A puzzle about desire (and other propositional attitudes)

Sam and Francis each read a different newspaper article. Sam's article said that there was a newly produced element named "copernicium", and Sam came to have a desire that he expressed by saying to his agent: "I want you to buy me a pound of copernicium." Francis' article said that there was a newly produced element named "quinium", and Sam came to have a desire that he expressed by saying to his agent: "I want you to buy me a pound of quinium." Now, there is such a thing as copernicium, but the word "quinium" is pure made-up nonsense, and the article Francis read was an April Fools hoax.

What did Francis desire? It seems we can't say that he desired that his agent buy him a pound of quinium, since the italicized words fail to express a proposition, as the word "quinium" is nonsense. Maybe what Francis desires, thus, is that his agent buy him a pound of the element named "quinium". That's a perfect coherent, though unsatisfiable, desire. (But then again, practically speaking, a pound of copernicium is also not buyable—it seems that only a few atoms have been produced.) But if that's what Francis desires, then by parity it seems that what Sam desires is that his agent buy him a pound of the element named "copernicium", rather than a pound of copernicium. But that need not at all be what Francis desires—he may not care at all what the element is named.

Perhaps what we should say is that the appetitive state picks out the proposition that best matches the structure of the appetitive state. In the case of Sam, what best matches is that his agent buy him a pound of copernicium? In the case of Francis, what best matches is that his agent buy him a pound of what is called "quinium". Francis' propositional object is a less good match than Sam's, but it's in fact the best match available (let's suppose), and hence it is the desire-magnet.

In the above "what is called 'quinium'" is short for a longer and more complex description. I don't know exactly how to formulate it, but perhaps: "dthat element which is referred to as 'quinium' in this article".

Little lemma on nonmeasurable functions

Let f be a nonmeasurable function ("non-measurable random variable") on a probability space. Then there are measurable functions f^L and f^U such that f^L≤f≤g^U everywhere, and such that for every pair of measurable functions a and b such that a≤f≤b we have a≤f^L and g^U≤b almost surely.

I.e., the function f^L is the unique-up-to-null-sets largest measurable function less than or equal to f, and f^U is the unique-up-to-null-sets smallest measurable function greater than or equal to g. Basically, f^L and f^U encode all the probabilistic information available about f.

Memory and personhood

As in the last post, I am going to argue against the conjunction of the following two views:

1. CogSkill: Personhood requires developed and complex cognitive skills, of a sort that fetuses lack, and that are had by no mammals other than humans or at most are had by humans, and some other primates and/or cetaceans.
2. NonStage: When a person comes into existence, that person is a new entity that comes into existence.

In the previous post, the arguments against the view that the non-personal infant ceases to exist at the advent of personhood were decisive. So I will dismiss this option, and assume that the view is that after the advent of personhood, there are two beings, one of which existed prior to the advent of personhood and the other of which is the person.

Now, surely there are some animals, say dogs, that lack the skills posited by CogSkills have memories of having had particular experiences in the past. It is very plausible, then, that human infants prior to gaining these skills will also have some such memories. Suppose, then, that Sally is an infant, prior to the advent of the relevant complex cognitive skills, who has a memory of some experience. Surely she does not lose all of her experiential memories when she comes to gain these skills. On the contrary, surely some memories play an on-going role in developing the cognitive skills, and remain at least for a short time after the skills are present and a person has come to be present.
After personhood has been achieved, on the view we are thinking about, there will then be two subjects of some experiential memory of a pre-personal experience E. One subject will be a person and one a human animal. But only one of these two subjects will be having a veridical memory. For the person is mistaken in remembering having had the experience E. For the person never had E, since the person didn't exist when E occurred. The human animal, on the other hand, did have E, and her memory of E is veridical. The idea that here we have two subjects of memory, one veridical and one not, seems quite absurd. And this is a reason to reject the conjunction of CogSkills with NonStage.

