Simplifying the laws

This morning I realized the following Nomic Simplification thesis is very likely true:

• NS: Any physical theory can be replaced by a practically empirically indistinguishable theory with extremely simple physical laws and very few natural kinds of physically fundamental entities and properties, at the cost of somewhat more complicated psychophysical laws and vastly more complicated and/or fine-tuned initial conditions. For concreteness, the simple physical laws could be the laws of Conway’s Game of Life or of classical mechanics with some simple laws.

What does the “practically” qualifier do here? Well, a theory might have empirical consequences that are not practically available to us, for instance because the mathematics of the theory is too nasty for us to compute the relevant predictions from. So I am restricting the empirical match to those empirical consequences that are practically available given the computational resources we have.

Moreover, NS seems to affect quite a number of issues. But before I get to that, let me give a hand-waving argument for NS that I find quite convicing.

By Church-Turing thesis, any such practically available empirical consequences can be computed by a finite subset of a Turing machine. Thus, we should be able to simulate the physical theory in question by means of a finite subset of a Turing machine, and a Turing machine needs only very simple physical laws. For instance, the laws of Conway’s Game of Life are extremely simple, and yet Turing complete—one can implement a Turing machine in the system. Moreover, we can run the Game of Life with one fundamental natural physical kind, namely cell, and one fundamental property, namely color, in addition to position. If we implement a Turing machine in the Game of Life that simulates the physical theory T in question, we will still need to layer psychophysical laws on top of that to generate empirical predictions. These might be somewhat more complicated than the best psychophysical laws for T, but not by far. For the translation between the Turing machine’s data and T’s physical ontology will not be that complicated (we can design a good GUI, as it were, by sufficiently complicating the code for the Turing machine—i.e., the initial conditions), and we can just add that translation layer to the best psychophysical laws for T. Now, we have good reason to think that any tenable psychophysical laws will be very complicated, and so adding the translation layer is unlikely to increase the complexity by a significant factor. Of course, the code encoding T is apt to be vastly complicated, and will correspond to the initial conditions for the Game of Life.

What goes for the Game of Life goes for classical mechanics with some simple laws—perhaps rigid bodies moving in classical mechanics frictionlessly and powered by flywheels that have been turning for ages.

What are some consequences of NS and of the Church-Turing argument behind it?

1. What got me thinking about NS is that Nancy Cartwright has argued that our messy world cannot be encapsulated by simple laws of physics that cover all eventualities, given the complexities of combination laws for different forces, and has opted for a story involving causal powers. But insofar as that story generates practically available empirical consequences, NS tells us that we can replace the story with an account that has very simple physical laws.

2. It is possible to uphold classical Newtonian physics given all the evidence we have at hand. For we can presumably make an arbitrarily large finite subset of a Turing machine in a world governed by classical physics. Of course, there will likely be horrendous fine-tuning of initial conditions.

3. Sometimes theists argue (or at least I’ve said stuff like this) that laws of nature that would allow a complexly interdependent ecosystem, embodied intelligence, and yet make evil impossible would likely have to be immensely complex. NS shows this is false.

4. We rightly prefer theories with simpler laws and fewer fundamental kinds and properties to theories with more of them other things being equal. NS teaches us, however, that simplicity of laws, fundamental kinds and fundamental properties can be easily ensured in ways that are counterintuitive. We should think it more likely that the fundamental laws, kinds and properties of our world are those of quantum mechanics and the standard model than that they are of Conway’s Game of Life. Thus, we need to make sure that we take “other things being equal” very seriously—in particular, avoidance of fine-tuning of initial conditions and/or seeking elegance in the initial conditions is very important for evaluating theories.

5. If we are willing to accept a very large multiverse, we might be able to simplify the laws, fundamental kinds, and fundamental properties in an aberrant way (say, Game of Life) while yet not having any fine-tuning problem. For in a sufficiently large multiverse, we can explain the existence of fine-tuned initial conditions in some life-supporting universe by means of randomness and the fact that we can only observe a life-supporting universe. How serious a problem this is is depends on whether we can generate a good probability measures in multiverses and argue that given the aberrantly simple laws the right probability measure will generate predictions that do not match our observations. In the Game of Life story, a plausible probability measure is given by making the color of each initial cell be an independent coin-flip random variable. I suspect that this would lead to the prediction that we should expect to see a much messier world than we do, and so we may be able to empirically rule out a multiverse version of the Game of Life hypothesis.

The general lesson is this. We can shift complexity considerations in a theoretical account back and forth betweeninitial conditions and the laws/kinds/properties. We can simplify each at the expense of the other.

Doing, refraining, and double effect

Some people are skeptical of distinctions between doing and refraining. It seems that anybody who accepts classical double effect reasoning must accept such a distinction.

Suppose you’re informed that if you don’t kill Alice, then Bob and Carol will be murdered, with all three innocent. The double effect reasoning says you may not kill Alice, since even if you are aiming to save Bob and Carol, the means to saving Bob and Carol is Alice’s death, and so you would be intending to kill Alice.

