Dignity, ecosystems and artifacts

1. If a part of x has dignity, x has dignity.

2. Only persons have dignity.

3. So, a person cannot be a proper part of a non-person. (1–2)

4. A person cannot be a proper part of a person.

5. So, a person cannot be a proper part of anything. (3–4)

6. If any nation or galaxy or ecosystem exists, some nation, galaxy or ecosystem has a person as a proper part.

7. So, no nation, galaxy or ecosystem exists. (5–6)

Less confidently, I go on.

8. If tables and chairs exist, so do chess sets.

9. If chess sets exist, so do living chess sets.

10. A living chess set has persons as proper parts. (Definition)

11. So, living chess sets do not exist. (4,10)

12. So, tables and chairs don’t exist. (8–9,11)

All that said, I suppose (1) could be denied. But it would be hard to deny if one thought of dignity as a form of trumping value, since a value in a part transfers to the whole, and if it’s a trumping value, it isn’t canceled by the disvalue of other parts. (That said, I myself don’t quite think of dignity as a form of value.)

Special treatment of humans

Sometimes one talks of humans as having a higher value than other animals, and hence it being appropriate to treat them better. While humans do have a higher value, I don't think this is what justifies favoring them. For to treat something well is to bestow value on them. But it is far from clear why the fact that x has more value than y justifies bestowing additional value on x rather than on y. It seems at least as reasonable to spread value around, and preferentially treat y.

A confusing factor is that we do have reason to preferentially treat those who have more desert, and desert is a value. But the reason here is specific to desert, and does not in any obvious way generalize to other values.

I don't deny that we should treat humans preferentially over other animals, nor that humans are more valuable. But these two facts should not be confused. Perhaps we should treat humans preferentially over other animals because humans are persons and other animals are not--but this is a point about personhood rather than about value. I am inclined to think we shouldn't argue: humans are persons, personhood is very valuable, so we should treat humans preferentially. Rather, I suspect we should directly argue: humans are persons, so we should treat humans preferentially, skipping the value step. (To put it in Kantian terms, beings with dignity are valuable, but what makes them have dignity isn't just that they are valuable.)

From aggregative value comparisons to hyperreal values

Suppose that we have n objects α₁, ..., α_n, and we want to define something like numerical values (at least hyperreal ones, if we can’t have real ones) on the basis of comparisons of value. Here is one interesting way to proceed. Consider the space of formal sums m₁α₁ + ... + m_nα_n, where the m_i are natural numbers, and suppose there is a total preorder ≤ (total transitive reflexive relation) on this space satisfying the axioms:

1. x + z ≤ y + z iff x ≤ y

2. mx ≤ my iff x ≤ y for all positive m.

We can think of m₁α₁ + ... + m_nα_n ≤ p₁α₁ + ... + p_nα_n as saying that the “aggregative value” of having m_i copies of α_i for all i is less than or equal to the “aggregative value” of having p_i copies of α_i for all i. The aggregative value of a number of objects is the “sum value”, where we don’t take into account things like the diversity or lack thereof or other “arrangement values”.

Now extend ≤ to formal sums m₁α₁ + ... + m_nα_n where the m_i are allowed to be positive or negative by stipulating that:

• m₁α₁ + ... + m_nα_n ≤ p₁α₁ + ... + p_nα_n iff (k+m₁)α₁ + ... + (k+m_n)α_n ≤ (k+p₁)α₁ + ... + (k+p_n)α_n for some natural k such that k + m_i and k + p_i are non-negative for all i.

Axiom (1) implies that the choice of k is irrelevant. It is easy to see that ≤ still satisfies both (1) and (2). Moreover, ≤ is still total, transitive and reflexive.

Next extend ≤ to formal sums r₁α₁ + ... + r_nα_n where the r_i are rational numbers by stipulating that:

• r₁α₁ + ... + r_nα_n ≤ s₁α₁ + ... + s_nα_n iff ur₁α₁ + ... + ur_nα_n ≤ us₁α₁ + ... + us_nα_n for some positive integer u such that ur_i and us_i is an integer for all i.

