Divine attributes

In previous posts I’ve noted piecemeal that standard definitions of omniscience and omnipotence are incomplete. God’s omnipotence isn’t just that God knows everything—it has to be that he knows it certainly and consciously. We might even say: with maximal certainty and vividness. God’s omnipotence isn’t just that God can do everything—he does it all effortlessly.

It has now occurred to me that both devotionally and philosophically it is fruitful to think about divine attributes by asking what is left out by the rather thin and colorless analytic accounts of them.

Take a flat account of God’s moral perfection as saying that God always does the morally right thing. Well, first, we have to add: and for the right reasons (indeed all the right reasons). Second, we should add that God does this with the perfect attitude—with the appropriate alacrity, without inappropriate regrets, etc.

Or consider the account of God’s being a creator on which God creates everything other than himself. We probably should minimally add that he does this with perfect freedom.

At the moment, this is all I have in the way of clear examples. But I think it’s a worthwhile avenue for exploration and devotion.

Beyond metaphysical immutability

For years I was convinced that the extrinsic constitution model of divine knowledge, which theists who accept divine simplicity must accept, solves the problem of divine immutability in an A-theoretic world where truth changes. The idea was that God’s knowledge of contingent facts is constituted by God’s unchanging essential features (which given simplicity are God himself) together with the changing contingent realities that God knows, that God’s gaze extends to. (This idea is not original to me. Aquinas already had it and probably many contemporary people have independently found it.)

But I now think that this was too quick. For let’s take the idea seriously. The point of the idea is that an unchanging God can have changing knowledge. But now notice that God’s knowledge is conscious. The language of “God’s gaze” that I used above (and which Boethius also uses in his famous discussion of divine knowledge of free actions) itself suggests this—God sees the changing reality. At one time God sees Adam sinless. At another time God sees Adam sinful. This is a difference in conscious state. Granted, this difference in conscious state is entirely metaphysically constituted by the changing reality. But it still means that God’s conscious state changes. It changes in virtue of its extrinsic constituent, but it is still true that God at t₁ is conscious of one thing and God at t₂ is conscious of something else instead. And I submit that that is incompatible with divine immutability.

I think there are two responses the classical theist who believes in changing truths can give. The first is to deny that God is conscious of the changes. I think this is unacceptable. The more vivid and the more vision-like knowledge is, the more perfect it is. The idea that God has merely unconscious knowledge of contingents does not do justice to the perfection of omniscience.

The second response is to bite the bullet and say that God’s conscious state changes but this is compatible with immutability as long as this does not involve an intrinsic change in God. I think this is untenable. That God’s conscious state does not change is, I think, a central part of the content of immutability, regardless of whether this conscious state is intrinsically or extrinsically constituted. For a non-physical being, change of conscious mental state is a paradigmatically central kind of change—regardless of the metaphysics of how that change of conscious state comes about. When God says in Malachi 3:6 that he does not change, it seems very implausible to think that the listener is supposed to say: “Sure, but sometimes God has one conscious state and sometimes another, and because this change is grounded extrinsically, that’s OK.” Malachi isn’t doing heavy-duty scholastic/analytic metaphysics. Similarly, when the early Church Fathers say that God is unchanging I doubt they would tolerate the idea that God’s conscious state changes. The extrinsic constitution story is an explanation of what makes God’s conscious state change, and I expect the Church Fathers wouldn’t have cared what the explanation would be—they would just deny the change.

Jumping from the Church Fathers to the modern period, Calvin says that God “cannot be touched with repentance, and his heart cannot undergo changes. To imagine such a thing would be impiety.” But if God’s conscious states are extrinsically constituted and can change, there would be nothing to prevent the idea of God’s “heart” undergoing changes: when people behave well, God feels pleased; when people behave badly and deserve vengeance, God feels vengeful. The differences in God’s feeling would be, one could imagine, constituted by the differences in human behavior and divine response to it. But it would be implausible to think that Calvin would say “Well, as long as the change is extrinsically constituted, it’s OK.” We then wouldn’t need Calvin’s famous story—itself going back to the Church Fathers—of the accommodation of divine speech to our needs. When Calvin insists that God’s heart cannot undergo changes, he isn’t just concerned about divine metaphysics. He is rightly concerned about a picture of a God with a changing mental life. And here at least, Calvin is with the mainstream of the Christian tradition.

