Substantivalism and locality

I find myself going back and forth between substantivalism and relationalism about spacetime. On a substantivalist theory, the points of spacetime are real.

But here is a problem. It seems essential to the concept of a point that geometric relations between points are essential to them. If two points are a certain distance apart, say, then they couldn’t be a different distance apart. But on General Relativity, where geometric properties are determined by the distribution of mass-energy in the universe, if geometric relations between points are essential to them, locality is violated. For imagine two events that are distantly spacelike separated. Then the geometric relation between the points at which the events are found depends on the distribution of mass-energy between the events. If the geometric properties are essential to the points, then influencing the mass-energy between the events will affect which points these events happen at. And that will be a non-local influence.

Perhaps we can say that only local geometric relations are essential to points. Perhaps the way to say this is that if a point x exists in worlds w₁ and w₂, then there is a set N of points such that every member of N exists in both worlds, and N is a neighborhood of x in both worlds, and the geometry on N is the same in both worlds.

An Aristotelian argument for presentism

Here is a valid argument:

1. Matter survives substantial change.

2. It is not possible that there exist two substances of the same species with the very same matter.

3. If matter survives substantial change, it is possible to have two substances of the same species existing at different times with the very same matter.

4. So, it is possible to have two substances of the same species existing at different times with the very same matter. (1,3)

5. If presentism is not true, and it is possible to have two substances at different times existing with the very same matter, it is possible to have two substances of the same species existing with the very same matter.

6. So, if presentism is not true, it is possible to have two substances of the same species existing with the very same matter.

7. So, presentism is true. (2, 5)

Let’s think about the premises. I think Aristotle is committed to (1)—it’s essential to his solution to the alleged problem of change. Claim (2) is a famous Aristotelian commitment. Claim (3) is very, very plausible—surely matter moves around in the world, and it is possible to set things up so that I have the same atoms that Henry VIII had at some point in his life. Claim (5) follows when we note that the only two plausible alternatives to presentism are eternalism and growing block, and on both views if two substances of the same species exist at different times with the very same matter, then at the later time it is true that they both exist simpliciter.

However, given that there is excellent Aristotelian reason to deny presentism, the above argument gives some reason for Aristotelians to deny (1) or (2). Or to be more radical, and just deny that there is any such thing as the “matter” of traditional Aristotelianism.

Matter and distinctness of substance

According to Aristotelianism, the distinctness of two items of the same species is grounded in the distinctness of their matter. This had better be initial matter, since an item might change all of its matter as it grows.

But now imagine a seed A which grows into a tree. That tree in time produces a new seed B. The following seems possible: the chunk of matter making up A moves around in the tree, and all of it ends up forming B. Thus, A and B are made of the same matter, yet they are distinct. (If one wants them to be at the same time, one can then add a bout of time-travel.)

Probably the best response, short of giving up the distinctness-matter link (which I am happy to give up myself), is to insist that a chunk of matter cannot survive substantial change. Thus, a new seed being a new substance must have new matter. But I worry that we now have circularity. Seed B has different matter from seed A, because seed B is a new substance, which does not allow the matter to survive. But what makes it a new substance is supposed to be the difference in matter.

Are we finite?

Here’s a valid argument with plausible premises:

1. A finite being has finite value.

2. Any being with finite value may be permissibly sacrificed for a sufficiently large finite benefit.

3. It is wrong to sacrifice a human for any finite benefit.

4. So, a human has infinite value. (2 and 3)

5. So, a human is an infinite being. (1 and 4)

That conclusion itself is interesting. But also:

6. Any purely material being made of a finite amount of matter is a finite being.

7. If human beings are purely material, they are made of a finite amount of matter.

8. So, human beings are not purely material. (5, 6 and 7)

I am not sure, all that said, whether I buy (2). I think a deontology might provide a way of denying it.

And, of course, work needs to be done to reconcile (5) with the tradition that holds that all creatures are finite, and only God is infinite. Off-hand, I think one would need to distinguish between senses of being “infinite”. Famously, Augustine said that the numbers are finite because they are contained in the mind of God. There is, thus, an absolute sense of the infinite, where only God is infinite, and anything full contained in the divine mind is absolutely finite. But surely there is also a sense in which there are infinitely many numbers! So there must another sense of the infinite, and that might be a sense in which humans might be infinite.

