A potential explanation why we don't observe violations of the PSR

A standard puzzle for the opponent of the Principle of Sufficient Reason (PSR) is to explain why we don’t observe objects coming into existence ex nihilo. Here is a thought that I think hasn’t been explored enough. Maybe when an object comes into existence ex nihilo, it is unlikely that the object would end up being spatiotemporally related to things already in existence. In other words, perhaps the typical object coming into existence ex nihilo forms a new universe, not spatiotemporally related with any other universe.

If this is right, then the opponent of the PSR should take multiverse hypotheses very seriously.

That said, such random multiverse hypotheses lead to very compellingly sceptical scenarios.

Physicalism, persons, fission and eliminativism

People are philosophically unhappy about nonlocality in quantum mechanics. It is interesting to me that there is an eerily similar nonlocality on standard psychological theories of personal identity. For on those theories:

1. You survive if your memories survive in one living person.

2. You perish if your memories fission between more than one living person.

Now imagine that your brain is frozen, the data from it is destructively read, and then sent to two different stations, A and B, located in opposite directions five light minutes away from your original brain. At each station, a coin is simultaneously flipped (say, in the rest frame of your original brain). If it’s heads (!), the data is put into a freshly cloned brain in a vat, and if it’s tails, the data is deleted.

On a psychological theory, if both coins land heads you perish by (2). But if exactly one coin lands heads, you survive at that station. So whether you exist at one station depends on what happens simultaneously (according to one frame) at a station ten light minutes away.

Note, however, that this is not explicable via quantum nonlocality, because quantum nonlocality depends on entanglement, and there is no relevant entanglement in this thought experiment. It would be a nonlocality beyond physics.

I think one lesson here is that ostensibly physicalist or physicalist-friendly theories of persons or minds can end up sounding oddly dualist. For if dualism were true, it wouldn’t be utterly surprising if facts about where your soul reappears could have a faster-than-light dependence on far away events, since souls aren’t governed by the laws of physics. Similarly, on functionalism plus psychological theories of personal identity, you could move between radically different physical embodiments or even between a physical embodiment and a nonphysical realization. That, too, sounds rather like what you would expect dualism to say.

If I were a physicalist, I would perhaps be inclined to be drawn by these observations towards eliminativism about persons. For these observations suggest that even physicalist pictures of the person may be too deeply influenced by the dualist roots of philosophical and theological reflection on personhood. If these roots are seen as intellectually corrupt by the physicalist, then it should be somewhat attractive to deny the existence of persons.

Another problem with evolutionary accounts of teleology

The crucial thought behind evolutionary accounts of proper function or teleology is that organisms succeed in reproducing because they are fulfilling a function, and wouldn’t have reproduced otherwise. In a paper with Koons, I offer a Great Grazing Ground objection to all such accounts.

Here, I want to offer a perhaps neater objection. Imagine Twin Earth just like Earth, with a biological history just like ours. But there is an extremely powerful alien, akin to Frankfurt’s counterfactual intervener, who has a script for all the details of biological history on that planet. That script, completely by chance, matches all the events on both Twin Earth and Earth. But the counterfactual intervener has the following immovable policy: if there is any deviation from the script on Twin Earth, the alien restores conditions to the same ones that would have resulted according to the script. Moreover, the alien’s restoration would occur before there is any deviation in reproduction or survival. But, by good fortune, no intervention is ever needed: everything actually follows the script.

Imagine, for instance, that a bird is attacked by a predator. On Earth, it escapes on its wings and reproduces. The same happens on Twin Earth. But on Twin Earth, had the bird not flown, the alien would have intervened, moved the bird out of danger, and then restored everything to the post-flight situation in the script. Consequently, on Twin Earth, it is false that had the bird not flown, it wouldn’t have reproduced. Indeed, apart from trivial cases like “Had x not reproduced, it wouldn’t have reproduced”, on Twin Earth the counterfactuals allegedly defining proper function or teleology hold. Yet events on Twin Earth are just as on Earth, and the alien doesn’t do anything but watch. And it is deeply implausible that simply by watching the alien destroys proper function or teleology.

An asymmetry between physical and emotional pain

Here is a puzzling asymmetry. It seems that:

• Typically, we should seek to remove serious physical pains, even when these pains are normal and we are unable to alleviate the underlying problem.

• Typically, when emotional pains are serious but normal, we should not seek to remove them, except by alleviating the underlying problem.