Axiom (2) implies that the choice of u is irrelevant. Again, it is easy to see that ≤ continues to satisfy (1) and (2), and that it remains total, transitive and reflexive.

Thus, ≤ is a total vector space preorder on an n-dimensional vector space V over the rationals with basis α₁, ..., α_n.

Let C be the positive cone of ≤: C = {x ∈ V : 0 ≤ x}. This is closed under addition and positive rational-valued scalar multiplication. Let K be the kernel of the preorder, i.e., {x ∈ V : 0 ≤ x ≤ 0} = C ∩  − C.

Now, let W be the n-dimensional vector space over the reals with basis α₁, ..., α_n. Let D be the smallest subset of W containing C and closed under addition and multiplication by positive real scalars: this is the set of real-linear combinations of elements of C with positive coefficients. It is easy to check that D ∩ V = C. Let L = D ∩  − D. Then L ∩ V = K.

Let E be a maximal subset of W that contains D, is closed under addition and multiplication by positive real scalars, and is such that E ∩  − E = L. This exists by Zorn’s Lemma. I claim that for any v in W, either v or  − v is in E. For suppose neither v nor  − v is not in E. Then let E′ = {e + tv : t > 0, e ∈ E}. This contains C, and is closed under addition and multiplication by positive reals. If we can show that E′ ∩  − E′ = L, then since E is a proper subset of E′, we will contradict the maximality of E. Suppose z ∈ E′ ∩  − E′ but not z ∈ L. Since E ∩  − E = L, we must have either z or  − z in E′ ∖ E. Without loss of generality suppose z ∈ E′ ∖ E. Then z = e + tv for e ∈ E and t > 0. Thus, e + tv ∈  − E. Hence tv ∈ (−e) + (−E) ⊆  − E, since e ∈ E and E is closed under addition. Since E is closed under positive scalar multiplication, we have v ∈  − E, which contradicts our assumption that  − v is not in E.

Define ≤^* on W by letting v≤^*w iff w − v ∈ E. Note that ≤^* agrees with ≤ on V. If v ≤ w are in V, then w − v ∈ C ⊆ E and so v≤^*w. Conversely, if v≤^*w, then w − v ∈ E. Now, since w − v is in V, and ≤ is total, if we don’t have v ≤ w, we must have w ≤ v and hence v − w ∈ C, so w − v ∈  − C. Since E ∩  − E = L, we have w − v ∈ L. But v, w ∈ V, so w − v ∈ L ∩ V = K. Thus, v ≤ w, a contradiction.

It’s also easy to see that ≤^* is total, transitive and reflexive. It is therefore representable by lexicographically-ordered vector-valued utilities by the work of Hausner in the middle of the last century. And vector-valued utilities are representable by hyperreals (just represent (x₁,...,x_n) with x₁ + x₂ϵ + ... + x_nϵ^n − 1 for a positive infinitesimal ϵ).

Remark 1: Here is a plausible condition on the extension ≤^* that we can enforce if we like: if Q and U are neighborhoods of v and w respectively, and for all q ∈ Q ∩ V and all u ∈ U ∩ V we have q ≤ v, then v≤^*w. For this condition will hold provided we can show that if Q is a neighborhood of v such that Q ∩ V ⊆ C, then v ∈ E. Note that any positive-real-linear combination of points v satisfying this neighborhood condition also satisfies this condition, and any sum of a point v satisfying this condition and a point in D will also satisfy it. Thus we can add to D all such points v, and carry on with the rest of the proof.

Remark 2: If we start off with ≤ being a partial preorder, ≤^* still becomes a total order. Then instead of proving it agrees with the partial preordering on V (or the initial ordering), we use the basically the same proof to show that it extends both the non-strict and strict orders: (a) if w ≤ v, then w≤^*v and if w < v, then w<^*v.

Question 1: Can we make sure that the values are real numbers?