Nor do I really know what it means to say that a human is infinite.

Lots of room for further research if one doesn’t just reject the whole line of thought.

A sharp world

Here are one way of believing in a totally sharp world:

1. Epistemicism: All meaningful sentences have a definite truth value, but sometimes it’s not accessible to us.

This has the implausible consequence that there is a fact of the matter whether, say, four rocks can make a heap, or about exactly how much money one needs to have to be filthy rich.

A way of escaping such consequences is:

2. Second-level epistemicism: For any meaningful sentence s, it is definitely true that s is definitely true, or s is definitely false, or s is definitely vague.

While this allows us to save the common-sense idea that there are people who are vaguely filthy rich, it still has the somewhat implausible consequence that it is always definite whether someone is definitely filthy rich, vaguely filthy rich, or definitely not filthy rich. I think it is easier to bite the bullet here. For while we can expect our intuitions about the meaning of first-order claims like “Sally is filthy rich” to be pretty reliable, our intuitions about the meaning of claims like “It’s vague that Sally is filthy rich” are less likely to be reliable.

Still, we can do justice to the second-level vagueness intuition by going for one of these:

3. nth level epistemicism: For any meaningful sentence s, and any sequence of D₁, ..., D_n − 1 of vagueness operators (from among "vaguely", "definitely" and "definitely not"), the sentence D₁...D_n − 1s is definitely true or definitely false.

(Say, with n = 3.)

4. Bounded-level epistemicism: for some finite n we have nth level epistemicism.

5. Finite-level epistemicism: For any meaningful sentence s, there is a finite n such that for any sequence of D₁, ..., D_n − 1 of vagueness operators, the sentence D₁...D_n − 1s is definitely true or definitely false.

The difference between finite-level and bounded-level epistemicism is that the finite-level option allows the level at which vagueness disapppears to vary from sentence to sentence, while on the bounded-level option, there is some level at which it always disappears.

I suspect that if we have finite-level epistemicism, then we have bounded-level epistemicism. For my feeling is that the level of vagueness of a sentence is definitely by something like the maximum level of vagueness of its basic predicates and names. Since there are only finitely many basic predicates and names in our languages, if each predicate and name has a finite level of vagueness, there will be a maximal finite level of vagueness for all our basic predicates and names, and hence for all our sentences. But I am not completely confident about this hand-wavy argument.

In any case, I find pretty plausible that we have bounded-level epistemicism for our languages, but we can extend the level if we so wish by careful stipulation of new predicates. And bounded-level epistemicism is, I think, enough to do justice to the idea that our world is really sharp.

The Alpha and the Omega

For a long time I have thought that the identification of God as the Alpha and the Omega in the Book of Revelation is very Aristotelian: God is the efficient and final cause of all. Indeed, Revelation 22:13 explicitly glosses as he arche kai ho telos. This may initially seem an over-metaphysicalization of Scripture, but I think it is a very Scriptural idea that particular aspects of God’s involvement in the world—us being comforted (in a way) that God is the arche and the telos of the upheavals in the Book of Revelation—are mirrors of God’s innate nature.

Substances and their existences

I used to think that:

1. x is a substance just in case  <x exists> is not grounded in any fact about any other entity other than x.

But it is plausible that a finite creature’s existing is its being created. And that Alice is created seems to be grounded in God creating Alice, which seems to be a fact about God.

There is a nice response to this worry. On standard medieval views, creation is a one-way relation. When God creates Alice, there is a relation of being-created-by-God in Alice but no relation of creating-Alice in God. We can say, then, that in an important sense the fact that God creates Alice is not a fact about God, but about Alice, where we say that a fact is about x provided the fact is in part a fact of x’s existing or there being some property or relation in x.

It’s interesting that the very plausible account (1) of substance combined with a theistically plausible view that the esse of a finite thing is its being-created yields the rather abstruse one-way relation thesis.

This line of thought does not, however, fit well with the claim that I made in The Principle of Sufficient Reason that for a caused entity, its esse is its being caused. For Alice is also caused by her parents. And while divine causation may be a one-way relation, it seems unlikely that creaturely causation is.