Thus, if one has lost a leg in an accident, it seems one should be given pain killers, whether or not the leg can be reattached, and even if one’s degree of pain is proper to the loss. But if one has lost a friend, the grief should not be removed, unless it can be done by restoring the friend (there is, after all, more than one sense of “lost a friend”).

Structurally, it seems that leg and friend cases are parallel: In both cases, there is a harm, which it is normal to perceive painfully.

Solution 1: The difference is due to instrumental factors. In the case of the loss of a friend, the pain helps one to restructure oneself mentally in the tragic new circumstances. In the case of the loss of a leg, however, assuming one is already seeking medical attention, the pain is unlikely to lead to any further goods.

Solution 2: Due to the Fall, typically our physical pains are excessive. We feel more pain for a physical loss than we should given that our primary ends are not physical in nature. The appearance of asymmetry is due to an equivocation on “normal”: the kind of pain we feel at physical damage is statistically normal for fallen human beings, but is not really normal. On the other hand, when we talk of normal emotional pains, there the pains are either really normal, correctly grasping the tragedy of the situation, or else they are actually deficient. (A standard theological intuition is that Jesus suffered mentally more at evils than any of us, because his virtue made him more acutely aware of the badness of these evils.)

Constructive presence

This morning, I was reading the Georgia Supreme Court’s Simpson v. State (1893) decision on a cross-state shooting, and loved this example, which is exactly the kind of example contemporary analytic philosophers like to give: "a burglary may be committed by inserting into a building a hook, or other contrivance, by means of which goods are withdrawn therefrom; and there can be no doubt that, under these circumstances, the burglar, in legal contemplation, enters the building."

Dualist eliminativism

Eliminativism holds that our standard folk-psychological concepts of mental functioning—say, thoughts, desires, intentions and awareness—have no application or are nonsense. Usually, eliminativism goes hand in hand with physicalism and scientism: the justification for eliminativism is the idea that the truly applicable concepts of mental functioning are going to be the ones of a developed neuroscience, and it is unlikely that these will match up our current folk psychology.

But we can make a case for eliminativism on deeply humanistic grounds independent of neuroscience. We start with the intuition that the human being is very mysterious and complex. Our best ways of capturing the depths of human mental functioning are found neither in philosophy nor in science, but literature. This is very much what we would expect if our standard concepts did not correctly apply to the mind’s functioning, but were only rough approximations. Art flourishes in limitations of medium, and the novelist and poet uses the poor tool of these concepts to express the human heart. Similarly, the face expresses the soul (to tweak Wittgenstein’s famous dictum), and yet what we see in the face is more complex, more mysterious than what we express with our folk psychological vocabulary.

There is thus a shallowness to our folk-psychological vocabulary which simply does not match the wondrous mystery of the human being.

Finally, and here we have some intersection with the more usual arguments for eliminativism, our predictive ability with respect to human behavior is very poor. Just think how rarely we can predict what will be said next in conversation. And even our prediction of our own behavior, even our mental behavior, is quite poor.

The above considerations may be compatible with physicalism, but I think it is reasonable to think that they actually support dualism better. For on physicalism, ultimately human mental function would be explicable in the mechanistic terminology of physics, and my considerations suggest an ineffability to the human being that may be reasonably thought to outpace mechanistic expressions.

But whether or not these considerations in fact support dualism over physicalism, they are clearly compatible with dualism. And so we have a corner of logical space not much explored by (at least Western) philosophers: dualist eliminativism. I do not endorse this view, but in some moods I find it attractive. Though I would like it to come along with some kind of a story about the approximate truth of our ordinary claims about the mind.

Disembodied existence and physicalism

Consider the following standard Cartesian argument:

1. I can imagine myself existing without a body.

2. So, probably, I can exist without a body.

3. If I can exist without a body, I am not physical.

4. So, I am not physical.

It is my impression that the bulk of physicalist concern about this argument focuses on the inference from (1) to (2). But it seems to me that it would be much more reasonable for the physicalist to agree to (2) but deny (3). After all, our best physicalist theory of the person is functionalism combined with a psychological account of personal identity. But on that theory, for me to exist without a body all that’s needed is for my memories to be transfered into a spiritual computational system which is functionally equivalent to my current neural computational system, and that seems quite plausibly possible.

The physicalist need not claim that I am essentially physical, only that I am in fact physical, i.e., that in the actual world, the realizer of my functioning is physical.