Response: No. Suppose you are comparing a sheep and a goat, and suppose that they are valued positively and equally—the one exception is ties are broken in favor of the sheep. Thus, n+1 copies of the goat are better than n copies of the sheep and both are better than nothing, but n copies of the sheep are better than n copies of the goat. To represent this with hyperreals we need to take the value of the sheep to be ϵ + g where g > 0 is the value of the goat, and where ϵ/g is a positive infinitesimal.

Question 2: Is the representation is “practically unique”, i.e., does it generate the same decisions in probabilistic situations, or at least ones with real-valued probabilities?

Response: No. Supose you have a sheep and a goat. Now consider two hypotheses: on the first, the sheep is worth  − ϵ + π goats, and on the second, the sheep is worth ϵ + π goats, for a positive infinitesimal ϵ. Both hypotheses generate the same aggregative value comparisons between aggregates consisting of n₁ copies of the goat and n₂ copies of the sheep for natural numbers n₁ and n₂, since π is irrational. But the two hypotheses generate opposite probabilistic decisions if we are choosing between a 1/π chance of the sheep and certainty of the goat.

Value and aptness for moral concern

In two recent posts (this and this) I argued that dignity does not arise from value.

I think the general point here goes beyond value. Some entities are more apt for being morally concerned about than others. These entities are more appropriate beneficiaries of our actions, we have more reason to protect them, and so on. The degreed property these entities have more of has no name, but I will call it “apmoc”: aptness for moral concern. Dignity is then a particularly exalted version of apmoc.

Apmoc as such is agent-relative. If you and I have cats, then my cat has more apmoc relative to me than your cat, while your cat has more apmoc relative to you. Thus, I should have more moral concern for my cat and you for yours. Agent-relativity can be responsible for the bulk of the apmoc in the case of some entities—though probably not in the case of entities whose apmoc rises to the level of dignity.

However, we can distinguish an agent-independent core to an entity’s apmoc, which I will call the entity’s “core apmoc”. One can think of the core apmoc as the apmoc the entity has relative to an agent who has no special relationship to the entity. (Note: My concern in this post is the apmoc relative to human agents, so the core apmoc may still be relative to the human species.)

Now, then, here is a thesis that initially sounds good, but I think is quite mistaken:

1. An entity’s core apmoc is proportional to its value.

For suppose I have two pet dragons, on par with respect to all properties, except one can naturally fly and the other is naturally flightless. The flying dragon has more value: it is a snazzier kind of being, having an additional causal power. Both dragons equally like being scratched under the chin (perhaps with a rake). The fact that the flying dragon has more value does not give me any additional reason to scratch it. More generally, the flying dragon does not have any more core apmoc.

One might object: if it is a matter of saving the life of one of the dragons, other things being equal, one should save the life of the flying dragon, because it is a better kind of being. However, even if this judgment is correct, it is not due to a difference in apmoc. If the flying dragon dies, more value is lost. The death of a dragon removes from the world all the goods of the dragon: its majestic beauty, its contribution to winter heating, its protection of the owner, its prevention of sheep overpopulation, and so on. The death of the flying dragon removes a good—an instance of the causal power of flight—from the world which the death of the flightless dragon does not. If the reason one should save the life of the flying dragon over the flightless one is that the flying one is a better kind of being, then the reason one is saving its life is not because the flying dragon has more apmoc, but because more is lost by its death. If I have a choice of saving Alice from losing a thumb or Bob from losing the little toe, I should save Alice from losing a thumb, not because Alice has more apmoc, but because a thumb is a bigger loss than a toe.

The above objection points out one feature. Sometimes bestowing what is in some sense “the same benefit” to entity will actually bestow a benefit proportional to the value of the entity. Saving an entity from destruction sounds like “the same benefit”, but is a greater benefit where there is more value to be saved. Similarly, if I have a choice between fixing a tire puncture in my car or in my bike, more value is gained when I fix the car’s tire, because the car is more valuable. However, this is not due to the car having more apmoc, but simply because the benefits are different: if I fix the car’s tire, the car would become capable of transporting around my whole family, while the bike would only become capable of transporting me.