There are three ways out of this worry. (i) We could say that creaturely causation is also a one-way relation. (ii) We could say that I was slightly wrong, and for a caused entity, its esse is its being primarily caused, i.e., caused by God. (iii) We could modify (1) to:

2. x is a substance just in case  < x exists> has a grounding in a fact that is neither about any entity other than x nor grounded in a fact about any entity other than x.

For we can then say that while Alice’s being-caused is grounded in her parents’ activity, which is a fact about her parents, it is also grounded in God’s causing Alice, which is not a fact about God in the sense of being grounded in a relation or property of God’s.

I like both (ii) and (iii). What is especially attractive about (ii) is that if the esse of Alice is her being caused, then the esse of Alice is highly disjunctive, being multiply grounded—in God’s causing Alice, in her parents causing her, in her parents’ gametes causing her, maybe even in her grandparents’ causing her, etc. But it doesn’t seem right to say that Alice’s esse is highly disjunctive. So a focus on primary causation seems attractive. And I think—but without a careful examination—that the arguments in Principle of Sufficient Reason work with that modification still.

Two looping trolley scenarios

As part of an argument against the Principle of Double Effect, Thomson argued that if one thinks that it is permissible to redirect a trolley that is heading towards a branch with five people (“Branch” in my diagram) so it heads on a branch towards one, then this redirection remains permissible if one adds a looping track to the right branch that comes back to the left branch, as long as the one person on the right branch is large enough to stop the trolley from hitting the five.

But, Thomson insists, in the looping case the trolley’s hitting the large person on the right branch is a means to the five being saved, and so the defender of Double Effect cannot hold that there is something especially bad about intentionally harming someone.

Subsequently, it’s been noted, implicitly or explicitly (Liao et al.) that there is an ambiguity in Thomson’s story. On one version, “SymLoop” in my diagram, the track becomes symmetric, so that just as the one would block the trolley from hitting the five if the trolley went to the right branch, the five would block the trolley from hitting the one if the trolley stayed on the left branch. On the other hand, in AsymLoop, the left branch continues on, and if the trolley were to go on the left branch without the five being there, inertia would carry it harmlessly forward and away from everyone concerned.

When talking about all looping trolleys with Harrison Lee, it has occurred to me that there is a not implausible view on which:

1. Redirection in Branch is permissible.

2. Redirection in SymLoop is permissible.

3. Redirection in AsymLoop is impermissible.

Here is why. In Branch, we have the standard Double Effect considerations, which I won’t rehearse.

Now, redirecting in AsymLoop is morally the same as a case where a trolley is heading down a straight unbranching path towards five people, and you grab a random large bystander and push them in front of the trolley to save the five (call this “Bystander Push”). For in both AsymLoop and Bystander Push, you are interposing a bystander between the trolley and the five. The only difference is the mechanics of who or what is moved (and motion is relative anyway). And most non-utilitarians agree that pushing the bystander in front of the trolley is wrong.

However, SymLoop is a bit different. Here we have six people towards whom a dangerous trolley is heading, and we try to rearrange the six people in danger in such a way that as few of them die as possible. What is analogous to SymLoop is not Bystander Push, but a case where the trolley is heading down a single straight path in a narrow tunnel (so narrow that stepping off the track won’t save one), on which there are five small people just in front of one large person, and we reorder the large person to be in front of the small ones. Call this Reorder Push.

I think there is good reason to think Reorder Push is permissible. We have a group in danger. By chance, the status quo is that the five small people are protecting the large person. But is that fair? They are smaller in body, but no smaller in dignity. If they were all the same size, so that no matter what order they were in, the same number would die, it would be fair to roll dice to figure out the order—or to just count the status quo as “the dice having already been rolled”. But when they are not the same size, there is a naturally preferred arrangement of the people in danger: the large one first, and then the small ones. (For a variant case, suppose the six people are all standing in a line in the tunnel perpendicular to the track, so that when the trolley comes, they all will die. It would be perfectly reasonable for the five small ones to move behind the one large one, and utterly unreasonable for the large one to move behind the five small ones—the large person shouldn’t get defended at the expense of five.)

If Reorder Push is permissible, so is redirection in SymLoop. In both cases, the trolley is heading towards six, and we are just rearranging.