Love, infants and personhood

Since the work of Mary Anne Warren, the following is accepted by many pro-choice philosophers:

1. CogSkill: Personhood requires developed and complex cognitive skills, of a sort that fetuses lack, and that are had by no mammals other than humans or at most are had by humans, and some other primates and/or cetaceans.

The following view is also held by a number of people, some pro-choice and some pro-life:

2. NonStage: When a person comes into existence, that person is a new entity that comes into existence.

NonStage is the denial of a view on which personhood is a stage property, like being an adolescent, a property that an entity comes to have at a particular stage of development. If NonStage is right, then I did not exist prior to being a person. Thus, if my existence began at conception, and NonStage is true, then I was a person from conception. On the other hand, if CogSkill is true, then NonStage implies that we who are persons did not exist as fetuses. CogSkill blocks the pro-life argument that fetuses are persons and hence ought not be killed. NonStage as combined with CogSkill blocks the pro-life argument that even if fetuses aren't persons, killing them deprives them of a future existence as a person, and hence is as bad as killing persons (I've defended this argument for a while; an expanded defense is here).

I will argue that the combination of CogSkill and NonStage is not a tenable view. Thus, if CogSkill is true, personhood is a stage property, and if NonStage is true, CogSkill is false.

So for a reductio ad absurdum assume CogSkill and NonStage, and consider Sally, a normal early human infant of three months of age, with a normal loving mother, Martha. Sally's cognitive skills are rather less developed than that of a normal adult dog. By CogSkill, since dogs don't have the cognitive skills needed for personhood, neither does Sally. (This is not at all a controversial conclusion among philosophers who accept CogSkill.)

Martha loves Sally, and does so quite appropriately, and indeed shold do so: it would be absurd to deny that mothers should love their babies.[note 1] But now observe an odd thing if NonStage is also true. When personhood shows up, a new entity comes into existence. And Martha, we may suppose, loves that entity, and does so appropriately, too. Call this entity "Sally₂". There are now two possibilities. Either Sally ceases to exist when Sally₂ comes into existence, or Sally continues to exist alongside Sally₂, or more precisely in exactly the same place as Sally₂ exists.

Suppose Sally ceases to exist when Sally₂ comes into existence. This is absurd. Then Martha ought to mourn Sally's demise when personhood comes into existence, and mourn it to a degree proportional to her strength of love for Sally. But while some regret for the passing of infancy may be appropriate, a mourning proportionate to the love is not appropriate. Moreover, even worse, Martha's love for Sally would give her reason to administer to Sally a drug that would prevent Sally from developing the skills needed for personhood. For personhood means the end of Sally's life on the hypothesis in question, and so Martha would be saving Sally's life by giving her this drug. And that's a horrific conclusion. In any case, I think none of the philosophers who accept CogSkill and NonStage think that Sally ceases to exist.

The remaining option for the defender of CogSkill and NonStage is that Sally continues to exist alongside Sally₂. Now, Martha should now have a maternal love for Sally₂. But she should surely also continue too love Sally. After all, parental love should be unconditional. Besides, nothing happened to Sally to make her any less lovable. On the contrary, surely Sally is more lovable, given that she now supports the personal activity of Sally₂.

So Martha will now need to love two living beings—Sally and Sally₂—with a maternal love. And that is absurd. When complex intellectual skills are gained, parents don't come to love a new living being—they love the same child, but now have additional reasons for loving that child.

If there are two living beings to love after the attainment of personhood, and only one before, then it follows that, all other things being equal, the wellbeing of a baby after the attainment of personhood should count for at least twice as much as the wellbeing of a baby prior to the attainment of personhood. And that doesn't seem right at all.

So we have reason to reject the conjunction of CogSkills with NonStage.

Weak and strong laws

I just sent this email to a colleague.  I thought it might amuse a wider audience.  Plus the idea in it is worth thinking about (though while the weak/strong terminology originated in the dream, the basic idea has been percolating for a while):

This morning, I had a dream where you told me that for some work of
mine (I don't know what) I need to read your chapter on laws of nature
in a book you're writing.  You then gave me a copy of the chapter and
it was 500 pages long. :-)  I don't think I read it, but I did have a
look at it, and I thought that in regard to the ideas you had in that
chapter--of which none were explicit in the dream--it would be helpful
to distinguish between "weak" and "strong" laws.