If I am right in the above, there is a disanalogy between how God’s mental state behaves across possible worlds and across times. We have to say that in different possible worlds God has different (extrinsically constituted according to divine simplicity) conscious states. But we cannot say that God has different conscious states at different times.

Some thinkers, especially open theists, want the doctrine of divine immutability not to be about metaphysics but about the constancy of God’s character, purposes and promises. I think they are wrong: the doctrine of immutability really does include what we might call metaphysical immutability, that God has no intrinsic change. But metaphysical immutability is not enough. A mental and especially conscious immutability is also central to how we understand divine immutability.

And this is not compatible with the A-theory of time, given omniscience. Which is too bad. While I myself am a B-theorist, the reasoning in yesterday’s post was giving me the hope that we could detach the A- and B-theoretic debate from theism, so that the theist wouldn’t need to take a stand on it. But, alas, I think a stand needs to be taken.

Could a being in time be eternal in Boethius' sense?

Famously, Boethius says that an eternal being, unlike a merely temporally everlasting being, embraces all of its infinite life at once, “possess[ing] the whole fulness of unending life at once”. What’s that mean?

Our life is strung out across time. Sitting right now I as I am I do not embrace the past and future portions of my life where I am lying down or standing up. If I fully and vividly knew my past and my future, I would be a little closer to being eternal, but it would still not be true that I possess the fullness of that life at once. For it would still be true that I now only possess the property of being seated and not the property of lying down or of standing up. So I think epistemic things are not enough for eternity. And this seems intuitively right—eternity is not an epistemic matter. (Could you have an eternal being that isn’t minded? I don’t see why not.) A necessary condition for being eternal is being unchanging.

But being unchanging is not sufficient. Suppose I were everlastingly frozen sitting in front of my laptop. It would still be true that in addition to the present part of my life there is the future part and the past part, and further subdivisions of these, even if they happen to be boringly all alike. The life of an eternal being does not have temporal divisions, even boring ones. It is all at once.

Here is a weird thought experiment. Imagine you are an everlasting point-sized being with a rich and changing mental life. Suppose all your life is spent at the one spatial location (x₀,y₀,z₀). But now imagine that you get infinitely multilocated across all time, in such a way that your numerically same life occurs at every x-coordinate. Thus, you live your everlasting and rich mental life (x,y₀,z₀) for every possible value of x, and it’s the very same life. Your life isn’t spatially divided. The life at x-coordinate  − 7.0 is not merely qualitatively but numerically the same life as the one at x-coordinate  + 99.4.

Now, one more step. Your life is within a four-dimensional spacetime. Assume that spacetime is Galilean or Minkowskian. Now imagine rotating your life in the four-dimensional spacetime in such a way that what was previously along the x-axis is along the t-axis and vice versa. So now your rich and temporally varied mental life becomes temporally unchanging, but all the variation is now strung out spatially along the x-axis. Furthermore, whereas previously due to multilocation you had your life wholly at every x-coordinate, now you have your life wholly—and the numerically same life—at every t-coordinate. Thus, you have an infinite life all at once at every time for everlasting time. Your life isn’t temporally divided: tomorrow’s life is not simply just like today’s, but it is the numerically same as today’s, because your life is fully multilocated at all the different times.

Here is an interesting thing to note about this. This “sideways life”, varying along the x-axis, satisfies the Boethian definition of eternity even though the life is found in time—indeed at every time. If this is right, then having an eternal life in the Boethian sense is compatible with being in time!

Of course, God is not like you are in my weird story. In my story, your life includes different instances of consciousness strung out along the x-axis, though not along the t-axis. Still this kind of inner division is contrary to the undividedness of the divine mind. An eternal God would not have such divisions either. Nor would he be spatial. Perhaps an argument can be made that if God possesses Boethian eternity, then he has to be timeless. But I think that’s not going to be an easy argument to make.