Let’s move away from fantasy. Suppose Alice and Bob are on par in all respects, except that Alice knows the 789th digit of π while Bob does not. Knowledge is valuable, and so if you have more knowledge, you have more value. But now if I have a choice of whom to give a delicious chocolate-chip muffin, the fact that Alice knows the 789th digit of π is irrelevant—it contributes (slightly) to value but not at all to core apmoc (it might contribute to the agent-relative aspects of apmoc in some special cases, since shared knowledge can be a partial constituent of a morally relevant relationshiop).

Granted, a piece of knowledge is a contingent contribution to value. One might think that core apmoc is determined proportionately to the essential values of an entity. But I think this is implausible. Most people have the intuition that, other things being equal, a virtuous person has more apmoc than a vicious one. But virtue is not an essential value—it is a value that fluctuates over a lifetime.

The case of virtue and vice suggests that there may be some values that contribute to core apmoc. I think this is likely. Core apmoc does not appear in a vacuum. But the connection between apmoc and value is complex, and the two are quite different.

Evaluating some theses on dignity and value

I’ve been thinking a bit about the relationship between dignity and value. Here are four plausible principles:

1. If x has dignity, then x has great non-instrumental value.

2. If x has dignity, then x has great non-instrumental value because it has dignity.

3. If x has dignity and y does not, then x has more non-instrumental value than y.

4. Dignity just is great value (variant: great non-instrumental value).

Of these theses, I am pretty confident that (1) is true. I am fairly confident (3) is false, except perhaps in the special case where y is a substance. I am even more confident that (4) is false.

I am not sure about (2), but I incline against it.

Here is my reason to suspect that (2) is false. It seems that things have dignity in virtue of some further fact F about them, such as that they are rational beings, or that they are in the image and likeness of God, or that they are sacred. In such a case, it seems plausible to think that F directly gives the dignified entity both the great value and dignity, and hence the great value derives directly from F and not from the dignity. For instance, maybe what makes persons have great value is that they are rational, and the same fact—namely that they are rational—gives them dignity. But the dignity doesn’t give them additional value beyond that bestowed on them by their rationality.

My reason to deny (4) is that great value does not give rise to the kinds of deontological consequences that dignity does. One may not desecrate something with dignity no matter what consequences come of it. But it is plausible that mere great value can be destroyed for the sake of dignity.

This leaves principle (3). The argument in my recent post (which I now have some reservations about, in light of some powerful criticisms from a colleague) points to the falsity of (3). Here is another, related reason. Suppose we find out that the Andromeda Galaxy is full of life, of great diversity and wonder, including both sentient and non-sentient organisms, but has nothing close to sapient life—nothing like a person. An evil alien is about to launch a weapon that will destroy the Andromeda Galaxy. You can either stop that alien or save a drowning human. It seems to me that either option is permissible. If I am right, then the value of the human is not much greater than that of the Andromeda Galaxy.

But now imagine that the Whirlpool Galaxy has an order of magnitude more life than the Andromeda Galaxy, with much greater diversity and wonder, than the Andromeda Galaxy, but still with nothing sapient. Then even if the value of the human is greater than that of the Andromeda Galaxy, because it is not much greater, while the value of the Whirlpool Galaxy is much greater than that of the Andromeda Galaxy, it follows that the human does not have greater value than the Whirlpool Galaxy.

However, the Whirlpool Galaxy, assuming it has no sapience in it, lacks dignity. A sign of this is that it would be permissible to deliberately destroy it in order to save two similar galaxies from destruction.

Thus, the human is not greater in value than the Whirlpool Galaxy (in my story), but the human has dignity while the Whirlpool Galaxy lacks it.

That said, on my ontology, galaxies are unlikely to be substances (especially if the life in the galaxy is considered a part of the galaxy, since following Aristotle I doubt that a substance can be a proper part of a substance). So it is still possible that principle (3) is true for substances.