Anyway, I think the distinction I was getting at in my dream was
between non-accidental generalizations that are not constraining of
the activity of finite beings and non-accidental generalizations that
are constraining of it.  So, perhaps, it's a law--a *weak* law--of
biology that all life on earth descends from some ur-organism U.  It's
certainly a non-accidental generalization.  But it's a
non-constraining law: it has no "oomph" to prevent violations.  (If
chemicals near some deep-sea vent were about to produce life, the law
wouldn't stop them.)  Likewise, it *might* be a weak law that all the
matter in existence is made from particles of types P_1, P_2, ...,
P_n.  On the other hand, the law of conservation of mass-energy is a
constraining law.

Do you think weak laws in this sense really are laws?

And do you have a chapter on laws that I should read? :-)

Lying and knowledge

This is purely anecdotal, but it is my impression that while it's not uncommon for people to honestly (mistakenly) make a false assertion it is fairly uncommon for people to lyingly (and accidentally) make a true assertion. If this anecdotal data generalizes, it supports the idea that people who are lying more often know whether what they are saying is true than people who are speaking honestly. So if we had a reliable way of telling when people are lying, this would be quite helpful with getting to the truth.

Assuming my speculation is right, I wonder whether there is some level of assertion—say, speaking with confidence—such that when honest people engage in that level of assertion, they are as likely to know whether they are speaking the truth as liars are.

None of this is praise of liars. I suspect that this is largely a function of the sorts of situations in which people find lying useful.

Acting otherwise and choosing otherwise

The traditional Humean compatibilist position, prior to Frankfurt's examples, is that a deterministic agent who is free could still have acted otherwise because

1. had she wanted to, she would have acted otherwise.

But the question relevant for determination of responsibility isn't whether one could have acted otherwise (uncontroversial Frankfurt cases, where Black acts only after the choice has been made, show that), but whether one could have chosen otherwise.

I wonder if a similar conditional-type of story can be told about the ability to choose otherwise? The obvious analogue to (1) is to say that

2. had she wanted to, she would have chosen otherwise.

But actually this condition is often false despite the agent being free. For it often, perhaps even always, happens in the situation of a free choice that the agent both wants to choose A and wants to choose B, but because she cannot go for both, she must choose between them. Suppose the agent chooses A. It is surely false that had she wanted to, she would have chosen B. For she did want to choose B, and did not—what better refutation is there of the subjunctive conditional than that the antecedent is true but the consequent is false?

But presumably in this case the agent didn't on balance want to choose B. So perhaps our compatibilist-friendly alternate possibilities condition is:

3. had she on balance wanted to, she would have chosen otherwise.

That may be true, but it is obviously a very weak condition. Perhaps even a trivial one. Indeed, we might reasonably say that what is constitutive of the agent's on balance wanting to choose A is precisely that she is such that given the choice she will choose A. If so, then (3) is trivially true in every case. And even if it's not trivially true in every case, it's going to be true in too many cases of freedom-canceling brainwashing to capture the alternate possibilities intuition.

It may be wiser, then, for the compatibilist to simply retreat from affirming any kind of alternate possibilities condition on freedom. But there is a cost to that.

(I am omitting consideration of the usual finkish objections (of which Frankfurt cases are one of the earliest examples) to conditional analyses. Maybe there is some way around those.)

Why does brainwashing take away responsibility?

Everybody agrees that brainwashing can remove responsibility for the resulting actions. But how does it do that?

In some cases, brainwashing removes decisions--you just act an automaton without making any decisions. Bracket those cases of brainwashing as not to my purpose. The cases of interest are ones where decisions are still made, but they are made inevitable by the complex of beliefs, desires, habits, values, etc.--the character, for short--implanted by the brainwasher. Of these cases, some will still be not useful for my purposes, namely those where the implanted character is so distorted that decisions coming from the character are not responsible simply by reason of insanity.