But suppose we don’t make a distinction between doing and refraining. Refraining from killing Alice has Bob and Carol’s death as a consequence. But this consequence is disproportionately bad, so by classical double effect reasoning, you are prohibited from refraining to kill Alice. Hence, killing Alice is wrong but so is refraining from killing her. Thus, this is a case of a real moral dilemma. But everyone who accepts classical double effect reasoning denies that this is a moral dilemma: you simply shouldn’t kill Alice, and then you’re doing nothing wrong.

So it seems that double effect cannot apply to both doings and refrainings equally. Thus, it seems that the right solution to the above problem is to say that double effect applies only to doings.

But there are cases where one might think double effect reasoning applies to refrainings as well. To adapt Rachels’ famous case, suppose innocent Tommy is drowning in a bathtub, and you can easily pull him out. But you’ve been informed that unless Tommy is dead by the end of the day, Bob and Carol will be murdered. Because it’s wrong to kill Tommy by double effect for doing, you were steeling yourself to accept Bob and Carol’s death. But now things have changed. Now it seems that double effect forbids you to save Tommy, because a consequence of saving Tommy is the death of Bob and Carol, and that’s disproportionate.

I am very unclear on this case. But maybe the judgment that you are forbidden to save Tommy is correct. Consider this case: you see someone drowning, and you could rescue them, but then someone points a gun at two hostages and informs you that if you save the drowning person, the hostages will be killed. Then you really should refrain from saving the drowning person.

Inseparability and real identity

On a standard (but disputed) interpretation of Scotus, x and y are inseparable (neither can consistently exist without the other) if and only if they really identical.

Let a be God’s asserting to Alice: “I am asserting to Bob the same thing I’m asserting to you but with your name in place of theirs.” Let b be God’s asserting to Bob: “I am asserting to Alice the same thing I’m asserting to you but with your name in place of theirs.” Then a and b are inseparable, since God cannot assert a falsehood. But clearly these two divine assertings are not really identical.

Anthropocentrism

Theists are sometimes accused of being anthropocentric in their worldview.

Yet in a typical naturalistic worldview, rational animals are at the axiological pinnacle of reality, the only beings with dignity. And the only rational animals we know of are humans. (Though I suppose naturalisms that have a large multiverse are committed to an extremely high probability of there being other rational animals.)

The theist, on the other hand, thinks that rational animals like us are near the bottom of the great chain of being, since there is a finite distance between us and nothingness, and an infinite distance between us and the top of the chain, namely God.

It's wrong to disconnect from the violinist

Take Judith Jarvis Thomson’s famous violinist case. Here is a quick and simple argument for why it’s wrong to disconnect from the violinist in order not to be connected to them for nine months.

1. It’s wrong to perform a positive action known to cause an innocent person’s death without a reason proportionate to the harm of death to someone who can be expected to live many years of a normal life otherwise.

2. The harm of death to someone who can be expected to live many years of a normal life otherwise is clearly disproportionate to being free for nine months from being connected to someone.

3. Disconnecting from the violinist is a positive action known to cause the death of an innocent person who can be expected to live many years of a normal life otherwise.

4. Thus, it is wrong to disconnect from the violinist in order not to be connected to them for nine months.

Premise 1 is a consequence of most versions of the Principle of Double Effect, but is also independently extremely plausible. Premise 3 is part of the story.

Why believe premise 2? Here’s one criterion of disproportionateness. A sufficient condition for a harm H₁ to be disproportionate to a harm H₂ is that a reasonable person would with little hesitation accept a harm that’s twice as bad as H₂ to avoid H₁. But a reasonable person would with little hesitation accept 18 months of being connected to someone to save their life, assuming they can be expected to live many years of a normal life if saved.

To see this, imagine you are the violinist, and you are about to die of kidney problems. But then someone shows up who offers to hook themselves up to you for 18 months, after which you will be cured. You might hesitate whether to accept their generosity. But you wouldn’t hesitate much before concluding they are offering you a great benefit, and if you were to hesitate much to accept it, that would only be because you might be concerned about being so much in debt to the generous benefactor. The fact that you would have to live for 18 months hooked up to them, a quite significant burden admittedly, would be a price well worth paying for your life.

Or imagine this. You have just been conceived. An angel now miraculously gives you the intelligence of a reasonable adult, and informs you that you have a cancer that will kill you within a few days. However, the angel tells you that if you just ask, you will be cured of that cancer, and can expect a normal human life. But there is a price to be paid for the cure: For the next 9 months you will be confined to a small space within another human being, after which for the next 9 months you will be unable to walk, talk, or exercise any significant personal freedom. This is a price well worth paying for life! It is a price we have all paid involuntarily, but surely anyone who is fortunate enough to live a normal human life will think that price would have been worth paying voluntarily. And yet those 18 months of dependency and lack of freedom are more constraining than 18 months of being hooked up to the violinist would be.

I can now argue as follows:

5. If it is wrong to disconnect from the violinist in the “standard scenario” above, abortion is wrong in the case of a normal pregnancy.