If this is right, then I have overcome an obstacle to combining classical theism with the A-theory of time. I am convinced that an omniscient being has to be in time if the A-theory is true. But if a being can be in time and yet eternal in the Boethian sense, then a classical theist may be able to accept the A-theory of time. After all, Boethius is paradigmatically a classical theist.

That said, my own view is that the above argument just shows that Boethius has not given us a fully satisfactory characterization of eternity. And I have other reasons to reject the A-theory besides theistic ones.

Towards quantifying the good of success

Yesterday, I argued that the good of success contributes to one’s well-being at the time of one’s striving for success rather than at the time of the success itself.

It seems, then, that the longer you are striving, the longer the amount of time that you are having the good of success. Is that right?

We do think that way. You work on a book for five years. Success is sweeter than if you work on a book for one year.

But only other things being equal. It’s not really the length of time by itself. It’s something like your total personal investment in the project, to which time is only one contribution. Gently churning butter for an hour while multitasking other things (using a pedal-powered churn, for instance) does not get you more good of success than churning butter with maximum effort for fifteen minutes, if the outputs are the same.

We might imagine—I am not sure this is right—that the good of success is variably spread out over the time of striving in proportion to the degree of striving at any given time.

What else goes into the value of success besides total personal investment? Another ingredient is the actual value of the product. If you’ve decided to count the hairs on your toes, success is worth very little. Furthermore, the actual value of the product needs to be reduced in proportion to the degree to which you contributed.

Thus, if Alice and Bob both churned butter and produced n pounds, the value of the output is something like bn, where b is the value of butter per pound. If the investments put in by Alice and Bob are I_A and I_B, then Alice’s share of the value is bnI_A/(I_A+I_B). But since the value of success is proportional also to the absolute investment, I think that the considerations given thus far yield a formula for the value of success for Alice proportional to:

• bnI_A²/(I_A+I_B).

Next note that one way to think about the degree to which you contributed is to think as above—what fraction of the total investment is yours. However, even if you are the only person working on the project, the degree of your contribution may be low. Let’s say that you have moved into a house with a mint bush. Mint bushes are aggressive. They grow well with little care (or so we’ve found). But you do water it. The mint bush added half a pound to its weight at the end of the season. You don’t, however, get credit for all of that pound, since even if you hadn’t watered it, it would likely have grown, just not as much. So you only get credit for the portion of the output that is “yours”. Moreover, sometimes things work probabilistically. If the success is mostly a matter of chance given your investment, I think you only get good-of-success credit in proportion to the chance of success—but I am not completely sure of this.

But here is something that makes me a little uncertain of the above reasoning. Suppose that you have some process where the output is linearly dependent on the investment of effort. You invest I, and you get something of value cI for some proportionality constant c. By the above account, to get the value of success, you should multiply this by I again, since the value of success is proportional to both the value of the output and the effort put in. Thus, you get cI². But is it really the case that when you double the effort you quadruple the value of the success? Maybe. That would be interesting! Or are we double-counting I?

Another question. When we talk about the value of the output, is that the objective value, or the value you put on it, or some combination of the two? Counting the hairs on your toes has little objective value, but what if you think it has significant value? Doesn’t success then have significant value? I suspect not.

But what about activities where the value comes only from your pursuit, such as when you try to win at solitaire or run a mile as fast as you can? In those cases it’s harder to separate the value of the output from the value you put on it. My guess is that in those cases there is still an objective value of the output, but this objective value is imposed by your exercise of normative power—by pursuing certain kinds of goals we can make the goal have value.

Let’s come back to counting hairs on toes. If you’re doing it solely for the sake of the value of knowledge, this has (in typical circumstances) little objective value. But if your hobby is counting difficult to count things, then maybe there is additional value, beyond that of trivial knowledge, in the result.

I suspect there are further complications. Human normativity is messy.

And don’t ask me how this applies to God. On the one hand, it takes no effort for God to produce any effect. On the other hand, by divine simplicity God is perfectly invested in everything he does. But since my metaethics is kind-relative, I am happy with the idea that this will go very differently for God than for us.