The interesting case, for discussion of compatibilism, is where the character is the sort of character that could also result from an ordinary life, and if it resulted from that ordinary life, decisions flowing from that character would be ones that the agent is responsible for.

So now our question is: Why is it that when this character results from the brainwasher's activity, the agent is not responsible for the decisions flowing from it, even though if the character were to have developed naturally, the agent would have been responsible?

I want to propose a simple explanation: In the paradigmatic case when the character (or, more precisely, its relevant features) results from the brainwasher's activity, the agent is not responsible for the character (that this is true is uncontroversial; but my point is not just that this is true, but that it is the answer to the question). Decisions that inevitably flow from a character that one is not responsible for, in external circumstances that we may also suppose one is not responsible for, are decisions that one is not responsible for. When the character results from an ordinary life, one is responsible for the character. But when the character results from brainwashing, typically one is not (the case where one freely volunteered to be brainwashed in this way is a nice test case--in that case, one does have at least some responsibility).

But now we see, just as in yesterday's post, that incompatibilism follows. For what makes us responsible for a character or circumstances are decisions that we are responsible for and that lead in an appropriate way to having that character. If we are only responsible for a decision that inevitably flows from a character in some external circumstances when we are responsible for the character or at least for the external circumstances, then the first responsible decision we make cannot be one that is made inevitable by character and external circumstance.

The way to challenge this argument is to offer alternate explanations of why it is that when character comes from brainwashing one is not responsible for actions that inevitably flow from that character given the external circumstances. My proposal was that the answer is that one's isn't responsible for the character in that case. An alternate proposal is that it is the inevitability that takes away responsibility. This alternative certainly cannot be accepted by the compatibilist.

Past history, responsibility and compatibilism

Suppose that in present circumstances C, which includes both external and internal (e.g., character, mental state, etc.) circumstances I decide to take out the trash. Compatibilists (and maybe libertarians as well) have to say that the causal history of how I came to be in C is relevant to determining whether I was responsible for deciding to take out the trash. On a fairly standard view, I am responsible for the decision only if I came to C via a process that I "owned" in some important sense—a process that involved the normal self-directed formation of character.

But why is the causal history of C at all relevant to grounding my responsibility, or lack thereof, for the decision? I want to suggest a very simple answer: The causal history of C partially grounds facts about what aspect of C I am responsible for, and facts about what aspect of C I am responsible for very naturally at least partially ground facts about how far I am responsible for the decision I make in C. The causal history of C is relevant precisely because it helps determine how far I am responsible for relevant features of C, such as my character, mental state, etc.

If this is right, then the following supervenience principle is very plausible:

1. If x and y make the same decision in the same way in the same circumstances, and are responsible for these circumstances in exactly the same way (degree, etc.), then x and y are responsible for their decision in exactly the same way (degree, etc.).

It doesn't matter how x and y got to C, as long as they ended up having the same responsibility facts in C. In particular, if there is some aspect of C that they aren't at all responsible for, the causal history of that aspect is irrelevant to determining how far they are responsible for their decision. For instance, suppose that both x and y have IQs of 124, but x got to that IQ because her mother forced her to various puzzles when she was a very small child (and hence not yet responsible for her actions) while y got to it purely for genetic reasons. Then the history of how they got to their IQs doesn't matter.

But while (1) is very plausible, it has a very controversial consequence:

2. If x and y make the same decision in the same way in the same circumstances, and neither is in any way responsible for the circumstances, and y is in no way responsible for the decision, then x is in no way responsible for the decision.

Now, if I am responsible for some decision, then there was a first decision that I was ever responsible for. Moreover, plausibly:

3. I can't be responsible for anything at all without being or having been responsible for some decision.

So prior to the first decision that I was ever at all responsible for, I was not responsible for anything at all. But then (2) shows that anybody in exactly the same circumstances as I was when I made my first decision, who chose in exactly the same way, would be responsible for the decision.