A pedagogical universe

Our science developed over milennia, progressing from false theory to less false theory. Why did we not give up long ago? I take it this is because the false theories, nonetheless, had rewards associated with them: although false, they allowed for prediction and technological control in ways that were useful (in a broad sense) to us.

Thus, the success of our science depends not just on a “uniformity of nature” on which the correct fundamental scientific theories are elegant and uniform. Most of our historical progress in physics has not involved correct scientific theories—and quite possibly, we do not have any correct fundamental theories in physics yet. The success of our science required low-hanging fruit for us to pick along the way, fruit that would guide us in the direction of truth.

We can imagine worlds where the ultimate physics requires an enormous degree of sophistication (much as we expect to be the case in our world) and there is little in the way of low-hanging fruit (except maybe for the lowest level of low-hanging fruit, involving the regularities needed to enable evolution of intelligence in the first place) in the form of approximately true theories that rewards us with prediction and control so that beings like us would just give up on science. Our world is better than that.

Indeed, our world seems to be pedagogically arranged for us, arranged to gradually teach us science (and other things), much as we teach our children, with intellectual and practical rewards. There is a design argument for the existence of God from this (closely related to this one).

Deceit and Double Effect

Suppose you inform me of something true, p, and as a result I come to believe it. Then very likely you’ve deceived me about something!

For there is surely some falsehood q that I believed previously with a high confidence. But presumably I did not believe the conjunction p&q before I got your information, since I didn’t believe p. But now that you’ve informed me of p, I am likely to believe p&q, and yet that is a falsehood.

Sometimes this argument doesn’t work (maybe sometimes I believed p&q when I didn’t believe q, and maybe sometimes my belief in p is sufficiently marginal that I still don’t believe p&q), but most of the time it does.

This means that we are typically deceiving people all the time in conversation! This sounds bad, unless we make a distinction between foreseeing and intending. You can foresee (now that you saw the above argument) that whenever you inform me of something this is likely to deceive me about something else. But merely foreseen deceit counts for very little morally as long as you don’t intend the deceit.

Could the PSR be contingent?

The Principle of Sufficient Reason (PSR) says that every contingent truth has an explanation. Most people who accept the PSR think it is a necessary principle. And there is good reason, because it seems more like a candidate for a fundamental necessary truth than a merely contingent fact. And epistemically, if the PSR is contingent, it is hard to see why we should think ourselves lucky enough for it to be true.

All that said, it is interesting to investigate the question a bit more. So, let’s suppose the PSR is contingently true. Then according to the PSR, the PSR has an explanation, like every other contingent truth. What could the explanation of the PSR be like?

Since we’ve assumed the PSR to be contingent, the explanation can’t simply involve derivation of the PSR from necessary metaphysical principle.

The explain a contingent PSR is to explain why no contingent unexplained thing has happened.

Here is one suggestion. Perhaps there is a necessary being which has the power to prevent the existence of contingent unexplained events. This necessary being freely, but with good reason that the necessary being necessarily has, chooses to exercise this power. Thus, the explanation of why no contingent unexplained thing has happened is that the necessary being freely chose to prevent all such things. And the necessary being’s free choice is explained by reasons.

I am not sure what I think of the plausibility of a hypothesis of a being as having the power to prevent things from popping into existence causelessly if such popping is otherwise metaphysically possible.

Here is another much less metaphysically loaded attempt. It seems to me that whether one accepts the PSR or not, one should accept instances of the following kind of explanatory schema for contingent events E:

1. Event E did not happen because there is no explanation of E.

If the PSR is necessarily true, then the fact that there is no explanation of E entails that E did not happen. However, I think we should accept instances of (1) even if the PSR is contingently true and even if it is not true at all. In those cases, that there is no explanation of E may not entail that E did not happen, but we shouldn’t think that explanations must entail the events they explain. (If we thought that, we would have to reject most scientific explanations.)

Now imagine we have an infinite list of all possible contingent events that could happen but did not happen, E₁, E₂, ..., and an infinite list of all contingent events that did happen, F₁, F₂, .... We can then say:

2. The PSR is true because E₁ did not happen, E₂ did not happen, E₃ did not happen, while on the other hand F₁, F₂, ... did happen.

And why did E_i not happen?

3. E_i did not happen because there is no explanation of E_i.

And of course each of the F_i does have an explanation, because the PSR is, we have assumed, true.