But I am not sure even of (3) in the case of substances. Suppose elephants are not persons, and imagine an alien sentient but not sapient creature which is like an elephant in the temporal density of the richness of life (i.e., richness per unit time), except that (a) its rich elephantine life lasts millions of years, and (b) there can only be one member of the kind, because they naturally do not reproduce. On the other hand, consider an alien person who naturally only has a life that lasts ten minutes, and has the same temporal density of richness of life that we do. I doubt that the alien person is much more valuable than the elephantine alien. And if the alien person is not much more valuable, then by imagining a non-personal animal that is much more valuable than the elephantine alien, we have imagined that some person is not more valuable than some non-person. Assuming all non-persons lack dignity and all persons have dignity, we have a case where an entity with dignity is not more valuable than an entity without dignity.

That said, I am not very confident of my arguments against (3). And while I am dubious of (3), I do accept:

5. If x has dignity and y does not, then y is not more valuable than x.

I think the case of the human and the galaxy, or the alien person and alien elephantine creature, are cases of incommensurability.

Value and dignity

1. If it can be reasonable for a typical innocent human being to save lions from extinction at the expense of the human’s own life, then the life of a typical human being is not of greater value than that of all the lion species.

2. It can be reasonable for a typical innocent human being to save lions from extinction at the expense of the human’s own life.

3. So, the life of a typical innocent human being is not of greater value than that of the lion species.

4. It is wrong to intentionally kill an innocent human being in order to save tigers, elephants and giraffes from extinction.

5. It is not wrong to intentionally destroy the lion species in order to save tigers, elephants and giraffes from extinction.

6. If (3), (4) and (5), then the right to life of innocent human beings is not grounded in how great the value of human life is.

7. So, the right to life of innocent human beings is not grounded in how great the value of human life is.

I think the conclusion to draw from this is the Kantian one, that dignity that property of human beings that grounds respect, is not a form of value. A human being has a dignity greater than that of all lions taken together, as indicated by the deontological claims (4) and (5), but a human being does not have a value greater than that of all lions taken together.

One might be unconvinced by (2). But if so, then tweak the argument. It is reasonable to accept a 25% chance of death in order to stop an alien attack aimed at killing off all the lions. If so, then on the plausible assumption that the value of all the lions, tigers, elephants and giraffes is at least four times that of the lions (note that there are multiple species of elephants and giraffes, but only one of lions), it is reasonable to accept a 100% chance of death in order to stop the alien attack aimed at killing off all four types of animals. But now we can easily imagine sixteen types of animals such that it is permissible to intentionally kill off the lions, tigers, elephants and giraffes in order to save the 16 types, but it is not permissible to intentionally kill a human in order to save the 16 types.

A schematic argument against naturalistic reductions

Here is an argument schema.

1. If X is reducible to the natural, then likely the vast improvement of natural science over the last three hundred years would have led to a much better knowledge of X.

2. If X is not reducible to the natural, then it is not likely that the vast improvement of natural science over the last three hundred years would have led to a much better knowledge of X.

3. The vast improvement of natural science over the last three hundred years has not led to a much better knowledge of X.

4. So, probably, X is not reducible to the natural.

Some options for X:

• ethics

• aesthetics

• value in general.

I think the best response would be to dispute (1), by saying that (1) is only plausible if we know how to do the reduction. The mere existence of a reduction, when we do not know how to run it, is not enough.

Maybe. But I still think we get some evidence against reductionistic theories in ethics, aesthetics and value in general from fact that great progress in science hasn’t led to great progress in these areas.

Gratuitous and objective evil

Suppose, highly controversially, that no defensible atheist account of objective value is possible. Now consider a paradigmatic apparently gratuitous horrendous evil E—say, one of the really awful things done to children described by Ivan in the Brothers Karamazov. The following two claims are both intuitive:

1. E is gratuitous

2. E is objectively evil.

But if there is no defensible account of objective evil on atheism, then (1) and (2) are in serious tension. For if there cannot be objective evil on atheism, then (2) cannot be true on atheism. Thus, (2) implies theism. But on the other hand, (1) implies atheism, since E gratuitous just in case if God existed, then E would be an evil that God has conclusive moral reason to prevent.