Suppose my first responsible decision is made in circumstances at t₀. Imagine a swamp being that comes into existence, out of the random confluence of swamp matter, at t₀ in exactly the same internal and external state as I had in t₀ (so an environment might need to come into existence from the swamp). If determinism is true, that swamp being is not responsible for the decision he makes. This is generally acknowledged by compatibilists, since compatibilists insist that an appropriate history is needed for freedom given determinism (without determinism, it is plausible that no history is needed; if x comes into existence at t₀, with a sufficient understanding of the moral features of options A and B, and chooses between A and B in the way libertarians say that choices are made, then x may well be free). But then by (2) neither was I responsible for the decision in the same circumstances, since the swamp being and I are alike in not being responsible for any aspect of the circumstances at t₀. And so I wasn't responsible for my first responsible choice, which is a self-contradiction. So determinism needs to be rejected.

I think (3) is a weak point in the argument. But the reliance on (3) can be eliminated when we strengthen (1) to apply to events other than decisions.

A problem for Lewis's account of counterfactuals

Let's say I have a bag of fifty ordinary chrome steel balls. They are of the same size up to a tolerance of 0.01 mm, but they do exhibit minor size variations below that tolerance. So one of these steel balls is smallest. On Lewis-type accounts of counterfactuals, we have to say that:

1. If one of the balls were made of brass, it would be the smallest of them.

For worlds where the smallest of the balls is made of brass are more like our world than worlds where another of the balls is made of brass (keeping everything else equal) since the area of spatiotemporal mismatch is smaller when it is the smaller ball that is made of brass.

But while we intuitively think that (1) might turn out to be true, it shouldn't turn out to be true simply because of such size considerations.

This is a non-temporal version of the coat thief problem (see, e.g., p. 42 here).

At least on average, a human life is good

A stranger is drowning. You know nothing about the stranger other than that the stranger is drowning. You can press a button, and the stranger will be saved, at no cost to yourself or anybody else. What should you do?

Of course you ought to press the button. That's simply obvious.

But it wouldn't be obvious if at least on average a human life weren't good, weren't worth living. If on average, a human life were bad, were not worth living, you would have to seriously worry about the likely bad future that you would be enabling by saving the stranger. It still might well be right to pull out the stranger, but it wouldn't be obvious. And if on average a human life were neutral, it wouldn't be obvious that it's a duty.

So our judgment that obviously a random stranger should be saved commits us to judging that at least on average a human life is good (or at least will be good).

Now suppose we get exactly one of the following pieces of information:

• The stranger is a member of a downtrodden minority.
• The stranger is currently a hospital patient (and is drowning in the bathtub of the hospital room).
• The stranger's mother did not want him or her to be conceived.
• The stranger is economically in the bottom 10% of society.

None of these pieces of information makes it less obvious that we should save the stranger's life. This judgment, then, commits us to judging that on average the life of a member of a downtrodden minority, or of a hospital patient or of someone whose mother did not want him or her to be conceived, or of someone economically in the bottom decile is at least on average good.

Suppose, however, that we get some more specific information, such as that the stranger is suffering horrendous pain that cannot in any way be relieved, or that the stranger will tomorrow be tortured to death. It may still be right to save the stranger, but it is no longer obvious that that's the right thing to do. So the on-average judgments above aren't simply derivative from a general judgment that all human life is worth living or from a deontic judgment that any drowning person who can easily be saved should be saved.

So, not only is the average human life worth living, but the average human life in conditions of significant adversity (being a downtrodden minority member, etc.) is worth living.

Now, I happen to think that every human life is worth living. But in this post I've only argued for a weaker claim.

The holiness of the Church and clerical scandals

Does gravely immoral activity by the clergy detract from the holiness of the Church as it is on earth, the Church militant? It sure seems so. But I want to argue, very speculatively (and I will withdraw the claim if it turns out that the Church teaches otherwise), that it directly detracts no more—or at least not significantly more—than equally gravely immoral activity by similar numbers of laity would.

