts that outlive the oak. Third, the temporal parts of particles seem to be just as physical as the particles, and you might think that it’s the job of physics and not metaphysics to tell us what physical objects there are, so positing the temporal parts steps on the physicist’s toes in a problematic way. Fourth, and I am not fully confident I understand all the ramifications here, we need some kind of primitive relation joining the temporal parts of the particle into a single particle, since otherwise we cannot distinguish the case where two electrons swap properties and positions (and thereby reverse the sign of the wavefunction) from the case where they don’t.

The second common solution is to deny (3), distinguishing parthood from an irreducible parthood-at-t, and then say that trees are merely composed-at-t from elementary particles. I find an irreducible parthood-at-t kind of mysterious, but perhaps it’s not too terrible.

I want to offer a different solution, with an unorthodox four-dimensionalist Aristotelianism. Like orthodox Aristotelianism, the unorthodox version introduces a further entity, a form. And now we deny that a tree is composed of the elementary particles. Instead, we say that a tree is composed of form and elementary particles. One minor unorthodox feature here is that we don’t distinguish the parthood of a form in a substance and the parthood of a particle in a substance: there is just one kind of parthood. The more unorthodox thing will be, however, that we allow elementary particles to outlive their substances. The resulting unorthodox four-dimensionalist Aristotelianism then allows one to accept all of (1)–(4), since the pine is no longer composed of parts that compose the oak, as the oak’s form is not a part of the pine.

But we still have to account for parthood-at-t. After all, it just is true that some electron e is a part of the oak at some but not other times. And this surely matters—it is needed to account for, say, the mass and shape of the oak at different times. How do we that? Well, we might suppose that even if in our unorthodox Aristotelianism particles can outlive their substances, they get something from the substance’s form, even if it’s not identity. Perhaps, for instance, they get their causal powers from the substance’s form. (We then still need to say something about unaffiliated particles—particles not inside a larger substance. Perhaps when a particle, considered as a bit of matter, gets expelled from a larger substance and becomes unaffiliated, it gains its own substantial form. It loses that form when it joins into a larger substance again. At any given time, it gets its causal powers from the substance’s form.) So we can say that e is a part of the oak at t if and only if e gets its causal powers from the oak’s form at t.

Aristotelianism and fundamental particles

A number of contemporary Aristotelians hold to the view that when a fundamental particle becomes or ceases to be a part of an organism, the particle perishes and is replaced by another. The reasoning is that the identity of parts comes from the whole substance, so parts are tied to their substances.

I’ve long inclined to this view, but I’ve also always found it rather hard to believe, feeling that a commitment to this view is a significant piece of evidence against Aristotelianism. I think I may now have found a way to reduce the force of this evidence.

Consider one of the main competitors to Aristotelianism, a non-Aristotelian four-dimensionalism with standard mereology that includes strong supplementation:

1. If y is not a part of x, then y has a part z that does not overlap x.

Together with antisymmetry (if x is a part of y and conversely, then x = y), it immediately follows that:

2. If everything that overlaps x also overlaps y and conversely, then x = y.

Now, suppose that we have a chair made of some fundamental particles. The planks from the chair are ripped off and reassembled into a model trebuchet, with no fundamental particles added or gained. Suppose the fundamental particles are simples. Then any z that overlaps the chair had better overlap at least one fundamental particle u of the chair (the Aristotelian will deny this: it might instead overlap the form) and since fundamental particles are simples it must have u as a part. But u is also a part of the trebuchet. Thus z overlaps the trebuchet, and so anything that overlaps the chair overlaps the trebuchet. And the converse follows by the same argument. Thus, the chair is the trebuchet, which is absurd.

Here is a standard solution to this: fundamental particles are not actually simples, because they have proper temporal parts, and temporal parts are parts. What are the true simples are the instantaneous slices of fundamental particles. Thus a z that overlaps the chair in a fundamental particle u need not overlap the trebuchet as the overlap can happen in disjoint temporal parts of u.

The main competitor to Aristotelianism, thus, has to suppose that fundamental particles are actually made up of their instantaneous slices. Now suppose the Aristotelian accepts this ontology of instantaneous slices of fundamental particles, but denies that there are fundamental particles composed of the slices. Problem solved! We don’t have the problem of fundamental particles persisting beyond the substances that they are parts of, because there are no fundamental particles, just instantaneous slices of fundamental particles.

Is there much cost to this? Granted, we have to deny that there are electrons and the like. But our non-Aristotelian four-dimensionalist mereologist either also denies that there are electrons or else has to construct the electrons out of electron slices, presumably by supposing some sort of a diachronic relation R that relates slices that are to count as part of the same electron. But if we have such a relation, then we can just paraphrase away talk of electrons into talk of maximal sets of electron-slices interrelated by R. If anything, we gain parsimony.

And if we cannot find such a diachronic relation that joins up electron-slices into electrons, then our non-Aristotelian four-dimensionalist has a serious problem, too.

Beyond persons?

I wonder if creation includes beings that are qualitatively as high above mere persons like us as mere persons are qualitatively above non-persons. Persons have agency and intellectuality (let’s say) and that gives them a dignity above non-persons. Is there some quality Q that is even more impressive than agency and intellectuality and that is actually found in some creatures?

We have no idea what that quality Q would be, and just as personhood is surely inconceivable to a non-person, Q would likely be inconceivable to us.

I think our only approach to the question is through divine revelation, and it may be that divine revelation just does not include enough information.

Here is my best line of thought towards a negative answer. Jesus Christ is king of creation. Moreover, plausibly, he is king of creation not just as God, but as a human being. As God, he presumably would have Q. But as a human being, he lacks Q. But just as having personhood seems a prerequisite for being king over persons, it seems that having Q would be a prerequisite for being king over those with Q.

On the other hand, one might think that God might want to make the possessors of Q humble, and being ruled over by a human being might be a good way to do that. So I don’t think we have a decisive answer.