From three or four problems of omniscience down to one

The three most influential problems of omniscience are:

1. Boethius’ problem of foreknowledge: What is known is necessarily so, and thus if God knows what you will do, you will necessarily do it.

2. Pike’s problem of foreknowledge: If you can act otherwise, you can thereby make it be that either God didn’t exist or that God wasn’t omniscient or that God had believed otherwise than God actually did, and you just can’t do that.

3. The simplicity and knowledge of contingents problem: If the world had been different, God’s beliefs would have been different, which implies that God’s beliefs are accidents of God, contrary to divine simplicity.

Of these, (1) is fully solved by Boethius/Aquinas by distinguishing between necessity of consequence and necessity of consequent. The problem in (1) is just a simple matter of a fallacy of modal scope ambiguity. It’s a non-problem.

I now want to argue that the most widely accepted solution to (3) also solves (2).

This solution, likely already known to Aquinas, is that God’s belief in contingent facts is partly extrinsically constituted by creatures, and all the contingency is on the created side. For instance, God’s belief that there are zebras is grounded in essential facts about God that do not vary between possible worlds and the actual existence of zebras, which only obtains in some possible worlds.

Suppose we apply this solution to (3). Then God’s belief that you will ϕ at t is partly grounded in your ϕing at t and partly in essential facts about God. At this point it is obvious that:

4. If you were not to ϕ at t, God wouldn’t have believed you would ϕ at t.

For the contingent part of the grounds of God’s believing that you would ϕ at t is your actually ϕing at t, so when you take that away, God’s belief goes away. And if instead you ψ at t, your action thereby constitutes the contingent part of the grounds of God’s believing that you would ψ at t, and so:

5. If you were to ψ at t, God would have believe you would ψ at t.

If God’s past belief is partly constituted by our actions, it is no surprise that there is counterfactual dependence between our actions and God’s past belief. In other words, the classical theist who accepts divine simplicity has a way out of Pike’s argument that is motivated completely independently of considerations of time and freedom, namely by embracing counterfactuals like (4) and (5) that Pike considers absurd.

Of course the extrinsic constitution of divine beliefs is somewhat hard to swallow, notwithstanding excellent work by people like W. Matthews Grant to make it more plausible (I myself have swallowed it). But once we do that, problem (2) is gone, and problem (1) was never there as it was based on a fallacy.

There is a fourth problem, a more recondite one, which is about the incompatibility between God’s knowledge of what time is objectively present (assuming the A-theory of time) and divine immutability. Probably the most extensive pressing of this problem is in Richard Gale’s On the Nature and Existence of God. But Aquinas (according to the very plausible interpretation by Miriam Pritschet in an excellent paper I heard yesterday at the ACPA) responds to the fourth problem precisely by using the extrinsic constitution of God’s knowledge of continent facts (indeed this is why I said that the solution to the simplicity problem was likely known to Aquinas). So even that fourth problem reduces to the third—or just doesn’t get off the ground if the B-theory of time is true.

Aquinas on God's knowledge of propositions

Does God know that the sky is blue?

That seems like a silly question. It’s not like we’re asking whether God knows future contingents, or counterfactuals of freedom. That the sky is blue is something that it is utterly unproblematic for God to know.

Except that it is tempting to say that God has no propositional knowledge, and knowing that the sky is blue is knowing a proposition.

It seems that Aquinas answers the question in Summa Theologiae I.14.14: “God knows all the propositions that can be formulated” (that’s in Freddoso’s translation; the older Dominican translation talks of “enunciable things”, but I think that doesn’t affect what I am going to say). It seems that God does have propositional knowledge, albeit not in the divided or successive way that we do.

But what he is up to in I.14.14 is not what it initially sounds like to the analytic philosopher’s ear.

For consider Thomas’s argument in I.14.14 that God knows all formulable propositions:

Since (a) to formulate propositions lies within the power of our intellect, and since (b), as was explained above (a. 9), God knows whatever lies within either His own power or the power of a creature, it must be the case that God knows all the propositions that can be formulated.