6. Therefore, abortion is wrong in the case of a normal pregnancy.

Now, one could vary the violinist story so that the analogue of premise 2 will no longer hold. Perhaps if the nine months were filled with torture, or if the violinist were to live only for a few months after the nine month period was over, then the analogue of premise 2 wouldn’t hold. In those cases, the Principle of Double Effect might well allow disconnecting from the violinist, and in those cases, the above argument against abortion fails.

Does it follow that in such hard cases of pregnancy, an abortion would be permissible? It does not follow, since there are further wrong-making features in the abortion case, including: (a) the parent-child relationship, (b) the fact that the abortion requires a lethal direct attack on another human being’s body (the analogue to the “tubes” connecting one to the violinist in the case of pregnancy may be the umbilical cord, which is the child’s organ), and (c) the fact that living in utero constitutes ordinary life-support for someone in the first nine months of their life. But that would be material for another post.

Brower's Aristotelian account of intrinsic change

Jeff Brower has a very original Aristotelian account of how three-dimensional substances endure and change accidentally, while being wholly present at all times at which they exist. The clever idea is that we leverage kooky objects, things like seated-Socrates. Seated-Socrates is an object distinct from Socrates, and seated-Socrates is seated in a primary way. On the other hand, Socrates, who is a three-dimensional substance, is a part of seated-Socrates, and that is what makes Socrates be seated derivatively. Now, here’s how change happens. Socrates is a part of both standing-Socrates, who exists at t₁, and of sitting-Socrates, who exists at t₂. There is no contradiction in the same entity being a part of two different entities, and there is (Brower claims) no contradiction in Socrates being derivatively standing and seated.

Here is a problem with this clever solution. Consider a different kind of change: Socrates losing his hair. By the same story, at t₁, Socrates is derivatively hairy, because he is a part of hairy-Socrates who is primarily hairy. At t₂, Socrates is derivatively hairless, because he is a part of hairless-Socrates who is primarily hairless. So far so good.

But there is a problem. Something is hairy if and only if it has hair as a part, and it is hairless otherwise. Let’s suppose t₁ is the present. Then Socrates is hairy, and hence has hair as a part. But since Socrates endures from t₁ to t₂, he is also wholly present at t₂. The Socrates of t₂ is identical with the Socrates of t₁. Since hair is a part of the Socrates of t₁, by Leibniz’s Law, hair is a part of the Socrates of t₂, and hence the Socrates of t₂ has hair as a part, and thus is hairy, a contradiction. Another way to see the point is this. Socrates has hair as a part (remember, it’s t₁ now). He is wholly present at t₂. Since he’s wholly present at t₂, he is at t₂ with all his parts. Since his hair is a part of him, it must be that he is present at t₂ with his hair as a part, and hence he is hairy at t₂, a contradiction.

Perhaps, though, I am being unfair, because the Brower account needs to be applied to temporary parthood relations, too. Thus, we might say this. At t₁, Socrates is a part of Socrates-with-hair-as-a-part, and at t₂ Socrates is a part of Socrates-without-hair-as-a-part. Socrates at t₁ derivatively has hair as a part by being a proper part of Socrates-with-hair-as-a-part, and Socrates at t₂ derivatively has no hair as a part by being a proper of Socrates-with-no-hair-as-a-part.

At this point, the primary–derivative stuff seems rather implausible. Maybe one can buy the idea that you can inherit being seated from an entity you are a part of, but the idea that you can inherit having x as a part from an entity that you are yourself a part of having x as a part seems absurd. You can inherit having x as a part from a part of you—that’s perfectly normal, as I inherit having neurons as parts from having a brain as a part which has neurons as parts—but not from a whole you are a part of.

But it seems to get worse. Brower’s account is a hylomorphic one, on this account Socrates is a form-matter composite. Now let’s suppose, as may well have happened, that Socrates grew from eight pounds at t₁ (say, 479 BC) to a hundred pounds at t₂ (say, 467 BC). Between t₁ and t₂, Socrates has gained some chunk m of matter. Then, m is not a part of Socrates at t₁ and is a part of Socrates at t₂. But we cannot account for this change by saying that Socrates is a part of Socrates-without-m at t₁ and a part of Socrates-with-m at t₂. For Socrates has his matter non-derivatively.

There may be an escape available from this, but it requires quite a bit of bullet-biting. First, we can simply deny that we have parts like hair. Instead, we have accidents of hairiness and hairlessness, but there is no such thing as hair. I find this moderately plausible, but I think it works best on a view on which our accidents are parts of us, as then we can at least do some justice to the intuition that hair is a part of us—it’s not, but at least an accident of hairiness is. And Brower’s account is one on which our accidents aren’t parts of us, but are parts of large kooky objects. In any case, if we deny that we have parts like hair (or fingers or hearts or anything else that we can gain or lose), we can get Brower out of the first problem.