This seems like an explanation of the contingent truth of the PSR.

Both options seem a bit fishy, though. I can’t say exactly what’s wrong with them, though.

A cosmological argument from a PSR for ordinary truths

Often in cosmological arguments the Principle of Sufficient Reason (PSR) is cleverly applied to vast propositions like the conjunction of all contingent truths or to highly philosophical claims like that there is something rather than nothing or that there is a positive contingent fact. But at the same time, the rhetoric that is used to argue for the PSR is often based on much more ordinary propositions, such as Rescher’s example of an airplane crash which I re-use at the start of my PSR book. And this can feel like a bait-and-switch.

To avoid this criticism, let’s suppose a PSR limited to “ordinary” propositions, i.e., the kind that occur in scientific practice or daily life.

1. Necessarily we have the Ordinary PSR that every contingent ordinary truth has an explanation. (Premise)

2. That there is an electron is an ordinary proposition. (Premise)

3. It is possible that there is exactly one contingent being, an electron. (Premise)

4. Necessarily, if no electron is a necessary being, then any explanation of why there is an electron involves the causal activity of a non-electron. (Premise)

5. Let w be a possible world where there is exactly one contingent being, an electron. (By 3)

6. At w, there is an explanation of why there is an electron. (By 1, 2 and 4)

7. At w, there is a non-electron that engages in causal activity. (By 4, 5 and 6)

8. At w, every non-electron is a necessary being. (By 5)

9. At w, there is a necessary being that engages in causal activity. (By 7 and 8)

10. So, there is a necessary being that possibly engages in causal activity. (By 9 and S5)

So, we have a cosmological argument from the necessity of the Ordinary PSR.

Objection: All that the ordinary cases of the PSR show is that actually the Ordinary PSR is true, not that it is necessarily true.

Response: If the Ordinary PSR is merely contingently true, then it looks like we are immensely lucky that there are no exceptions whatsoever to the Ordinary PSR. In other words, if the Ordinary PSR is merely contingently true, we really shouldn’t believe it to be true—we shouldn’t think ourselves this lucky. So if we are justified in believing the Ordinary PSR to be at least contingently true, we are justified in believing it to be necessarily true.

Preliminary notes on Cartesian scoring rules

Imagine an agent for whom being certain that a proposition p is true has infinite value if p is in fact true. This could be a general Cartesian attitude about all propositions, or it could be a special attitude to a particular proposition p.

Here is one way to model this kind of Cartesian attitude. Suppose we have a single-proposition accuracy scoring rule s(r, i) which represents the epistemic utility of having credence r when the proposition in fact has truth value i, where i is either 0 (false) or 1 (true). The scores can range over the whole interval [ − ∞, ∞], and I will assume that s(r, i) is finite whenever 0 < r < 1, and continuous at r = 0 and r = 1. Additionally, I suppose that the scoring rule is proper, in the sense that the expected utility of sticking to your current credence r by your own lights is at least as good as the expected utility of any other credence. (When evaluating expected utilities with infinities, I use the rule 0 ⋅ ±∞=0.)

Finally, I say the scoring rule is Cartesian with respect to p provided that s(1, 1)=∞. (We might also have s(0, 0)=∞, but I do not assume it. There are cases where being certain and right that p is much more valuable than being certain and right that ∼p.)

Pretty much all research on scoring rules focuses on regular scoring rules. With a regular scoring rule, is allowed to have an epistemic utility −∞ when you are certain of a falsehood (i.e., s(1, 0)= − ∞ and/or s(0, 1)= − ∞), the possibility of a +∞ epistemic utility is ruled out, and indeed epistemic utilities are taken to be bounded above. Our Cartesian rules are all non-regular.

I’ve been thinking about proper Cartesian scoring rules for about a day, and here are some simple things that I think I can show:

1. They exist. (As do strictly proper ones.)

2. One can have an arbitrarily fast rate growth of s(r, 1) as r approaches 1.

3. However, s(r, 1)/s(r, 0) always goes to zero as r approaches 1.

Claim (2) shows that we can value near-certainty-in-the-truth to an arbitrarily high degree, but there is a price to be paid: one must disvalue near-certainty-in-a-falsehood way more.

One thing that’s interesting to me is that (3) is not true for non-Cartesian proper scoring rules. There are bounded proper scoring rules, and then s(1, 1)/s(1, 0) can be some non-zero ratio. (Relevant to this is this post.) Thus, assuming propriety, going Cartesian—i.e., valuing certainty of truth infinitely—implies an infinitely greater revulsion from certainty in a falsehood.