Now, it may seem that the reasoning behind Reorder Push should be rejected by a non-consequentialist. But I don’t think so. Prior to learning of Thomson’s Loop case (and hence not in order to generate a response to Loop), I wrote a paper on Double Effect where using an idea of Murphy’s I defend a distinction between accomplishing someone’s death and accomplishing someone’s being in lethal danger. On the view I defend, it’s always wrong to accomplish someone’s death, at least under such conditions as juridical innocence, but accomplishing someone’s being endangered, even lethally, is not always wrong. In particular, it’s not always wrong when the person consents to it, or when one has appropriate authority over the person. Thus, just as it is permissible to jump on a grenade to save comrades, it is permissible to push someone on a grenade with with their consent (suppose that the hero is unable to themselves jump, and the person pushing the hero is unable to reach the grenade with their own body), and it may be permissible for an officer to push a non-consenting soldier onto the grenade.

Now, the trolley case is not a case of intentional killing but of intentionally setting up a situation that in fact has lethal danger in it. One does not intend the death of the one in redirecting the trolley, but instead one intends the absorption of kinetic energy—which absorption happens to be a lethal danger to the absorber. This is not absolutely morally forbidden, but is only forbidden in some cases. In particular, it is not forbidden in cases of consent. That’s why pushing a random bystander is wrong, but it is not wrong to push a volunteer who is otherwise unable to move. In the same way, redirection in either SymLoop or AsymLoop would be permissible with the consent of the large person on the right track. But as the case is normally set up, you don’t have this consent.

Now, without the consent of the large person, AsymLoop and SymLoop come apart, as do Bystander and Reorder Push. Grabbing someone towards whom the trolley is not heading, and putting them in front of the trolley, whether by pushing (Bystander Push) or by moving the trolley (AsymLoop) is a wrongful case of accomplishing their lethal endangerment. But when that person happens to be in the lucky status quo where they are in the path of the trolley, but are being protected by the bodies of the five, they ought to refuse that costly protection. They ought in justice to consent to reordering or redirection. Now, in some cases, actual consent and obligation-in-justice to consent have different moral effects (e.g., in sexual cases the difference is very significant), but in other cases they may have similar moral effects. It is quite reasonable to say that in endangerment cases, actual consent and obligation to consent have similar moral effects. (One hint of this is that endangerment cases are ones where authority can have an effect to consent; sexual cases, for instance, are not like that—authority does nothing in the absence of consent there.) Thus, even without consent, redirection in SymLoop is permissible—but not so in AsymLoop.

Final remark: I wonder if it matters whether it is justice or something else that requires the consent in these kinds of cases. Intuition: One has a moral duty to jump in front of a trolley that is heading towards a hundred (but mabe not towards five) people. If so, and if it doesn’t matter whether the obligation is in justice or in some other way (say, charity), then once enough lives come to be at stake, then redirection in AsymLoop and pushing the non-consenting bystander become permissible. But if the obligation has to be one of justice, then one might hold that the redirection and pushing remains wrong even when there are more lives at stake.

Acknowledgment: The thinking here is greatly influenced by arguments from Harrison Lee about volunteering in loop trolley cases, but the conclusions differ.

Full professor position at Baylor Philosophy Department

We have an open area full professor position in our Department. If you qualify, I encourage you to apply. If you know someone who qualifies, I encourage you to encourage you to apply. Email me if you need more information or encouragement.

Waco is a lovely place. Here is a bittern at sunset last week. The spot is an easy one mile bike trail-ride along the river from campus.

Sony A7RII with Retina Xenon Schneider-Kreuznach F/1.9 50mm lens (wide-open, cropped).

Taking, not stealing

Aquinas says that when a starving person takes food needed for survival from someone who has too much, the act is a case of taking but not stealing. Aquinas’ reasoning is that property rights subserve survival, and in case of conflict the property rights cease, and the food ceases to be the property of the one who has too much, and so it is not theft for the poor to take it.

I think what is going on may be a bit more subtle than that. Suppose Alice and Bob both have too much and Carl is starving. Both Alice and Bob refuse their surplus to feed Carl. According to Aquinas’ analysis, both Alice and Bob lose their ownership.