Second, we deny that we can identify Socrates’ matter in a changing way. When we say that Socrates is a matter-form composite at t₁ and at t₂, we insist that it is the very same matter and the very same form that are parts of Socrates at t₁ and at t₂. Sure, the matter changes size, shape and mass, but we account for this entirely in terms of Socrates’ accidents. Numerically, we have exactly the same matter throughout Socrates’ life, both when he is eight pounds and when he is a hundred pounds. When Socrates eats, he doesn’t gain matter: he grows in size, getting new accidents of size, shape and mass. When Socrates loses his hair, he doesn’t lose matter: he shrinks slightly, getting new accidents of size, shape and mass. At this point, “matter” is largely detached from common-sense intuitions about matter. It is just a technical philosophical construct. There is nothing wrong with technical philosophical constructs, but many Aristotelians (not I!) want the stuff they say about matter and form to do justice to common-sense intuitions about matter.

This bullet-biting almost works. It has a theological problem, however. On what I think is the right account of the afterlife, when Socrates died, he lost all of his matter, but continued to exist as a disembodied being. And this change Brower cannot account for in his hylomorphic story. Socrates had matter as a part of him in 400 BC but not in 398 BC, and so we cannot say in 400 BC that he is wholly present in 398 BC, nor can we use the hylomorphic account to explain how he becomes disembodied, because then he would have to derivatively have matter in 400 BC, derivatively from a kooky enmattered-Socrates, whereas substances have matter primarily on the kind of Aristotelianism that Brower espouses. Thus, it seems, Brower would need to be a corruptionist—he would need to think that although our soul survives death, we do not. This would be an unfortunate theological position, and in any case Brower is actually a survivalist.

There is a way out of all of this. Don’t think of us as hylomorphic compounds having form and matter as parts. Instead, think of us as something like forms with accidents. These accidents can include the accident of materiality, the accident of hairiness (and having hair isn’t any longer a case of having a part that is hair). And then account for materiality not in terms of having matter as a part, but in terms of having accidents of materiality. I actually like the story as far as it goes, but the next step I don’t like, but it’s necessary for Brower’s story if it is to allow disembodied survival: Give the kooky-object story of accident possession, including the possession of materiality. Socrates is material derivatively because he is a part of material-Socrates who has materiality primarily.

Explanatory parsimony versus theoretical parsimony

Like the previous Ptolemaic model, Copernicus’ heliocentric model of the solar system required epicycles to predict the astronomical observations of the positions of the planets in the night sky. (The reason was that Copernicus’ orbits were circular instead of elliptical, and I suppose he needed epicycles to simulate the ellipticality.) Indeed, by Gingerich’s count, the Copernican system had more epicycles than the Ptolemaic.

What advantage did the Copernican theory have over the Ptolemaic, then?

The Copernican theory did not need epicycles to predict the qualitative movements of the planets in the night sky, with the famous retrograde motion where sometimes planets move from night to night in the opposite of their usual direction. Such qualitative features are nicely accounted for by the fact that the planets, including earth, are all orbiting the sun, and thus sometimes the earth overtakes a slower outer planet which thus appears to be moving backwards. On the other hand, Ptolemaic theory is both quantitatively and qualitatively wrong without epicycles: it needs epicycles to predict the existence of retrograde motion.

We think of the Copernican theory as superior due to its greater simplicity. But the theory as a whole is not simpler. However, it provides a simpler explanation of a puzzling or significant phenomenon.

This suggests an interesting theoretical virtue, which we might call not just parsimony, but explanatory parsimony, where the theory offers a particularly parsimonious explanation of one or more specific phenomena against a competitor, even if there happens to be little difference in the theories’ overall parsimony as needed for explaining all the phenomena, and even if there is less overall parsimony, as Gingerich claims was the case for Copernicus.

Take a more human case. We could explain the assassination of JFK in terms S₁, a theory about Oswald working alone, or we could explain it in terms of, S₂, where Oswald is working together with the CIA. The non-conspiracy explanation is more parsimonious: it involves two persons—Oswald and JFK—as opposed to many more. But notice that neither S₁ nor S₂ is capable of explaining all the humanly significant phenomena of 1963. To that end, both theories need to be enriched to include the activities of all of the 3.2 billion people of 1963. Let T₁ and T₂ be such respective enrichments of S₁ and S₂. These are vast theories.

Is T₁ more parsimonious than T₂? I doubt it. After all, the people at the CIA who, according to S₂, were working with Oswald were still doing something according to T₁, and indeed something that explains events of human significance. This activity is included in T₁.

Theory T₁ superior to T₂ not in terms of overall parsimony—or even the overall parsimony of the explanatorily fundamental posits—but in terms of how large a portion of (or approximation to?) the theory is needed to explain the specific events around the assassination of JFK. On T₁, a much smaller theory (with primary focus on two persons) S₁ is sufficient for the assassination, while on T₂, a much larger portion S₂ is needed.

If this is right, then we like focused explanations to be neater and smaller, even if the overall story is equally complex.