A consequence of (2) is that you can have proper Cartesian scoring rules that support what one might call obsessive hypothesis confirmation: even if gathering further evidence grows increasingly costly for roughly the same Bayes factors, given a linear conversion between epistemic and practical utilities, it could be worthwhile to continue to continue gathering evidence for a hypothesis no matter how close to certain one is. I don’t think all Cartesian scoring rules support obsessive hypothesis confirmation, however.

A simple moral preference circle with infinities

Here is a simple moral preferability circle. Suppose there are infinite many human strangers numbered ..., −3, −2, −1, 0, 1, 2, 3, ... all of whom, in addition to two cats, are about to drown. Consider these options:

A. Save the strangers numbered 0, 1, 2, ....

B. Save the strangers numbered −1, −2, −3, ... and one cat.

C. Save the strangers numbered 1, 2, 3, ... and both cats.

Option B beats Option A: If we had to choose between strangers 0, 1, 2, ... and strangers −1, −2, −3, ..., we should clearly be indifferent. Toss in the cat, and now it looks like we have a reason to save the second set of strangers.

Option C beats Option B: If we had to choose between strangers −1, −2, −3, ... and strangers 1, 2, 3, ..., we should be indifferent. But now observe that in Option C one more cat is saved, and it sure looks like we should go for C.

Option A beats Option C: Option A replaces the two cats with stranger 0, and surely it’s better to save one human over two cats.

If you don’t think we have moral reasons to save cats, replace saving the cats from drowning with saving two human strangers from ten minutes of pain.

I am now toying with an intuitively very appealing solution to problems like the above: we have no moral rules in such outlandish cases. I think this can be said on either natural law or divine command theory. On natural law, it is unsurprising if our nature does not provide guidance in situations where we are far from our natural environment. On divine command theory, why would God bother giving us commands that apply to situations so far from ones we are going to be in?

Musings on personal qualitative identity

Consider the popular concept of “identity”, in the sense of what one “identifies with/as”. Let’s call this “personal qualitative identity”. We can think of someone’s personal qualitative identity as a plurality of properties that the person correctly takes themselves to have and that are important, in a way that needs explication, to the person’s image of themselves.

There are a few analytic quibbles we could ask about what I just said. Couldn’t someone have properties they do not actually have as part of their identity? Surely there are lots of people who have excellences of various sorts at the heart of their self-image but lack these excellences. I don’t want to count mistakenly self-attributed properties as part of a person’s identity, because there is a kind of respect we have towards another’s personal qualitative identity that requires it to be factive. In these cases, maybe I would say that the person’s taking themselves to have the excellences is a part of their identity, but not the actual possession of the excellences.

In an opposed criticism, one might want to require the person to know that they have the properties, and not merely to correctly think they have them. But that is asking for too much. Suppose Alice identifies as ethnically Slovak, on the basis of misreading the handwriting on an old geneological document that actually said she was Slovenian. But suppose the document was wrong, and Alice in fact is Slovak rather than Slovenian. Surely it is correct to say that being Slovak is a part of her identity, even though Alice does not know that she is Slovak.

But the really central and difficult thing in the concept of personal qualitative identity is the kind of “self-identificational” importance that the person attaches to them. We have plenty of properties that we correctly believe, and even know, ourselves to have, but which lack the kind of first-person importance that makes them a part of the personal qualitative identity. There is a contradiction in saying: “It is a part of my (personal qualitative) identity that I am F, but I don’t care about being F.”

In particular, the properties that are a part of the personal qualitative identity enjoy an important role in motivating the person’s actions. Of course, any property one takes oneself to have can motivate action. I don’t much care that my eyes are blue, but my self-attribution of the blueness of my eyes motivates me to write “blue” under “eye color” on government forms. But the properties that are a part of the personal qualitative identity enter into one’s motivations more often, in wider range of contexts, and in a way more significant to oneself.

There is an ambiguity here, though. When one is motivated to act a certain way by a property in one’s identity, is one motivated by the fact that one has the property or by the fact that one identifies with that property? I want to suggest that the right answer should often be the first-order one. It is my duty as a parent to provide for my children, and I identify with my having that duty. But whether I identify with having that duty or not is irrelevant to the reason-giving force of that duty: if I didn’t identify with that duty, I would be just as obligated by it. Indeed, it seems to me to be a failure when I am moved not by my duty but by my identification with the duty. The thought “this is my duty” can be a healthy thought, but adding “and I identify as having it” is morally a thought too many, though sometimes, morally deficient as we are, we need the kick in the behind that the extra thought provides.