Two kinds of change

I ran across this old post of mine and it made me think that there is an interesting distinction between two kinds of change which one might label as objectual and factual change. Objectual change is change in objects, including both an object’s acquiring or losing properties and an object’s coming or ceasing to be. Factual change is change in reality itself—the facts of reality themselves change, with future facts coming to be present (and on open future views getting filled out) and present facts coming to be past. We can put this in terms of change of facts, change of truth value of (“fully closed”) propositions, or change of reality as a whole.

When A-theorists accuse B-theorists of having a static picture of the universe and B-theorists respond with the at-at theory of change (change is a thing’s having a property at one time and lacking it at another), they are talking past each other to some degree. The A-theorist is talking of factual change. The B-theorist is talking of objectual change. The A-theorist is simply right that on the B-theory there is no factual change: the facts about reality were, are and will ever be the same. That there is objectual change on the B-theory does not contradict this. But at the same time, the A-theorist’s accusation of static factuality is something the B-theorist should proudly admit as a feature and not a bug: truth does not change.

That there is objectual change is a part of our uncontroversial data about the world. That there is factual change is the A-theory in a nutshell, and hence begs the question against the B-theorist.

At this point it seems we have an impasse. Where should the debate go? I think one thing to figure out is whether one of the kinds of change depends on the other. Suppose it turns out that objectual change would need to depend on factual change. Then the A-theorist has won: the B-theory has no change at all. Note that the at-at theory of change is not a sufficient response to a claim that objectual change depends on factual change. For the at-at theory depends on the concept of time (change is having different properties at different times), and if time itself requires factual change, then the at-at theory itself requires the A-theory. This suggests that if the at-at theory is going to be the B-theorist’s response, the B-theorist owes the A-theorist an account of what makes time be time (McTaggart insisted on the latter point).

What about the other direction? That one is kind of interesting, too. One might think that factual change would need to arise from objectual change. Aristotle apparently did. It’s not clear, however, how one gets the A-theorist’s change of reality, where future facts become present and present facts become past, out of changes in objects. Perhaps one can read McTaggart’s infamous argument against the coherence of the A-theory as an attempt to show that this task can’t be done, at least in the special case where the objects are events.

Can we offer such an argument? Maybe. We aren’t going to be able to get factual change simply from the fact that objects have different ordinary properties at different times, say a light being green at t₁, orange at t₂, and red at t₃. For there is no way to use such facts to ground which of these times are past, present or future. So it seems that if we’re to get factual change from objectual change, we’re going to have go the route McTaggart suggests, and try to ground it in terms of objects’ temporal A-properties, say this light’s being past, present, or future. But that seems problematic. For the change between past, present and future does not happen in the lifetime of the light. During the lifetime of the light, the light is always present—it is only past after its existence and it is only future before its existence! But a change that does not happen during an object’s lifetime is, of course, a Cambridge change, like a horse’s becoming posthumously famous. And Cambridge change must always be relative to something else changing really. But then it is in the latter change that we should be grounding our factual change. And now we are off on a vicious regress, much as McTaggart (perhaps for somewhat different reasons) thought.

This suggests to me that just as the B-theorist denies that objectual change depends on factual change, the A-theorist should deny that factual change arises from objectual change. As more than one philosopher has noted, the A-theorist should respond to McTaggart by taking A-temporality, understood as factual change, as primitive.

Mononoetism

Every so often I come against someone who is defending a Christological view I want to call “mononoetism”: that Christ has only one mind. While the Third Council of Constantinople condemned the errors that Christ has only one will (monothelitism) or only one natural operation (monoenergism), I do not know of any conciliar condemnation of mononoetism. Nonetheless, I think the reasoning behind the condemnations of monothelitism applies to mononoetism.

Mononoetism could in principle come in three sorts: Christ has only one mind and it’s a human mind; Christ has only one mind and it’s a divine mind; Christ has one hybrid human-divine mind. I think the first and second options are non-starters. If Christ has only a human mind, he’s not consubstantial with the Father. If Christ has only a divine mind, he has not taken on the human nature. So we should only consider the hybrid human-divine mind view.

But a hybrid human-divine mind view seems to be the kind of “confusion and mixture” between human and divine natures that the Council of Chalcedon objects to. Indeed, the letter of Pope Agatho, approved by the Council, shows that the opposition to monothelitism is just a working out of the teaching of earlier Councils, and Agatho’s reasoning applies just as much to the mind. Just replace “will” with “mind” here:

While if it is asserted that there is but one will in him (which is absurd), those who make this assertion must needs say that that will is either human or divine, or else composite from both, mixed and confused, or (according to the teaching of all heretics) that Christ has one will and one operation, proceeding from his one composite nature (as they hold). And thus, without any doubt, the difference of nature is destroyed, which the holy synods declared to be preserved in all respects even after the admirable union. Because, though they taught that Christ was one, his person and substance one, yet on account of the union of the natures which was made hypostatically, they likewise decreed that we should clearly acknowledge and teach the difference of those natures which were united in him, after the admirable union. Therefore if the proprieties of the natures in the same our one Lord Jesus Christ were preserved on account of the difference [of the natures], it is congruous that we should with full faith confess also the difference of his natural wills and operations, in order that we may be shown to have followed in all respects their doctrine, and may admit into the Church of Christ no heretical novelty.

Next, let’s think about the Trinity, and ask if there are three minds or one in the Trinity. On the mononoetism under consideration, Christ has to have the hybrid mind without also having a divine mind (or else he would have two minds: a hybrid one and a divine one). Then if all three Persons have one mind, it follows that the Father and Holy Spirit also have a hybrid human-divine mind, which is plainly absurd—it implies a partial Incarnation by the Father and by the Holy Spirit. So the mononoetist has to hold that each Person of the Trinity has a distinct mind. Mononoetism about Christ implies trinoetism about God.

Trinoetism about God seems to violate divine simplicity, but a trinoetist about God is likely to deny that, holding that mind does not go with the single divine substance or ousia but with the three Persons or hypostases. But let’s think this through. The argument from mononoetism about Christ to trinoetism about God is a special case of a general principle that what there is one of in Christ there is three of in God and vice versa. If the general principle holds, then we have to hold that there is one will in God. For if there were three wills in God, we would have one will in Christ, and that’s the condemned heresy of monothelitsm about Christ. Furhermore, the idea of three wills in God requires a story about why it is metaphysically impossible for these wills to disagree (for if they could disagree, then the three persons couldn’t each be omnipotent!). The best story would be a subordinationist one—the Son and Holy Spirit’s wills are obedient to the Father. But this seems contrary to the equality of the Trinity.