Here is an interesting application. Physicists have a strong preference for local theories, in the broad sense of the word according to which the behavior of a system depends only on what is happening near the system. But notice that in practice locality is often an approximation. Each system is affected to some degree by everything in its past light cone. To get a full explanation of the system, we need the whole past light cone. But we still have locality, because we get explanations of how the system works to a high degree of approximation in terms of how things are nearby, because all of the forces of physics drop off with distance. A preference for locality is thus a special case of a preference for explanatory parsimony: we want the approximate behavior of the system to have a more parsimonious explanation, even if the fully precise behavior needs a profligate one.

The general feature thus is this. It counts in favor of a theory if a puzzling or significant coarse-grained feature of our observations is explained in a more parsimonious way according to the theory, even if there is no parsimony advantage with respect to finer grained observations.

From a Bayesian point of view, this translates into a view on which we should have higher priors for theories that explain more of puzzling or significant phenomena with less.

Is the anthropocentrism in the notion of “puzzling or significant phenomena” a problem? Maybe not on my natural law epistemology: our epistemology is human epistemology.

I wonder if there is a philosophy of religion application. For instance, consider that theism provides a parsimonious explanation of the coarse-grained fact that there are rational animals: a perfect being has good reason to create rational animals given the objective value of such animals. But once we look at more fine-grained facts, such as that the rational animals have ten fingers and ten toes, it can be contended that we no longer have a more parsimonious explanation. Indeed, to explain all the details of humans, the theist is likely to need to invoke evolutionary mechanisms just as the naturalist does. Could the theist say that the more parsimonious explanation of the coarse-grained fact still counts for something?

I am also now thinking that this story gives the nominalist a good response to the Platonist in the context of yesterday’s post. The fact that a theory includes lots of fundamental nameable things is not very significant. What is significant is the ideology that needs to be brought to bear on particular explanations. When explaining our reaction to seeing grass, say, the Platonist needs to invoke not just the predicate “instantiates” but also the name “greenness”, while the nominalist only needs the predicate “is green”.

Platonism, nominalism and parsimony

Platonist: Platonism is ideologically way more parsimonious than nominalism. For Platonism has one fundamental predicate applying to objects: “instantiates”. Nominalism, on the other hand, has many: “is charged”, “has mass”, “is ____ units away from”, etc.

Nominalist: Platonism also has properties or relations such as charge, mass, or being ____ units away from.

Platonist: Yes, it has these properties among its objects, but there are no fundamental predicates corresponding to them. Platonism has extra fundamental objects, but that’s a question of ontological, not ideological parsimony.

Nominalist: But the Platonist has names for these objects: “charge”, “mass”, etc. And if fundamental predicates count against ideological parsimony, so do names of fundamental entities.

Platonist: If names of fundamental entities count against ideological parsimony, then either we have an objectionably anthropocentric notion of parsimony on which the parsimony of a theory depends on how many fundamental things we have in fact named, or else we are counting nameable fundamental things, and we have to say that a theory on which there are 10⁹⁰ fundamental particles is far less ideologically parsimonious than one on which there are 10⁸⁰ of them, since they’re all nameable. But it seems absurd to decide how many particles we have on grounds of ideological parsimony.

Nominalist: But Platonism has an additional categorial division, between properties (including non-monadic ones, if we want to be charitable and not count relations separately) and non-properties.

Platonist: Yes, but this division is not fundamental, since it can be entirely defined in terms of the Platonist’s one fundamental predicate, and logical and modal operators that nominalists also need: a property is an x such that possibly there are things that instantiate x. (Granted, this requires a sparse Platonism that doesn’t have properties like square circularity.)

Nominalist: But surely there is a difference in kind that explains why some things can be instantiated and others cannot.

Platonist: Sure, but not a difference in fundamental kind. Fundamentally, Platonism should be considered a one-category theory with one predicate, and lots and lots of names.

Personhood and supreme beauty

Start with the Socratic intuition that the most beautiful thing on earth is a human being living well. Extrapolating:

1. Persons living well are more beautiful than any impersonal entity.

Add a Platonic assumption:

2. Nothing is more beautiful than the Form of Beauty.

(Quick argument: Platonic Beauty is resemblance to the Form of Beauty, and nothing resembles x more than x itself does.)

3. There is a person who lives well.

Thus:

4. If the Form of Beauty is an impersonal entity, then there is a person who is more beautiful than the Form of Beauty. (1 and 3)

5. So, the Form of Beauty is a personal entity. (2 and 4)

6. The Form of Beauty is immaterial.

7. So, there is an immaterial personal entity that is supremely beautiful. (2, 6 and 7)

(A personal entity is one that is one or more persons.)

Substances as proper parts and constituent ontology

Here’s an argument against the claim that a human is sometimes (or always) a proper part of a larger whole such as a committee or an ecosystem, assuming constituent ontology.

1. An object is human iff humanity is a proper part of the object.

2. Proper parthood is transitive.

3. If a human x is a part of y, then x’s humanity is a proper part of y. (1 and 2)

4. So if a human is a proper part of something, that something is a human. (1 and 3)

5. No human is a proper part of a human.

6. So, no human is a proper part of anything. (4 and 5)

It seems that constituent ontologists have to have a pretty restricted theory of composition.