But now notice an ambiguity in “God knows the proposition that the sky is blue.” In one sense, which I will call “alethic”, this just means God knows that the sky is blue. In another sense, the “objectual”, it means that God knows a certain abstract object, the proposition that the sky is blue. In the objectual sense, God also knows the proposition that the sky is green—God fully knows that proposition, just as he knows other objects, like the person Socrates. But God does not, of course, have the alethic knowledge here—God does not know that the sky is green, because the sky is not green.

If it was the alethic sense that Thomas was after, his argument would be invalid. For in article 9, the discussion clearly concerns objectual knowledge. Exactly the same argument establishes that God knows the proposition that the sky is green as that he knows the proposition that the sky is blue. Furthermore, the Biblical quote Thomas gives in support of his view is “The Lord knows the thoughts of men” (Psalm 93:11). But the Lord doesn’t know all of them to be true, doesn’t know all of them alethically, because not all of the thoughts of humans are true.

Furthermore, if it was alethic knowledge that Aquinas was after, it would be inaccurate to say God knows all propositions. For only “half” of the propositions can be known alethically—the true ones!

All that said, I think we can still bootstrap from the objectual to the alethic knowledge. God’s knowledge of objects is perfect (Aquinas relies on this perfection multiple times in Question 14) and hence complete. If God knows something, God also knows all of its properties, intrinsic and relational. Thus, if God knows a proposition objectually, and that proposition has a truth value, God knows that truth value. In particular, if that proposition is true, God knows that it is true. And that seems to suffice for counting as knowing the proposition alethically.

So, it looks like Aquinas is committed to God objectually knowing both the propositions that the sky is green and that the sky is blue, and also knowing that the former is false and the latter is true—which seems to be enough for God to count as knowing that the sky is blue. (Though I could see this last point getting questioned.)

Freedom: a problem for presentism and growing block

A number of people have told me that they have the intuition that a four-dimensional picture of reality like that in the B-theory undercuts free will.

I want to suggest that there is one way in which it is a presentist picture of temporal reality that undercuts free will. (A similar argument applies to growing block, but curiously enough not to shrinking block.)

Assume that open future views are false: there are always determinate facts about contingent future events. (If your reason for thinking that four-dimensional theories undercut free will is because you are an open futurist, then you won’t be impressed by what I say.) Suppose it is a fact that tomorrow morning I will have oatmeal for breakfast. On presentism, this fact can only be grounded in what is present, since on presentism, what is present is all there is. Maybe it’s grounded in the present existence of a future-tensed fact or maybe it’s grounded in my having a future-tensed property of being such that I will eat oatmeal in nine hours. But in any case, things right now are already such as to ground and guarantee that I will have oatmeal for breakfast. Moreover, this was already true five minutes ago—five minutes ago, things were also already such as to ground and guarantee that I will have oatmeal for breakfast tomorrow. This sure feels like it should undercut free will! It seems pretty intuitive that freedom isn’t compatible with there existing grounds that guarantee the action prior to the choice.

On the other hand, on a four-dimensional view while it is a fact that I will eat oatmeal for breakfast tomorrow, the grounds of this fact are not located in the present—and were never located in the past. Rather, the grounds of this fact are where they should be—at tomorrow morning. How things are on the present slice of reality, or on past slices, does not determine (assuming indeterminism) what I will have for breakfast tomorrow. That’s left for tomorrow.

The neatest way out for the presentist is to deny with Merricks that contingent truths about the future and past have any grounds. But that’s also costly.

After writing the above, I came across this related paper by Hunt. No time to revise right now to see what similarities or differences there are.

The good of success is not at the time of success

It’s good for one to succeed, at least if the thing one succeeds in is good. And the good of succeeding at a good task is something over and beyond the good of the task’s good end, since the good end might be good for someone other than the agent, while the good of success is good for the agent.

Here’s a question I’ve wondered about, and now I think I’ve come to a fairly settled view. When does success contribute to one’s well-being? The obvious answer is: when the success happens! But the obvious answer is wrong for multiple reasons, and so we should embrace what seems the main alternative, namely that success is good for us when we are striving for the end.