So let’s take it that God has but one will. Mononoetism about Christ has, however, led us to the idea that God has three minds. How does one will in three minds work? A will decides between options presented by a mind. But now things start to fall apart again. Even if the contents of the allegedly distinct minds of Father, Son and Holy Spirit are the same, there is still the question of which mind is the one that is informing the one divine will. If only one or two minds are informing the divine will, we lose the equality of Persons in the Trinity—one or two Persons are partly left out of decisions. So probably one has to say that the one divine will, uniquely, is equally and overdeterminately informed by three minds. This doesn’t seem right. For a person’s will looks to the person’s own mind. (Objection: If Alice loves Bob, she looks to Bob’s mind in her decisions. Response: Yes, but only indirectly by mirroring the contents of Bob’s mind in her mind.) And, besides this, it seems that divine simplicity requires that the divine will and the divine mind are the same thing, which completely rules out the idea of one will with three minds.

We can repeat the argument of the previous paragraph with operations or energeiai. Monoenergism about Christ is condemned. Christ has two operations. On general principles, then, we would expect one operation in the Trinity, just as one will. But if there are three minds, it seems there are three operations, since a mind operates (its operation grounds the thinking of the person or persons who with the mind).

Next, let’s think about the alleged hybrid human-divine mind of Christ. In forming this hybrid mind, the divine mind of Christ seems to have changed—it has hybridized. For if it has not changed, then we still have the divine mind in addition to the hybrid one. But divine minds cannot change, since God cannot change! Indeed, the divine mind is presumably timeless. If it is timeless, it eternally exists. Thus it seems that on mononoetism Christ does have two minds after all, and so we do not have mononoetism: he has the hybrid mind and the eternally existing divine mind. This is, however, a kind of difficult argument to run. Can one not make the exact same objection to the Incarnation? How can the divine Person not change in the Incarnation? Well, orthodoxy says that the divine Person remains a divine Person. But on the hybrid human-divine mononoetism, the divine mind does not remain a divine mind, or else Christ would have two minds.

Perhaps, though, the mononoetist can try for a “smaller” version of the Incarnation: just as the divine Person comes to take on humanity, so we have one Person with two personal natures, human and divine, the divine mind comes to take on human mentality, so we have one Mind with two mental natures, human and divine. Perhaps ths would allow one to avoid the rather monstrous sounding “hybridization” that I have been assuming earlier. But here is a problem. By divine simplicity, the only distinctions in God are relational distinctions between the Persons. If God has one mind, that mind is identical to God. As argued earlier, if there is one mind in Christ, there are three in God, one per Person. But by the only-relational-distinctions principle, the mind of each person must be identical to the Person. If then the divine mind of the Logos comes to take on human mentality, so that it is both a human mind and a divine mind, like the Logos taking on humanity so that the Logos is both human and divine, then since the divine mind is identical with the Person, the Logos, it follows that the Person also takes on human mentality. Thus, the Logos is now three things: God, human and a human mind. We can say that the Logos became man, but we can also the Logos became a man’s mind. This requires a kind of inhuman relationship between the man and the man’s human mind: Jesus is Jesus’s human mind (which on this version of mononoetism is also identical with Jesus’s divine mind). Of course, Cartesians who think you are your mind won’t think there is anything strange about that. But they are wrong! And it would be very odd if Cartesianism were true about Jesus but about no one else. That would seem to undercut the idea that Jesus is like us in all human things but sin.

It is thus quite difficult to hold to mononoetism about Christ while rejecting monothelitism and monoenergism. And in any case there is a neat inductive argument: two wills, two operations, so probably two minds.

Octopuses, aliens, squirrels and AI

I’ve been toying with an argument for dualism along these lines:

1. Octopuses are conscious.

2. Technologically advanced aliens are or would be conscious.

3. Squirrels are conscious.

4. Current LLMs are not conscious.

Claims 1–3 require a pretty strong multiple realizability. On materialism, our best such multiple realizability is a functionalism. But it is likely that our current LLMs have more sophisticated general intelligence than squirrels. Thus, a functionalism that makes 1–3 true also violates 4.

Dualism, on the other hand, can allow for all of 1–4 by supposing the hypothesis that all and only intellectually sophisticated living things have souls.

Could a physicalist do the same? I think the difficulty is that life is very fuzzy on physicalism, in a way in which consciousness should not be. On dualism, however, we can suppose that God or the laws of nature have a seemingly arbitrary threshold of what life is.

A Stoic thesis

Combine these two rather Stoic theses:

1. No one can make the fully virtuous person worse off

2. Doing what is morally wrong always makes you worse off

and you get:

3. No one can make the fully virtuous person do what is morally wrong.

It is going to be crucial to this post that (3) includes cases of inculpably doing what is morally wrong. I myself think (1) is false, say for the that Aristotle cites, namely that severe pain makes even the virtous worse off. But nonetheless I want to defend (3).

It may be possible to first destroy a virtuous person’s virtue, and then get them to do what is morally wrong. Hitting someone on the head or brainwashing them can severely damage the psyche in a way that can remove the rational habits that constitute virtue. I do not count this a counterexample to (3), because in this case when the victim performs the wrong action, they have previously lost their virtue.

One might try to rule out the case of head injury and brainwashing by restricting (3) to culpable wrongs, but I don’t want to do that. I want to defend (3) in the case of inculpable wrongs, too.

A consequence of (3) is a fairly strong source incompatibilism about our action. Not only is it that neural manipulation cannot make you perform a free action, but it cannot make you perform an action. This fits well with dualism, but does not require it, because it might be that brain states that constitute acts of will have to have functional characteristics incompatible with outside control.