One way out is to distinguish “ontologically constituent parthood” from “integral parthood”, and say that an object is human iff humanity is an ontologically constituent part. Then the conclusion of the argument is going to be that no human is an ontologically constituent part of anything. But this requires multiplication of fundamental ideology.

There is another a way out of this. Let’s suppose that there are proper parts and immediate proper parts, with proper parthood being grounded in immediate proper parthood. Thus, perhaps, my fingers are immediate proper parts of my hand, my hand is an immediate proper part of my arm, and so on. Mediate parthood is then a chain (of length 0 for improper parts) of immediate parthood. There is no multiplication of fundamental ideology, since parthood is defined in terms of immediate proper parthood. Moreover, this is not unmotivated. Parthood seems intuitively hierarchical rather than flat. My big toe is a part of my leg because it is a part of my foot.

Now, notice that if we say this, we might hypothesize that an object’s essence is an immediate proper part of it. (Dialectical note: A constituent ontologist who accepts (1) and who buys the concept of immediate proper parthood has to agree with this hypothesis. For if my humanity were a mediate part of me, then I would have a proper part of which my humanity was a proper part, and by (1) that proper part would be human. But clearly no human is a proper part of me.)

Given that hypothesis, we can modify the constituent ontology claim (1) to:

7. An object is human iff humanity is an immediate proper part of the object.

And now humans can be parts of larger wholes, without infecting them with humanity.

Distinguishing eternalism and growing block at the end of time

Imagine that Alice lives in a classic growing block world, while Twin Alice lives in an eternalist world. Otherwise, the two worlds are exactly alike at all times. Moreover, in both worlds time started at noon, and ends at midnight.

Now let’s consider things from the point of view of both Alices right at the last moment of time, namely midnight.

In both cases, reality is a four-dimensional block, twelve hours long along the temporal axis. In both cases, there is a past but no future. However, the following would be true as asserted by Alice, but not as asserted by Twin Alice:

1. An hour ago, the block of reality was eleven hours long.

Question: What grounds the fact that (1) is true for Alice but not for Twin Alice? In other words, what grounds the fact that Alice inhabited a growing block world rather than an eternalist world?

This seems quite mysterious to me. And this seems to me to weaken the main arguments for why growing block is preferred to presentism and moving spotlight, namely that growing block gives you a better account of the grounds of claims about the past. But not in the case of (1). It seems that the growing blocker needs to ground (1) in one of the ways in which the presentist grounds claims about the past, say by positing a past-tensed fact at midnight of the block of reality having been eleven hours long an hour ago, or a past-tensed property, etc. And even so we have a puzzle.

My puzzle looks different depending on whether the eternalist world has A-eternalism or B-eternalism. If it has A-eternalism, then we can distinguish the two worlds as follows: the growing block world at the last moment of time does not have a spotlight anywhere, while the A-eternalist world does have a spotlight shining on midnight. But if that’s the answer we take, then there is a cost: there seems to be no difference between the growing block world at midnight and the B-eternalist world at midnight, and yet (1) is true in the growing block world and false in the B-eternalist world.

What did I mean by a classic growing block world? Well, in response to Merricks-style arguments that growing blockers can’t know that their thoughts are happening now, some have opted or a faded growing block, on which the past is missing some properties, like consciousness. On such a modified growing block theory, we have some hope of grounding the difference at the last moment of time between growing block and B-eternalism, because the B-eternalist world does not have a faded past. But now we can modify the story: suppose the B-eternalist world literally had a faded past (a past with no consciousness, say).

I think that if I was a growing blocker, I would be inclined to say something like this. The growing block theory is necessarily true in any world with time. What grounds the difference between being in a growing block world and an eternalist world is that an eternalist world doesn’t have time—it just has a fourth spatial dimension that enters differently into the laws of nature from the other three. Moreover, it is a necessary truth that at time t, time t is at leading edge of reality. This necessary truth does not need further grounding, but itself grounds (1) when combined with the fact that currently reality is twelve hours long.

I don’t like this invocation of an ungrounded necessary truth here. I wonder if it is much better than a Merricks-style presentism where truths about past facts are ungrounded (though admittedly contingent).

Is it wrong to assert falsehoods?

Years ago, when I was thinking hard about lying, I conjectured that perhaps we simply have a moral duty not to assert falsehoods. This way, we wouldn’t need to define lying for moral purposes–a very difficult task—because the wrongs in the vicinity of lying would all end up either being the assertion of a falsehood or the doing of something that one thinks is the assertion of a falsehood (and one should do neither wrong nor that which one thinks is a wrong). Of course, often, the assertion of a falsehood would be a non-culpable wrong, because one doesn’t know that one is asserting a falsehood.

I put that conjecture aside for a long time, and then just came back to it due to an email from a friend. But it now occurred to me that I have a pretty decisive argument against the idea that it’s wrong to assert falsehoods.