Consider the three features we desire the Church as found on earth to have: doctrinal orthodoxy, liturgical integrity and holiness of life.

The doctrinal orthodoxy and liturgical integrity of the clergy does indeed especially contribute to the doctrinal orthodoxy and liturgical integrity of the Church. If a priest or especially a bishop is unorthodox, all other things being equal, that in itself detracts more from the orthodoxy of the Church on earth than when a lay person is unorthodox, simply because of the teaching role of the clergy. Similarly, if a priest or bishop engages in liturgical anarchy, say by changing some prayers at Mass, that detracts from the liturgical integrity of the Church more than if a lay person does so, all other things being equal.

But when a deacon, priest or bishop (including a pope) is wicked, that no more (and no less) directly detracts from the holiness of the Church than when a non-cleric person is wicked, when the degree of wickedness is the same. We can see this by considering the happier flip-side. Think of a non-cleric like St Teresa of Avila (she was a nun, of course, but a nun is a non-cleric[note 1]) and a priest like St John of the Cross. The holiness of their lives directly contributed to the holiness of the Church. But it would, I think, be mistaken to say that St John's holiness contributed more, or was a more central contribution, than St Teresa's just because St John was a priest and St Teresa was not. To say that would be to engage in clericalism, and is perhaps a species of the same error that leads to Donatism. The clergy's activity makes a special constitutive contribution to the Church's orthodoxy and liturgical integrity. But a layperson's holiness is just as constitutive of the holiness of the Church as the holiness of a deacon, priest or bishop. Mary makes a greater direct contribution to the holiness of the Church than any deacon, priest or bishop—not counting Christ the High Priest—ever did or would.

Of course, wickedness in a deacon, priest or bishop (and especially when the bishop is pope) typically has a greater negative effect on the Church's holiness, because it is more likely to scandalize others, leading them either to imitate the wickedness or abandon the faith. This indirectly detracts from the Church's holiness.

Suppose every single Catholic priest next year committed some particular grave and scandalous sin. That would be a terrible thing, would have a very unfortunate negative effect on the Church, and may God preserve us from this disaster. But it would no more directly detract from the Church's holiness than if some other group comprising 0.04% of the world's Catholic population committed an equally grave sin.

That said, a sin that is otherwise of the same sort may be graver when committed by a cleric, because (a) the cleric bears a responsibiity for avoiding the further negative effects and (b) is less likely to be excusable through ignorance. The above assumes we are dealing with sins of equal gravity.

Christ promised that the Church would be holy. The above argument shows that an argument based on clerical crimes that the Catholic Church cannot be Christ's Church because Christ's Church is holy is no stronger than argument based on equal numbers of non-clerical crimes would be. But an argument based on the crimes committed by non-clerics would fail: we do not expect the Church's holiness to imply the sinlessness of her members. The Church while holy as a body—the body of Christ—is yet a Church for sinners who need Christ's reforming grace. Thus the argument based on clerical crimes also fails.

And then, of course, there is always Boccaccio's argument.

From ease to counterfactuals?

Consider the concept of how easy it is for a proposition to be made true, given how things are. It is by far easiest for propositions that are already true: nothing more needs to happen. It is hardest for self-contradictory propositions, like that Socrates is not Socrates: there is no way at all for it to happen. Contingently false propositions that require changes that go far back in time are going to be harder to be made true than ones that don't. And we can talk of the ease of p being made false as just the ease of not-p being made true. So, we can offer this account of counterfactuals:

• p→q holds if and only if it is easier for p to be made true than for the material conditional p⊃q to be made false.

This yields the Lewis-Stalnaker account of counterfactuals provided that we stipulate that a is easier to be made true than b if and only if there is a world where a holds which is closer than every world where b holds.