As a final clarification, I understand “making” as reliable, but not necessarily 100% reliable. Someone with significant free will cannot be 100% reliably made to do wrong, even if they are not virtuous. But at the same time, while a fully virtuous person cannot be reliably tempted away from right action, they might still have significant free will and be able to do wrong, so a temptation might unreliably get them to do wrong. Furthermore, I am thinking of “making” on something like a specific occasion. Thus, perhaps, if you tempt a virtuous person a million times, while restoring their brain to the pre-temptation state between temptations, by the law of large numbers you can expect them to fail at least once.

Let’s think about (3) some more.

Threats aren’t going to reliably get the fully virtuous person do the wrong thing. Sometimes, it is reasonable to bow to a threat. If someone holds a gun to your head and tells you to cover the side of your neighbor’s house with a giant smiley face graffiti, it’s reasonable to go along with it. But morality is reasonable, and where it is reasonable to bow to a threat, doing so is not only not culpable but simply not wrong. Indeed, it would typically be a failure of respect for human life to refuse to paint the graffiti when one’s life is threatened. In cases, however, where it is unreasonable to knuckle under, the fully virtuous person will reliably withstand the threat.

Physical control of another’s body or brain isn’t going to produce morally wrong action, because it doesn’t produce action at all. It is not wrong to kill someone by being pushed off a cliff on top of them, because it’s not an action to fall off a cliff. Similarly, if someone implants a remote control for one’s muscles, even if in the brain, then the resulting muscle spasms are not actions, and hence are not morally wrong actions.

Cases of omissions are interesting. It is easy to make someone fail to do what they promised, say by imprisoning them. If one thinks that such a failure counts as an inculpable wrongdoing, and if (3) is supposed to apply to omissions as well, then we have a counterexample. I do want (3) to apply to omissions. But I think that all that’s morally required by a promise is a reasonable amount of effort—where what counts as reasonable depends on the case. If you promise to come to a party but are in the hospital after a serious accident, it’s not morally required—indeed, it’s morally forbidden—that you rip the IV out of your arm and drag yourself on hands knees to the party. Indeed, (3) is a part of my reason for thinking that promises only require reasonable effort, so this is the first example where I have (3) giving us evidence for a substantive moral thesis. I think something similar is true in the case of commands, legislation and the like. You can’t ask for more than reasonable effort! Asking for more adds insult to injury. The parents whose children starve because the parents were unjustly imprisoned have not done wrong in failing to feed them.

Cases of ignorance are also interesting. If Alice is serving wine to her guests and Bob pours poison in the wine whe she isn’t looking, some might say that Alice has done wrong in poisoning her guests. Certainly, actual-result act utilitarianism implies this. But so much the worse for actual-result act utilitarianism. It is much better to say that Alice has done no wrong, as long as it was reasonable for her to have no suspicion of Bob. Cases of ignorance of through-and-through moral facts, on the other hand, are arguably incompatible with full virtue.

Where I think (3) becomes most interesting is in cases where we have a normative power over what is right or wrong for another to do. Using our normative powers, we can make someone who would otherwise have done wrong not be doing wrong. There is a story of a hasid whose house is being robbed, and when the thief is carrying his property away, the hasid yells: “I renounce my property rights.” In doing so, the hasid releases the thief from the duties of restitution, and makes it be the case that the thief is not sinning by continuing to carry the goods away.

Are there cases where we can use our normative powers to reliably make someone do wrong? Definitely. You can know that someone under your authority will very likely refuse to follow a certain command, and you can nonetheless issue the command. But this is obviously a case of someone who is lacking full virtue.

I think the best bet for using our normative powers to reliably make someone perfectly virtuous do wrong is when our exercise of normative powers creates a duty but does so in a way that the perfectly virtuous person does not know about. For instance, one might command the fully virtuous person in circumstances where they will likely not hear the command. Or one might pass legislation that they won’t know about. There are two ways to defend (3) in these cases. The first is to have a communication condition on commands and legislation—they are only morally binding when person subject to them either is informed about them or ought to be informed about them. The second is to say that all that’s morally required is that one make a reasonable effort to obey commands and laws in general, not that one make a reasonable effort to obey each specific command or law (since if one doesn’t know about a command or law, one doesn’t need to make a reasonable effort to obey it). I somewhat prefer the first option of a communication condition—the vicious lawbreaker does wrong in disobeying a specific law, and not just law in general (though according to James 2:10, they are also doing wrong in disobeying law in general).

In any case, I think (3) puts some significant constraints on the shape of moral obligation and the nature of action, but these constraints seem defensible. Though maybe I am failing to notice some better counterexample.

Existing and existing at a time

If we accept growing block or eternalism as our theory of temporal reality, we have to make a distinction between existing simpliciter (i.e., being in the domain of unrestricted quantifiers) and existing-at-a-time (including tensed existence at the present). To exist at time t is not the same as its being the case at t that one exists simpliciter.

Suppose, for instance, closed-future growing block. Then we can say the following about Bucephalus (circa 355 BC–326 BC):

1. In 330 BC: Bucephalus exists-in-330-BC.

2. In 330 BC: Bucephalus exists simpliciter.

3. In 2025: Bucephalus exists simpliciter.

4. In 2025: It’s not the case that Bucephalus exists-in-2025.

5. In 3000 BC: Bucephalus does not exist simpliciter.

6. In 3000 BC: Bucephalus exists-in-330-BC.

Existence-at-a-time is not really existence—it is just spatiotemporal locatedness. (Of course, we have a grounding problem about how on closed-future growing block facts about the future are grounded, but bracket that.)

Now, on both growing block and eternalism, if something exists-now it exists simpliciter. Could one have a theory on which this inference is denied?

Perhaps Platonism denies it. Only timeless and unchanging things really are. Changing things in time become rather than really are. Similarly, it is said that God said to St Catherine of Siena: “I am he who is and you are she who is not.”

But is there a theory of time on which the inference is denied? I once explored a version of B-theory like that. Now I want to consider a version of A-theory like that.

Consider pastism, on which to exist simpliciter is to exist pastly, and take a version of pastism on which there are moments of time (probably the best version of pastism on offer is one where there are no moments). Suppose t₁ is the first moment of Bucephalus’ life. Then on pastism, at t₁ Bucephalus doesn’t exist, but Bucephalus exists-at-t₁. Is this coherent? It does have this odd consequence. Suppose t₁ is also the last moment of time (so Bucephalus exists at exactly one moment). Then Bucephalus exists-at-t₁, but it is never the case that Bucephalus exists simpliciter. Still, it’s not clear that a logical contradiction has occurred.