Consider a case where you know that someone has a false opinion on something, but you ask them their opinion on the topic anyway, for the sake of some minor good. There are many examples of such minor goods. You want to draw someone into an interesting conversation. You are asking a student a question on an oral exam where you know that the student will get it wrong but nonetheless you feel the student should have a chance at it like their peers. You’re on a panel and you know what your co-panelist thinks—and disagree with it—but you elicit their opinion so that the audience will know it, too.

However, in doing these things, you are leading another person to do wrong, if asserting falsehoods is always wrong. Yet these cases don’t seem like cases where you do wrong.

There are two possible subcases: you intend them to assert the thing you know to be false and you merely intend them to assert their opinion whatever it might be (while knowing that their opinion is in fact incorrect). In the first subcase, the action will be much more problematic if asserting falsehoods is always wrong. Granted, you are not intending that they do wrong qua wrong, but you are intending that they assert p when you know that asserting p is wrong. This is a pretty serious case of cooperation in evil. And this kind of case does happen, and apparently innocently so: perhaps you ask the opinion of a student in a class precisely because you think this student’s opinion is p, and you would like to have p represented in the discussion. In the second subcase, you intend only the expression of opinion as such, and you can make a reasonable Double Effect defense—but only if there is a proportionate good at stake. However, given that you know that this person’s expression of opinion will be a wrongdoing, that proportionate good would have to be fairly weighty. And yet we innocently elicit such opinions without “fairly weighty” reasons.

I guess if one thought that it’s wrong to assert a falsehood, instead of asking a first-order question like “Is it wrong to steal from the rich and give to the poor?” one might ask a second-order question like “Do you think it is wrong to steal from the rich and give to the poor?” For then perhaps the other person answers truly as long as they are sincere. But I don’t think we need to do such tricks. Plus, it’s not clear that a “Do you think …?” question is really a second-order question—it may just be a social form for asking the first-order question.

More on minimal diachronic fusions and temporal parts

This is yet another attempt to answer the question of the conditions under which in an atomic world with classical mereology we have unrestricted minimal diachronic fusions, with neater assumptions (and in particular without atomism).

Say that an object is instantaneous provided that it exists at exactly one time.

Assumptions:

1. Classical (atemporal) Mereology.

2. Parthood-at-t is reflexive and transitive, and x is a part at t of y only if x and y both exist at t.

3. SO: If x and y exist at t, but x is not a part of y at t, then x has some part at t that does not overlap y at t.

4. I-Parthood Bridge: If x is instantaneous, then x is a part of y if and only if x is a part of y at the time at which x exists.

5. I-Temporality: Every part of an instantaneous object is instantaneous.

Say that a function is admissible provided that it is a non-empty function from times to sets of objects such that all the objects in f(t) exist at t. Define minimal diachronic fusions as in Sider’s paper. Say that a t-temporal part of x is a minimal diachronic fusion of the function f(t′) = x defined only for t′ = t.

Theorem: Given Assumptions 1-5, the following are equivalent:

1. Every admissible function f has a minimal diachronic fusion.

2. For every object x and every time t at which x exists, x has a t-temporal part.

3. For every object x and every time t at which x exists, there is an instantaneous part y of x that exists at t.

Notes: Since Sider in his paper explicitly accepts 1–3. I don’t love 3. It’s hard to deny 4.

I am actually a bit worried about 5, because I am worried about the possibility of objects that have both a temporal and atemporal mode of existence, and such an object could be instantaneous (i.e., its temporal mode of existence could be at only one time) while yet having a part that is atemporal. I think I might be able to handle the case of objects with a temporal and atemporal mode of existence by strengthening the concept of a minimal diachronic fusion and a temporal part to forbid the object from having an atemporal mode of existence.

In any case, the result shows that in Sider’s setting, the crucial question is whether every object has an instantaneous part at every time at which it exists.

Proof of Theorem: Clearly (A) implies (B).

Assume (B). Let y be a t-temporal part of x. This exists at t and only at t, so it’s instantaneous. It is, further, a fusion-at-t of x itself. If we can show that y is a part of x at t, then by I-Parthood Bridge, we will have y a part of x, and thus we will have (C). Suppose y is not a part of x at t. Then by SO there is a z at t that is a part of y and does not overlap x. But this contradicts fusion-at-t.

It remains to show that (C) implies (B). Assume (C). Let S be the set of all x for which there is a t and a y in f(t) such that x is an instantaneous part of y existing at t. Let z be the (atemporal) fusion of S. We need to prove that z is a minimal diachronic fusion of f.

This requires us to show that for any time t in the domain of f, z is a fusion-at-t of f(t), and that z exists ony at the times in the domain of f.

Suppose y ∈ f(t). We must show that y is a part of z at t. Suppose it’s not. Then by SO, y has a part x at t that does not overlap z at t. By (C), let u be an instantaneous part of x that exists at t. Then u ∈ S, and so u is a part of z. By I-Parthood Bridge, u is a part of z at t and u is a part of x at t. Hence x overlaps z at t, a contradiction.