In fact, I think there is an interesting moral danger that I think has not been much talked about. If the property F is in my personal qualitative identity, then I also have the higher order property I_F of having F in my identity. Logically speaking, this higher order property may or may not itself be a part of my identity. While in some cases it may be appropriate for I_F to be a part of my identity in addition to F, in most if not all of those cases, I_F should be a less central part of my identity than F, and in many cases it should not be a part of my identity at all. This is because the actual rational motivational force is often largely exhausted by my one’s having F, while a focus on I_F adds an illusion of additional rational force.

In general, I think that it is important to be critical about our personal qualitative identities. There are substantive and personally important normative questions about which of one’s properties should enter into the identity. A failing I know myself to have is that I end up promoting generalizations about myself into parts of my personal qualitative identity by having them play too strong a motivational role. That “I am the kind of person who ϕs” should not play much of a role in my deliberations. What matters is whether ϕing, on a given occasion, is a good or a bad thing. Yet I find myself often deciding things on the basis of being, or not being, a certain kind of person. That's deciding on the basis of navel-gazing.

I find the following norm appealing: a property F should be a part of my identity if and only if independently of my attitude to F, my having F has significant rational importance to a broad range of my deliberations. But this austere norm is probably too austere.

Derivative value

Some things have derivative value. One kind of derivation is from whole to parts: a stone can have a special value by virtue of being a part of something of great significance, say a temple. Another kind of derivation is from parts to whole: a golden statue has a value deriving from the value of its atoms. Yet another kind is from friend to friend: if I do good directly to a friend of yours, I benefit you as well.

The distinction between derivative and original value is orthogonal to that between instrumental and non-instrumental value, and probably also to that between intrinsic and extrinsic value.

It is easy to create puzzles with derivative value, because derivative value is not simply additive and double counting must be avoided. Imagine a golden statue made by someone with minimal artistic skill. The maker of that statue then produced something literally worth its weight in gold, and yet they added almost no value to the world, because almost all of the value of the poorly made statue is derivative. Melting down a golder statue worth exactly its weight in gold does no harm to the world! Similarly, dissolving a ten-member committee need be no more harmful than dissolving a five-member one.

If two people are drowning, one friendless and one with ten friends, perhaps there is additional reason to save the one with ten friends, though the point is not clear. But if there is additional reason, it does not scale linearly with the number of friends. If someone had a thousand of friends, that needn’t create much more a reason to save them than if they had a hundred, I suspect.

It is tempting to initially think of derivative value as a faint shadow of original value. Sometimes this is true: the death of Alice considered as a derivative harm to her distant friends is a mere shadow of the badness of that death considered as a harm to Alice. But sometimes it’s not true: the death of Alice considered as a derivative harm to her closest friends approaches the original badness of that death considered as a harm to her. And the inartistic golden statue’s derivative value is not a whit less than the original value of its gold components.

Can we at least say that derivative value is always at most equal to the original value? Maybe, but even that is not completely clear. That Alice is loved by God makes it be the case that a harm to Alice is a harm to God. But it could be that the derivative badness to God gives us reasons to protect Alice that are stronger than those coming from the original badness to Alice, and the derivative badness here might exceed the original badness. (Recall here Anselm’s idea that sin is infinitely bad, because it offends the infinite God.) Perhaps, though, cases of love do not give rise to purely derivative value, because the derivative value is created by an interaction between the original value of the beloved and the original value of the lover. On the other hand, insofar as the inartistic golden statue’s value is purely derivative, it cannot exceed the original value of the parts.

The non-additiveness of derivative value throws a wrench in simple consequentialist systems on which we maximize the total value of everything. Perhaps, though, it is possible to talk about overall value, which is not additive in nature, so this need not be a knock-down argument against consequentialism. But it definitely seems to complicate things.

Note that similar phenomena occur for other properties than value. When one takes ten pounds of gold and makes a statue of it, one may create a ten pound object (assuming for the sake of argument that statues really exist), but one doesn’t add ten pounds to reality. We need to avoid double-counting in the case of derivative mass just as much as for derivative value.