Nonetheless, it does seem absurd to suppose that something exists-now but doesn’t exist, even if it’s not strictly contradictory.

Presentism and B-theory

It’s common to say that presentism entails the A-theory. But that’s not so clear. Suppose that time can pass in the absence of change. Now imagine a world of with a beginning or an end of time, objects, but no change, no temporal parts, and no events except ones that last for all time. In that world, we automatically have a kind of presentism: all the objects and events that exist always exist presently. Yet a B-theorist could accept the possibility of such a world, too: the world need not have a distinguished present moment of time. Thus, a B-theorist could say that A-theory is impossible (say, because of McTaggart’s dubious arguments) but presentism is possible—though contingently false.

We obviously don’t live in such a world. Though Parmenides may have thought he did.

Theism, pantheism, panentheism and cosmopsychism

If God didn’t create anything, pantheism (everything is God), panetheism (everything is in God or is God) and cosmopsychism (the whole of reality is conscious) would be true. And it’s possible for God not to create anything.

Some odd theories of temporal reality, with eschatological applications

The three major theories of temporal reality are presentism (reality includes only the present), growing block (reality includes the present and past) and eternalism (reality includes past, present and future).

A recent option that has been considered is thick presentism on which reality includes a short segment of time including the present. This lets one have some of the intuitive advantages of presentism (dinosaurs and Martian settlements don’t exist) while at the same time neatly solving the problem of diachronic causation. Moreover, it raises an interesting explanatory problem: why does our world have the kind of temporal reality it does.

I think that if thick presentism is metaphysically possible, likely so are a number of other views:

1. Very thick presentism

2. Time-variable thickness thick presentism

3. Growing block

4. Space-variable thickness thick presentism

5. Swiss-cheese temporal reality.

On very thick presentism, the band of reality in thick presentism becomes extremely thick, say a million years. For there seems to be no compelling reason why the band of reality posited by thick presentists would have to be thin.

On the time-variable thick presentism, we have a thick presentism where the thickness varies with time. This is likely something that the thick presentist has to countenance. For, plausibly, some moment within the thick present has to be distinguished as “very present” to avoid violating the law of non-contradictions (since objects will have contradictory properties within the thick present). Suppose that that moment happens to be at the middle of the thick present. Then when the very present gets closer and closer to the beginning or end of time, the band of reality must get thinner and thinner. Or suppose the moment happens to be at the end of the thick present (I think that may be the better theory). Then when the very present gets closer to the beginning of time, the band of reality gets thinner and thinner. We also get time-variable thick presentism by applying patchwork principles to recombine worlds with thick presentisms of different thicknesses.

Growing-block with a finite past is just a time-variable thickness thick presentism where the very present is at the end of the thick present and the thickness of the thick present at t is equal to the duration from the beginning of time to t. And if we allow it with a finite past, why not with an infinite one—assuming an infinite past is possible?

Applying patchwork principles to thick presentisms with different thicknesses, we can get a space-variable thick presentism—here, the present may be ten minutes thick, but there it may be ten years thick.

Once we allow that, why not go all the way and allow a swiss-cheese temporal reality, where at any given time various chunks of the four-dimensional manifold are included or left out in a pretty arbitrary fashion (perhaps subject to some restrictions to make causation work)?

Now, here’s a fun theological speculation. Some thinkers are worried about eternalism and growing block on theological grounds: they worry that these theories imply that horrendously evil events like the Holocaust will eternally be a part of reality, and that this is inappropriate. But once we have expanded the range of options as we have, we can have some interesting theological theories.

For instance, perhaps, growing block is true between now and the Second Coming. Then at the Second Coming the band of reality gets very thin, so that after the Second Coming, the band of reality includes only the times from the Second Coming to the then-present. We can think of this as giving a surprising reading of the “Behond, I make all things new” of Revelation 21:5—the past events and object suddenly get wiped out of reality. Or, as a variant, perhaps partial eternalism becomes true after the Second Coming: reality now includes all times from the Second Coming on.

But one may worry that that wipes out too much—for instance, it wipes out the glory of the Cross (I am grateful to a graduate student for this worry). Very well. Then we go for a swiss cheese version where we have selective removal from reality—the Holocaust goes but the Cross stays, say.

All this has a certain resemblance to Hud Hudson’s hypertime story. But it’s different in two ways. First, it doesn’t need hypertime. Second, I am assuming here a variant of a standard presentist picture on which there are tensed truths, and the tensed truths function according to standard temporal logics. Thus, if it is true that p, it will always be true that it was true that p. What changes is what events and substances fall within the domain of restricted quantifiers—quantifiers do not commute with “at t” and other temporal operators.

For instance, on the “I make all things new” theories, right now all three of these are true:

1. There exists an x such that at 327 BC: x is a horse named “Bucephalus”

2. At 327 BC: there exists an x such that x is a horse named “Bucephalus”.

3. At 2000 AD: there exists an x such that at 327 BC: x is a horse named “Bucephalus”.

After the second coming, when the past objects and events are wiped out, we still have (b) and (c) holding, but (a) does not hold.

On a hypertime variant of “I make all things new”, once the past was wiped out, we would have none of (a)–(c).

I do not endorse any of these odd possibilities, because I am a die-hard B-theorist.

Presentism and the intrinsicness of past tensed properties

Many presentists think that objects have past-tensed properties. Thus an object that is now straight but was bent has the property of having been bent. (Some such presentists use these properties to ground facts about the past.)

But assuming for simplicity that being bent is an intrinsic property, we can argue that having been bent is an intrinsic property as well. Here’s why. If being bent doesn’t describe an object in relation to the existence, non-existence or features of any other object (assuming being bent is intrinsic), neither does having been bent. Nor is having been bent “temporally impure”—it does not describe the object in terms of anything happening at other times, since nothing can happen at other times on presentism. It does not describe the object in relation its past or future temporal slices or past or future events involving the object, since on presentism there are no past or future objects, and there are no past or future events.