Next, we must show that everything that overlaps z at t also overlaps some y ∈ f(t) at t. Suppose x overlaps z at t. Let u be a part at t of both x and z. Let v be an instantaneous part of u that exists at t. Then v is a part of u at t by I-Parthood Bridge. Thus, v is a part of z at t by transitivity. Hence, v is a part of z by I-Parthood Bridge.

So, v overlaps some w ∈ S. Let s be a common instantaneous part of v and w (the existence of s follows from (C) and I-Temporality). By I-Parthood Bridge (using the fact that a part at a time exists at that time), s exists at t, since v exists only at t. Thus s is an instantaneous part, existing at t, of some y ∈ f(t) (since s is a part of w, and w is a part of such a y). Hence s is a part of y at t by I-Parthood Bridge. Moreover, s is a part of v at t by I-Parthood Bridge, and hence by transitivity it is a part of u at t, and likewise of x at t. Thus, z overlaps y at t.

We have shown that z is a fusion-at-t of f(t).

It remains to show that z exists only at times in the domain of f. Suppose z exists at a time t. Let x be an instaneous part of z existing at t by (C). Then x overlaps some member y of S. Any member y of S is an instantaneous object existing at some time t′ in the domain of f. Now, x and y will have to have a common instantaneous part (again using (C) and I-Temporality). That instaneous part must exist at precisely t as well as at precisely t′ by I-Parthood Bridge. Thus, t = t′, and so t is in the domain of f.

Psychological continuity and my first psychological state

Assume that human psychological states depend on brain states.

On psychological continuity theories of personal identity, if a time t is such that I did not have a psychological state at t, then I did not exist at t. Now consider the first time t₁ at which I have a psychological state (for simplicity, I am assuming that the set of times at which I have a psychological state is closed at the bottom; otherwise, the argument gets more complicated). Let ψ₁ be that psychological state. I think—this is perhaps a bit controversial, but very intuitive—that whether I have a psychological state at a given time does not depend on what happens after that time. But the brain states that psychological states depend on are, plausibly, unavoidably diachronic.

Since my having ψ₁ at t₁ cannot depend on how things are after t₁, it follows that it must depend on the brain state at and before t₁.

At first sight, this looks like an obvious contradiction for the psychological continuity theorist. Since I had no psychological states before t₁, I didn’t exist before t₁, and so I couldn’t have had any brain state before t₁.

But there is a way out. While I couldn’t exist before t₁, the brain that is now mine could have. What the psychological continuity theorist can say is that my psychological state at t₁ depends largely on the state that this brain had before I came into existence (together with the instantaneous state the brain has at t₁, when I do exist). This is somewhat counterintuitive.

Another way out, of course, is to drop the physicalism, and allow for neurally-ungrounded psychological states.

Parts and priority

Schaffer says that pluralists think that parts are ontologically prior to their wholes. But this seems wrong, even as restricted to bottom-up pluralists who think the fundamental realities are microphysical.

For consider that (assuming the materialism that bottom-up pluralists typically do) I am a part of the Milky Way Galaxy (both a part-at-a-time and an atemporal part). But it seems quite wrong to say that I am ontologically prior to the Milky Way. My fundamental particles may be ontologically prior to the Milky Way, but I am not.

Further, many bottom-up pluralists accept classical mereology. But now while it seems right, if I put myself in the mindset of a typical non-Aristotelian metaphysician, to say that my atoms, molecules, cells, and organs are prior to me, it seems wrong to think that “weird scattered parts” are prior to me. Imagine for instance ordering all my molecules from bottom to up, and then take the fusion of all the even-numbered molecules. That fusion exists and is a part of me by classical mereology, but it doesn’t seem like the sort of thing that’s prior to me. It seems to be something that emerges from my simples in parallel with me at best.

If this is right, then what are the priority relations between objects for bottom-up pluralists? For unrestricted compositionalists, I think the natural suggestion is this: The simples are prior to all the wholes made of them, and that’s the only priority relation there is. This has some counterintuitive results. For instance, it seems plausible that my molecules are prior to me, or that the individual people of France are prior to France. That’s probably a bullet that the unrestricted compositionalist should bite. For one of the primary arguments for unrestricted composition is worries about vagueness and continuous series, and as soon as we start inserting some additional priority relations, we are likely to get analogous worries. But it is an uncomfortable bullet to bite, because it undercuts many of the intuitive motivations for bottom-up views, such as that the Lego blocks are prior to the Lego sculpture.

A related point applies to top-down priority monistic views, at least assuming classical mereology. Maybe the Milky Way is prior to me, but it doesn’t seem right to say that the fusion of all people whose height in inches is even is prior to me (my height in inches is even). So the top-down priority monist seems to need a complicated story of when a whole is prior to its parts.

If we have highly restricted mereology, it becomes easier to say how the priority relation runs. If, say, van Inwagen is right and all we have are simples and organisms, then we can say that parts are always prior to wholes, and be done with it, as the only cases will be that simples are prior to cells and cells to multicellular organisms. Or we can reverse it and say that multicellural organisms are prior to their cells, cells are prior to their cells (while unaffiliated cells as well as unaffiliated simples are fundamental). In either case, the story is neat and simple.