Before getting to the positive arguments for why the good of success doesn’t apply to us at the time of success, let me say something about one consideration in favor of that view. Obviously, we often celebrate when success happens. However, notice that we also often celebrate when success becomes inevitable. Let’s now move to the positive arguments.

First, success at good tasks would still be good for one even if there were no afterlife. But some important projects have posthumous success—and such success is clearly a part of one’s well-being. And it seems implausible to respond that posthumous success only contributes to our well-being because as a matter of fact we do have an afterlife. Note, too, that in order to locate the good of success at the time of success, we would not just need an afterlife, but an afterlife that begins right at death. For instance, views on which we cease to exist at death and then come back into existence later at the resurrection of the dead (as corruptionist Christians hold) won’t solve the problem, because the success may happen during the gap time. I believe in an afterlife that begins right at death, but it doesn’t seem like I should have to in order to account for the good of success. Furthermore, note that to use the afterlife to save posthumous success, we need a correlation between the timeline the dead are in and the timeline the living are in, and even for those of us who believe in an afterlife right at death, this is unclear.

Second, suppose your project is ensure that some disease does not return before the year 2200. When is your success? Only in 2200. But suppose your project is even more grandiose: the future is infinite and you strive to ensure that the disease never returns. When is your success? Well, “after all of time”. But there is no time after all of time. So although it may be true that you are successful, that success does not happen at any given time. At any given time, there is infinite project-time to go. So if you get the good of success at the time of success, you never get the good of success here. Even an afterlife won’t help here.

Third, consider Special Relativity. You work in mission control on earth to make sure that astronauts on Mars accomplish some task. You are part of the team, but the last part of the team’s work is theirs. But since light can take up to 22 minutes (depending on orbital positions) to travel between Earth and Mars, the question of at what exact you-time the astronauts accomplished their task depends on the reference frame, with a range of variation in the possible answers of up to 22 minutes. But whether you are happy at some moment should not depend on the reference frame. (You might say that it depends on what your reference frame is. But there is no unambiguous such thing as “your” reference frame in general, say if you are shaking your head so your brain is moving in one direction and the rest of your body in another.)

Here is an interesting corollary of the view: the future is not open (by open, I mean the thesis that there are no facts about how future contingents will go). For if the future is open, often it is only at the time of success that there will be a fact about success, so there won’t be a fact of your having been better off for the success when you were striving earlier for the success. That said, the open-futurist cannot accept the third argument, and is likely to be somewhat dubious of the second.

More on A-theory and divine timelessness

Argument One:

1. If from x’s point of view there is an objective fact about what time it presently is, then x is in time.

2. If x knows an objective fact about something, then from x’s point of view there is an objective fact about it.

3. If the A-theory of time is true, then there is an objective fact about what time it presently is.

4. God knows all objective facts.

5. So, if the A-theory of time is true, then God knows an objective fact about what time it presently is. (3 and 4)

6. So, if the A-theory of time is true, from God’s point of view there is an objective fact about time it presently is. (2 and 5)

7. So, if the A-theory of time is true, God is in time. (1 and 6)

Note that no claim is made that if the A-theory of time is true, God changes.

Argument Two:

1. God is actual.

2. Everything actual is in the actual world.

3. If the A-theory of time is true, the actual world is a temporally-centered world (one where there is a fact as to what time is present).

4. Anything that is in a temporally-centered world is in time.

5. So, if the A-theory of time is true, God is in time.

Many will dispute 3, but if we think of worlds as ways for everything to be, then I think it is hard to dispute 3.

I wonder if a classical theist who is an A-theorist might be able to respond that, yes, God is in time but God is not a temporal being. Compare that by doctrine of omnipresence, God is in space, but God is not a spatial being. Still, I think there is a difference. For as the above arguments show, the claim that God is in time is more limiting than the claim that God is spatially omnipresent—it is a claim that God is at the one objectively present point of time (he was and will be at others, of course).

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.