But if having been bent is an intrinsic property of an object, it seems that, by a plausible patchwork principle or by intuitions about the omnipotence of God, an object could come into existence just for one instant and yet have been bent at that instant. Which is absurd.

More on promulgation of laws

Laws need to be promulgated to be valid. Why? A Thomistic story is that valid laws create genuine reasons to act, and reasons are the sort of thing that’s available to a reasonable person. So, the laws need to be practically available to reasonable governed persons. In particular, if everyone has forgot about a law, and the books it was written in have burned down, the law is gone—promulgation is an ongoing affair. And the “practically” rules out such things as: “If you go to room 19235 in the Library of Congress, and enter a certain seven digit combination in the lock that only Congress knows, the doors will open and you will have books of all the laws in front of you.”

All this does not mean that the laws have to be made known to the reasonable persons. For it is encumbent on reasonable persons to educate themselves on laws that are relevant to them. However, since in a modern state the body of laws is too large for a typical reasonable person to study them all, availability also requires more than, say, that the laws be in public libraries, on the Internet, and to hired lawyers.

For it is not reasonable to expect that every reasonable person before they perform some ordinary action will go and search the laws. Rather, as participants in a society we rightly get a sense of what actions are ordinary, intrinsically moral, and done by people without any consciousness that some law might constrain them. And in the case of such actions, it’s not reasonable to be expect someone to look further. If there is a law prohibiting such an action, then I am inclined to think it is invalid—it is failing the promulgation condition, at least in this context.

An interesting thing about this view is that it gives some of the same results as the idea that unenforced laws are not valid. When a law has not been generally enforced, eventually ordinary people will forget (if they ever knew) that the law was there, and will go about their ordinary actions without any consciousness that they might be constrained by a law here. And then it’s not reasonable to expect people to know about the law, and the promulgation condition fails. However, not all cases of unenforced laws are like that. In some cases, people generally do know that there is a law, but they also know it is unenforced and generally ignored, and in such cases there is no promulgation failure.

Here is a somewhat hypothetical example. Ordinary people buy coffee filter cones without any worry that there might be some law requiring them to report the number of cones they purchased to the state and to keep track of destroyed cones in a log. If there is such a law, certainly no one enforces it. Thus, the ordinary reasonable person has no duty to look up whether there is such a law the first time they buy a coffee filter cone in any given state, and if it turns out that there is such a putative law, it has failed to be promulgated to them, and it’s not valid (i.e., it’s not a law) at least in the case of ordinary consumers. (I said this is somewhat hypothetical. Texas has a law governing “precursor chemical laboratory apparatus”. One of the controlled items on their report form is filter funnels, which is precisely what a coffee filter cone is. One assumes that that’s not what they mean, but I am not a lawyer. Transformers are also listed so maybe phone chargers would need to be reported to the state?)

On the other hand, there are non-ordinary actions where a reasonable participant in society knows that it’s not unlikely there are relevant laws, and it is reasonably expected that one find out what the laws are—hiring a lawyer if necessary. If I were to set up shop selling explosives, for instance, I would know that there are likely to be local, state and federal regulations I need to educate myself on.

I should note that my intuitions are driven by my conviction that valid laws are morally binding. So genuine laws aren’t like mere rules in a game or something like that. One could have a hybrid view on which we distinguish between laws and laws^*, where a law is morally binding on the governed while a law^* is something the state merely has moral permission to enforce in principle. If this distinction were to work, one could have a stronger promulgation condition for laws and a weaker one for laws^*.

The command version of divine command theory

Suppose that morality is grounded in God’s commands. What are God’s commands?

The most obvious idea would be that God’s commands are speech acts of command or legislation like: “Thou shalt not steal.”

But this is implausible. For such speech acts to be binding, they must be promulgated. But where? If we take seriously that these are genuinely speech acts, we have three main options:

1. A text from God

2. One or more human individuals speaking for God

3. A voice in people’s heads, from God or a representative of God.

I don’t think any of these are plausible once we take into account that morality applies to all, but no text has been accessible to all, no human individuals seemingly speaking for God have been audible to all, and lots of people have never heard such a voice in their heads.

So, I think, the divine command theorist needs to understand “command” in some less literal sense. I think the most plausible story would connect with Biblical descriptions of God’s law written in people’s minds or hearts. There will then be a substantive question of what kind of a feature of the mind or heart the commands are, with the two main options being:

4. Emotions (sentimentalist divine command)

5. Intuitions (cognitivist divine command).

(Combinations are also possible.)

But both cases face the following problem: How do we distinguish the attitudes, emotional or cognitive, that constitute divine commands from attitudes of the same sort that do not. Some people have moral attitudes that are screwed up—this might reduce or remove culpability, but nonetheless the screwed up attitudes are not divine commands.

I see three main options for making the distinction:

1. The properly functioning moral attitudes define morality.

2. Morality is defined by the moral attitudes that God has directly instilled either in each individual or in the ancestors of all individuals from whom they are passed on genetically and/or culturally.

3. God’s mental attitudes of approval or disapproval for moral attitudes distinguishes whether the attitudes define morality.

Option (a) pushes divine command theory very close to theistic natural law. Some people will like that (C. Stephen Evans likes to say that natural law is compatible with divine command theory).

Option (b) is interesting and promising.

Option (c) pushes the command version of divine command, which is what I have been exploring, closer to the divine will version. And it has problems with divine simplicity on which God doesn’t have intrinsic contingent features, and the approval/disapproval sounds to me like it would likely need to be an intrinsic contingent feature of God.

Lying and epistemic utility

Epistemic utility is the value of one’s beliefs or credences matching the truth.

Suppose your and my credences differ. Then I am going to think that my credences better match the truth. This is automatic if I am measuring epistemic utilities using a proper scoring rule. But that means that benevolence with respect to epistemic utilities gives me a reason to shift your credences to be closer to mine.

At this point, there are honest and dishonest ways to proceed. The honest way is to share all my relevant evidence with you. Suppose I have done that. And you’ve reciprocated. And we still differ in credences. If we’re rational Bayesian agents, that’s presumably due to a difference in prior probabilities. What can I do, then, if the honest ways are exhausted?