But I think things may be a bit more subtle than that. Suppose that shortly after Alice and Bob’s wrongful refusal, Carl suddenly wins the lottery. It does not seem right to say that Carl can now take Alice and Bob’s surplus. Yet if Alice and Bob lost their ownership upon refusal to feed Carl, then either the surplus now belongs to Carl or it belongs to nobody, and in either case it wouldn’t be stealing from Alice and Bob for Carl to take it. Similarly, if after Carl’s lottery win, Alice were to take Bob’s surplus food, Alice would be stealing from Bob.

We could say that Alice and Bob regain their property when Carl wins the lottery, but it is strange to think that something that belongs to nobody or to Carl suddenly becomes Alice’s, despite Alice having no deep need of it, just because Carl won the lottery.

Here is a different kind of case that I think may shed some light on the matter. As before, suppose Alice has a surplus. Suppose Eva the mobster has informed David that if David doesn’t take Alice’s surplus, then Eva will murder Alice. Any reasonable person in Alice’s place would agree to having her surplus taken by David, but Alice is not a reasonable person. David nonetheless takes Alice’s surplus, thereby saving her life.

I think David acts rightly, precisely because as Aquinas thinks one needs to resolve a conflict between property and life in favor of life. But I don’t think we can analyze using Aquinas’ loss of ownership account. For if David takes Alice’s stuff, then Eva who made David do it is a thief (by proxy). But if under the circumstances Alice loses her ownership, then Eva is not a thief. I think the right thing to say is that Alice retains her ownership, but it is not wrong for David to take her stuff in order to save her life.

What should we say, then? Is David a thief, but a rightly acting thief? That is indeed one option. But I prefer this one. When you own something, that gives you a set of rights over it and against others. I suggest that these rights do not include an unconditional right not to be deprived of the use of the item. Specifically, there is no right not to be deprived of the use of the item when deprivation of use is the only way for someone’s life to be saved. This applies both in Aquinas’s case of starvation and in my mobster case. It is not an infringement on Alice’s ownership over her surplus when Carl takes her stuff to survive or when David takes her stuff in order to save Alice’s life. But when Carl’s need terminates, he does not get to then take Alice’s stuff, as if Alice had lost ownership, and the mastermind behind David’s taking the stuff, who unlike David isn’t acting to save Alice’s life, is a thief.

In fact, if we think about it, it becomes obvious that there is no unconditional right not to be deprived of the use of an owned item. Suppose I have my car on a plot of land that I own, and I foolishly sell you all the land surrounding the small rectangle that the car is physically on top of. By buying the land, you deprive me of the use of my car, barring your good will—I cannot drive the car off the rectangle without trespass. But you don’t steal my car by thus depriving me of its use.

Thus, neither Carl (when in need) nor David is stealing, even though both take something owned by someone else.

Aquinas quotes St. Ambrose with approval: “It is the hungry man’s bread that you withhold, the naked man’s cloak that you store away, the money that you bury in the earth is the price of the poor man’s ransom and freedom.” While St. Ambrose’s sentiment is very plausibly correct, on my account above it is not correct to take it literally. When Alice wrongfully withholds her surplus from starving Carl, the surplus is not literally owned by Carl. It is still owned by Alice, who has a duty to pass ownership to Carl, and Carl in turn is permitted to use Alice’s surplus—but it remains Alice’s, even if wrongfully so.

Indeed, here is an argument against the hypothesis that ownership literally passes to the needy. Suppose Carl is starving, and Alice and Bob refuse their surplus. Now, shortly after Carl coming to be starving, so does Fred. On an account on which ownership literally passes to the needy, Alice’s and Bob’s surplus belongs to Carl, and if Carl comes to claim it and at the same times so does Fred, Carl gets to defend that surplus, violently if necessary, from Fred, as long as that surplus is all needed for Carl’s survival. But it seems plausible that as long as Carl’s and Fred’s need is now equal, they have equal rights, even if Carl came to be needy slightly earlier. Furthermore, suppose Alice has ten loaves of bread and Carl needs one to survive. Which loaf of bread becomes Carl’s possession? Surely not all of them, and surely no specific one. It seems better to say: while Carl is in dire need, Alice has no right to withhold surplus from her. As soon as Carl and any other needy person has taken enough not to be in dire need, Alice may defend the rest of her surplus.