But we need not make this stipulation. We might instead take the easier to be made true relation as more fundamental. (And while we might define a closeness relation in terms of it—say, by saying that w₁ is closer than w₂ iff <w₁ is actual> is easier to be made true than <w₂ is actual>—depending on which axioms easier to be made true satisfies, that might not yield an account equivalent to the Lewis-Stalnaker one.)

On some assumptions, this is a variant of the central idea in yesterday's post.

A sufficient condition for a subjunctive conditional

Start with the idea of grades of necessity. At the bottom, say[note 1], lie ordinary empirical claims like that I am typing now, which have no necessity. Higher up lie basic structural claims about the world, such as that, say, there are four dimensions and that there is matter. Perhaps higher, or at the same level, there are nomic claims, like that opposite charges attract. Higher than that lie metaphysical necessities, like that nothing is its own cause or that water is partly composed of hydrogen atoms. Perhaps even higher than that lie definitional necessities, and higher than that the theorems of first order logic. This gives us a relation: p<q if and only if p is less necessary than q.

Let → indicate subjunctive conditionals. Thus "p→q" says that were it that p, it would be that q. Let ⊃ be the material conditional. Thus "p⊃q basically says that p is false or q is true or both. Then, the following seems plausible:

1. If ~p<(p⊃q), then p→q.

I.e., if the material conditional has more necessity than the denial of its antecedent, the corresponding subjunctive conditional holds.

Suppose it's a law of nature that dropped objects fall. Then the material conditional that if this glass is dropped, then it falls is nomic and hence more necessary than the claim that this glass is not dropped, and the subjunctive holds: were the glass dropped, it would fall.

Moreover, the subjunctives that (1) can yield hold non-trivially, if there are grades of necessity beyond metaphysical necessity (on my view, those are somewhat gerrymandered necessities), and this yields non-trivial per impossibile conditionals. Let p be the proposition that water is H₃O, and let q be the proposition that a water molecule has four atoms. Then ~p<(p⊃q), because p⊃q is a definitional truth while ~p is a merely metaphysical necessity. Hence were p to hold, q would hold: were water to be H₃O, a water molecule would have four atoms.

I wonder if the left-hand-side of (1) is necessary for the non-trivial holding of its right-hand-side.

Do we need the concept of laws of nature?

Laws of nature do two things for us. They delineate what is fixed beyond the power of physical beings and they are universal generalizations that explain their instances.

But there is no need for these two functions of laws to be united in a single concept. There are explanatory universal generalizations that do not limit powers. For instance all life on earth is based on DNA or RNA. This is an explanatory generalization, but it is not limiting of powers: there is nothing physically or biologically impossible about producing life with neither DNA nor RNA as far as we know.

One might link the two functions by using the power-limiting aspect to ground the explanatory aspect. Why does this particle not move faster than at the speed of light? Because no physical being can make it so that (and no non-physical being did).

But it is difficult to explain the power-limiting aspect of laws. Humeans basically just give up on it. A main alternative is to take it as primitive.

But why not just give up on the concept of laws and keep separate the ideas of limitations on powers and of explanatory generalizations?

The limitations on powers are just that: physical things not having the power to do such-and-such.

And what makes the explanatory generalizations explanatory on this view isn't some sui generis nomic explanation, but simply one of the other accepted forms of explanation. Why does the platypus and the gecko have DNA? Because they evolved from a common ancestor that did. Once we fill out a causal story we have a perfectly fine explanation here.

Now it's going to be harder to use one of the non-nomic forms of explanation in the case of something more fundamental like the conservation of mass-energy. But not for the theist who can say that God had as such willed that mass-energy be conserved, since then explanation by subsumption under the conservation law gets its explanatory oomph from a standard mode of explanation, namely the agential one.

It is tempting to try to combine the notions of power-limitation and explanatory generalization into the concept of a law. I doubt this will work. The universal generalization that all who die with their will full of charity will see God is power-limiting--no one can stop it--and explanatory. But it's not a law of nature.

My suggestion is to keep the notions separate as separate as their tasks.