I can lie! Suppose your credence that there was once life on Mars is 0.4 and mine is 0.5. So I tell you that I read that a recent experiment provided a little bit of evidence in favor of there once having been life on Mars, even though I read no such thing. That boosts your credence that there was once life on Mars. (Granted, it also boosts your credence in the falsehood that there was such a recent experiment. But, plausibly, getting right whether there was once life on Mars gets much more weight in a reasonable person’s epistemic utilities than getting right what recent experiments have found.)

We often think of lying as an offense against truth. But in these kinds of cases, the lies are aimed precisely at moving the other towards truth. And they’re still wrong.

Thus, it seems that striving to maximize others’ epistemic utility is the wrong way to think of our shared epistemic life.

Maximizing others’ epistemic utility seems to lead to a really bad picture of our shared epistemic life. Should we, then, think of striving to maximize our own epistemic utility as the right approach to one’s individual epistemic life? Perhaps. For maybe what is apt to go wrong in maximizing others’ epistemic utility is paternalism, and paternalism is rarely a problem in one’s own case.

Divine speech acts

Suppose random quantum processes result in deep marks on a stone that spell out:

• Thou shalt not eat goat. – God

What would need to be true for it to be the case that God said (or wrote) that, thereby forbidding us to eat goat?

I assume that God always cooperates with creaturely causation, so divine causation is involved in the above production. However, such divine cooperation with the production of something that looks like an inscription or sounds like an utterance does not suffice to make it be the case that God said the thing. Imagine that a cult leader makes the above inscription. God is still cooperating with the cult leader’s causality, but we don’t want to attribute the inscription to God’s authorship.

One obvious answer is by analogy to our language. A part of what makes a performance a speech act of a particular sort is a certain kind of intention, e.g., that the performance be taken to be that sort of speech act. So maybe it just depends on God’s intentions. If God merely intends cooperation with quantum processes, there is no inscription, just random marks on stone that happen to look like an inscription. But if God intends the marks to be taken to be an inscription, they are an inscription.

This solution, however, is unhelpful given divine simplicity. The intention is a contingent feature of God, and on divine simplicity the contingency of contingent divine features is always grounded in some contingent arrangement of creatures. There cannot be two worlds that are exactly alike in their created aspects but where God has different intentions in the two worlds. So given divine simplicity, there has to be a characterization of what makes the marks a divine command in terms of what creation is like. (My view of divine intentions is, roughly, that God intends F in doing A iff intending F would be a good reason for God to do A. This presupposes divine omnirationality.)

Here is one possibility.

1. Something that looks or sounds like a speech act is a divine speech act if and only if it was directly produced by God without secondary causes.

But this seems mistaken. Imagine that in the sight of a tribe, God created a stone and a stylus ex nihilo, and then miraculously moved the stylus in such a way as to inscribe the prohibition on eating goat. Then, surely, the members of the tribe upon seeing the stylus moving through the air and gouging clear text in the stone would be right to attribute the message to God. But the inscription was not directly produced by God: it was produced by means of a stylus.

Perhaps:

2. Something that looks or sounds like a speech act is a divine speech act if and only if it was a deterministic result of something done by God without secondary causes.

This still seems a bit too restrictive. Imagine that while God used the stylus to inscribe the stone in our previous story, he nonetheless allowed for ordinary quantum randomness in the interaction between the hard stylus and the softer stone, which randomness ensured that there was a tiny probability that no inscription would result—that, say, stylus atoms would quantum tunnel through the stone atoms.

One might replace “deterministic” with “extremely probable”. But just how probable would it have to be?

Here is a different suggestion that seems to me more promising.

3. Something that looks or sounds like a speech act is a divine speech act to humans if and only if a normal human who knew all the metaphysical and physical facts about the production of this act, as well as the human social context of the production, would reasonably take it to be a divine speech act.

This suggestion allows for the possibility that a normal human would be mistaken about whether something is a divine speech act—but the mistake would then be traced back to a mistake about the relevant metaphysical, physical and social facts.

The applicability of (3) is still difficult. Take the initial example where the apparent divine prohibition on eating goat appears from quantum randomness. Would a reasonable and normal human who knew it to have appeared from quantum randomness with ordinary divine cooperation of the sort found in all creaturely causation think it to be a divine speech act? I don’t know. I don’t know that I am a reasonable and normal human, and I don’t actually know what to think about this.

Causation and the grounding problem for presentism

The past-grounding problem for presentism is of explaining what grounds facts about the past. The tensed-property solution is that presently existing objects have past-tensed properties like “Existing a hundred million years after a dinosaur” which ground the facts about the past.

Here is a problem. The presently existing objects exist at least partly because of how the world was a hundred million years ago. If how the world was a hundred million years ago is grounded in the properties of presently existing things, then we have a circularity in the order of explanation: the present objects’ existence is partly-explained by how the world was, and how the world was is grounding-explained by the objects’ possession of the properties, while the objects’ possession of the properties is partly ontologically explained by the objects’ existence.

Objection 1: This won’t bother one if one thinks one can have explanatory circularity as long as the explanations are of different sorts. But I think explanations of different sorts are still explanations, and circularity is still bad.

Objection 2: It seems that B’s being caused by A is explanatorily prior to B’s existing, so sometimes an instance of property possession is prior to existence. But I think this is mistaken. What’s prior to B is A’s exercise of causality, not B’s being caused by A.

Objection 3: If we solve the past-grounding problem by making use of past-tensed properties of God, then the problem disappears. For God doesn’t exist now because of how the world was a hundred million years ago. God exists now because God is a necessary being. I think this is a good response if one doesn’t believe in divine simplicity, but I am convinced of divine simplicity, which prohibits God from having contingent properties.

Nomically possible branches and open future views

Some open future views rely on the concept of a nomically possible branch—a complete sequence of how things might go given the laws of nature.

The problem with the concept is this. A nomically possible branch seems to be something like an exhaustive collection of propositions about all times, specifying precisely what happens at all times, with the collection as a whole compatible with the laws of nature. But now consider a world where indeterminism never gives out on any branch: no matter how things go, at every time there will still be more branching. (Our world may well be like that.) Then on an open future view, the propositions making up a branch cannot be all true together—for at no time t can the exhaustive propositions about t’s future be true, as that would violate open futurism given that branching never gives out.