Tiebreakers

You need to lay off Alice or Bob, or else the company goes broke. For private reasons, you dislike Bob and want to see him suffer. What should you do?

The obvious answer is: choose randomly.

But suppose that there is no way to choose randomly. For instance, perhaps an annoying oracle which has told you the outcome of any process that you could have made use of random decision. The oracle says “If you flip the penny in your pocket, it will come up heads”, and now deciding that Alice is laid off on heads is tantamount to deciding that Alice is laid off.

So what should you do?

There seems to be something rationally and maybe morally perverse in one’s treatment of Alice if one fires her to avoid firing the person that one wants to fire.

But it seems that if one fires Bob, one does so in order to see him suffer, and that’s wrong.

I have two solutions, not mutually exclusive.

The first is that various rules of morality and rationality only make sense in certain normal conditions. Typical rules of rationality simply break down if one is in the unhappy circumstance of knowing that one’s ability to reason rationally is so severely impaired that there is no correlation between what seems rational and what is rational. Similarly, if one is brainwashed into having to kill someone, but is left with the freedom to choose the means, then one may end up virtuously beheading an innocent person if beheading is less painful than any other method of murder available, because the moral rules against murder presuppose that one has freedom of will. It could be that some of our moral rules also presuppose an ability to engage in random processes, and when that ability is missing, then the rules are no longer applicable. And since circumstances where random choices are possible are so normal, our moral intuitions are closely tied to these circumstances, and hence no answer to the question of what is the right thing to do is counterintuitive.

The second is that there is a special kind of reason, a tie-breaker reason. When one fires Bob with the fact that one wants to see him suffering being a tie-breaker, one is not intending to see him suffer. Perhaps what one is intending, instead, is a conditional: if one of Alice and Bob suffers, it’s Bob.

Playing with photo developing

My ten year old and I developed a roll of 35mm film that I shot over the past year in my grandfather's Voigtlander Vito I camera. I've never developed film before. 

2022 Heart of Texas Fair. Fomapan 200.

A deterministic collapsing local quantum mechanics without hidden variables beyond the wavefunction

I will give a really, really wacky version of quantum mechanics as a proof of concept that if one wants, one can have all of the following:

1. Compatibility with experiment

2. Determinism

3. Collapse

4. No “hidden variables” beyond the wavefunction: the wavefunction encompasses all the information about the world

5. Locality

6. Schroedinger evolution between collapes.

Here’s the idea. We suppose that the Hilbert space for quantum mechanics is separable (i.e., has a countable basis). A separable Hilbert space has continuum-many vectors, so each quantum state vector can be encoded as a single real number. We suppose, further, that collapse occurs countably many times over the history of the universe. We can now encode all the times and outcomes of the collapses over the history of the universe as a single real number: the outcome of a collapse is a quantum state vector, encodable as a real number, the time of collapse is of course a real number, and a countable sequence of pairs of real numbers can be encoded as a single real number.

We now consider the wavefunction ψ of the universe. For simplicity, consider this as a function on R³ⁿ × R where n is the number of particles (if the number of particles changes over time, we will need to tweak this). Say that x ∈ R³ⁿ is rational provided that every coordinate of it is a rational number. We now add a new law of nature: ψ(x,t) has the same value for every rational x and every time t, which value encodes the history of all the collapses that ever happen in the history of the universe.

Since standard quantum mechanics does not care about what happens to the wavefunction on sets of measure zero, and the set of rational points of R³ⁿ has measure zero, this does not affect Schroedinger evolution between collapses, and so we have 6. We also clearly have 2, 3 and 4. If we suppose a prior probability distribution on the collapses that fits with the Born rule, we get 1. We also have 5, since any open region of space that contains an experiment will also contain the real number encoding the collapse history.

Of course, this is rather nutty. It just shows that because the wavefunction has more room for information than just the quantum state vector—the quantum state vector can be thought of as an equivalence class of wavefunctions differing on sets of measure zero—we can stuff the hidden variables into the wavefunction. Those of us who think that the state vector is the real thing, not the wavefunction, will be quite unimpressed.