For a while I thought that a decent solution to this is to say that a branch only needs to satisfy the weaker condition that for every time t, all the propositions in the branch about times up to t can be true together with the laws of nature.

But my recent example of random transtemporal causation is problematic for this solution. Suppose that today an indeterministic event E causes a green flash of light to happen on a random future day, and that the laws guarantee that no green flashes happen for any other reason. Then a branch that contains E but no green flashes of light satisfies the weaker possibility condition: for at every time t, all the propositions in the branch about times up to t can be true together with the laws of nature, since E does not causally guarantee that a green flash will happen at or before t, but only that a green flash will happen at some time or other.

Probably the best move for the open futurist is to deny causation across temporal gaps or any other mechanism that nomically guarantees that some event will happen without guaranteeing a time by which it will happen.

Requests and obligations

By requesting something from someone, we create a reason for them to fulfill the request. On an individualistic view of human beings, this is a rather awesome power—somehow I reach into your space of reasons and create a new one.

It is tempting to downplay the force of reasons created by a request. After all, it seems that a mere request can always be legitimately turned down.

But that’s not right. There are times when a request creates an obligation. For it may be that apart form the request one’s reasons for an action were nearly conclusive, and with the request they become conclusive.

And besides that, a successfully transmitted request always creates a moral obligation to consider the request. Sometimes, the request may be quickly rejectable on the basis of a background policy. But a quick rejection still requires a consideration.

Questions, of course, are a type of request: they are a request for an answer. Thus, they too always create a moral obligation.

Wolterstorff on worship and intention

In Acting Liturgically, Wolterstorff offers a necessary and sufficient condition for when someone “is performing acts of worship or just saying the words and making the gestures”:

if a participant performs some prescribed verbal or gestural action with the intention of not thereby performing whatever be the act of worship prescribed to be performed thereby, then he has not performed that act of worship; otherwise he has

In other words:

1. One worships with the action as the community does if and only if one does not intend to dissent from the community’s understanding of the action.

But both directions of the biconditional are false.

Case 1: Alice visits a foreign country where she does not know the language and enters an ornate religious building. She believes the building to be a pagan temple and, seeing people kneeling, she thinks them to be thereby worshiping some pagan deity. She feels an urge to pray to God, and she kneels with the dual intention of thereby worshiping God and of not doing what the local community is doing. Her worship is heartfelt and sincere. But unbeknownst to her, the building is a church and the people are worshiping God by kneeling.

Alice is worshiping God by kneeling. An intention to worship God by kneeling while acting in a heartfelt and sincere way is sufficient for the kneeling to constitute worship of God. But by Wolterstorff principle, because she also intends—perhaps in Wolterstorff’s own words (she might be a reader of his)—to “not thereby perform[…] whatever be the act of worship prescribed to be performed” by the kneeling, she is not performing “that act of worship”. But that act of worship—the one the community has prescribed the kneeling to constitute—is worship of God. So if Wolterstorff’s no-intended-dissent condition is necessary for worship, Alice doesn’t worship God. But she does. So the no-intended-dissent condition is not necessary.

Objection: Alice is not worshiping communally but individually. The community is worshiping communally. So, Alice does not perform what the community understands the action to be, namely communal worship.

Response: Add to the story that this particular church has a special meaning for “kneeling”: it’s not just worship, but individual worship.

Case 2: Bob visits a foreign country where he does not know the language and enters an ornate religious building. He believes the building to be a Christian church and, seeing people kneeling, he thinks them to be worshiping God. He intends to worship God, kneels and prays in a heartfelt and sincere way. The thought that there might be some pagans in this country does not even occur to him, since the country is known for being very Christian. He kneels with the intention of worshiping God. But unbeknownst to him, the building is a pagan temple and the people are worshiping a pagan deity by kneeling.

Since it doesn’t occur to Bob that the community’s kneeling might be worship of a pagan deity, he does not form any intention to dissent from the community’s understanding. Granted, his own explicit intention to worship God disagrees with the community’s understanding of what they are doing. But to have an intention that in fact disagrees with the community’s understanding of what they are doing is not the same as intending to do otherwise than the community understands. Compare: If an expert uses complicated verbage to deny the existence of life on Mars, and I misunderstand him to be saying there is life on Mars, and I say “Indeed, there is life on Mars”, I am not intending to say otherwise than the expert did—even though what I am intending to say is, as a matter of fact, otherwise than what the expert said.

It is tempting to say that explicit intentions about the meaning of the action trump implicit ones, and so both Alice and Bob are worshiping God, and neither is worshiping a pagan deity. But that’s not quite right. A religious person may intend for the community’s understanding of an action to trump at least certain aspects of their own understanding. For instance, when a Christian prays the Nicene Creed, they may have their own understanding of “consubstantial with the Father”, but they would do well to defer to the Church for what it really means. Thus, their explicit intention to worship the Son as X (where X is their understanding of consubstantiality with the Father) is overridden by their faithful intention to worship the Son under whatever description the Church means by these words.

So, probably, what we want to say is that the individual worshiper can have a complex of set of intentions with priorities between them. For instance, the faithful Christian who prays the Nicene Creed may have intentions where their understanding of “consubstantial” is subordinated to the community’s understanding, but only within some limits. If it were to turn out that what the community means by “consubstantial with the Father” is that the Father and the Son are finite deities with beards of equal bushiness, then the faithful Christian’s intention to worship an immaterial and infinite God trumps their intention to go with the community’s understanding. I suspect there is no good way to encapsulate the complex ways that the prioritization between intentions can go in a simple definition like Wolterstorff’s.

Could there be a grain of truth in Wolterstorff’s condition? I think one could say that one defaults to worshiping as the community does in the absence of overriding intentions. I am not sure I would agree with that, but it might be true.

I am grateful to Tyler Sharp and Juliana Kazemi for pointing me to Wolterstorff’s very interesting ideas on this, and for conversations on this. In a recent conference presentation, they gave an example that has a lot of similarity with Case 2.