On our initial assumption about atheism, then, we need to choose between (1) and (2). And here there is no difficulty. That the things described by Ivan are objectively evil is way more clear than that God would have conclusive moral reason to prevent them, even if the latter claim is very likely in isolation.

Is a defensible atheist account of objective value possible? I used to think there was no special difficulty, but I’ve since come to be convinced that probably the only tenable account of objective value is an Aristotelian one based on form, and that human form requires something like a divine source. That said, even if objective value is something the atheist can defend, nonetheless knowledge of objective value is very difficult for the atheist. For objective value has to be (I know this is controversial) non-natural, and on atheism it is very difficult to explain how we could acquire the power to get in touch with non-natural aspects of reality.

But if knowledge of objective value is very difficult for the atheist, then we have tension between:

1. E is gratuitous

2. I know that E is objectively evil.

And (3) is still, I think, significantly more plausible than (1).

The 2018 Belgium vs Brazil World Cup game

In 2018, the Belgians beat the Brazilians 2-1 in the 2018 World Cup soccer quarterfinals. There are about 18 times as many Brazilians and Belgians in the world. This raises a number of puzzles in value theory, if for simplicity we ignore everyone but Belgians and Brazilians in the world.

An order of magnitude more people wanted the Brazilians to win, and getting what one wants is good. An order of magnitude more people would have felt significant and appropriate pleasure had the Brazilians won, and an appropriate pleasure is good. And given both wishful thinking as well as reasonable general presumptions about there being more talent available in a larger population base, we can suppose that a lot more people expected the Brazilians to win, and it’s good if what one thinks is the case is in fact the case.

You might think that the good of the many outweighs the good of the few, and Belgians are few. But, clearly, the above facts gave very little moral reason to the Belgian players to lose. One might respond that the above facts gave lots of reason to the Belgians to lose, but these reasons were outweighed by the great value of victory to the Belgian players, or perhaps the significant intrinsic value of playing a sport as well as one can. Maybe, but if so then just multiply both countries’ populations by a factor of ten or a hundred, in which case the difference between the goods (desire satisfaction, pleasure and truth of belief) is equally multiplied, but still makes little or no moral difference to what the Belgian players should do.

Or consider this from the point of view of the Brazilian players. Imagine you are one of them. Should the good of Brazil—around two hundred million people caring about the game—be a crushing weight on your shoulders, imbuing everything you do in practice and in the game with a great significance? No! It’s still “just a game”, even if the value of the good is spread through two hundred million people. It would be weird to think that it is a minor pecadillo for a Belgian to slack off in practice but a grave sin for a Brazilian to do so, because the Brazilian’s slacking hurts an order of magnitude more people.

That said, I do think that the larger population of Brazil imbues the Brazilians’ games and practices with some not insignificant additional moral weight than the Belgians’. It would be odd if the pleasure, desire satisfaction and expectations of so many counted for nothing. But on the other hand, it should make no significant difference to the Belgians whether they are playing Greece or Brazil: the Belgians shouldn’t practice less against the Greeks on the grounds that an order of magnitude fewer people will be saddened when the Greeks lose than when Brazilians do.

However, these considerations seem to me to depend to some degree on which decisions one is making. If Daniel is on the soccer team and deciding how hard to work, it makes little difference whether he is on the Belgian or Brazilian team. But suppose instead that Daniel is has two talents: he could become an excellent nurse or a top soccer player. As a nurse, he would help relieve the suffering of a number of patients. As a soccer player, in addition to the intrinsic goods of the sports, he would contribute to his fellow citizens’ pleasure and desire satisfaction. In this decision, it seems that the number of fellow citizens does matter. The number of people Daniel can help as a nurse is not very dependent on the total population, but the number of people that his soccer skills can delight varies linearly with the total population, and if the latter number is large enough, it seems that it would be quite reasonable for Daniel to opt to be a soccer player. So we could have a case where if Daniel is Belgian he should become a nurse but if Brazilian then a soccer player (unless Brazil has a significantly greater need for nurses than Belgium, that is). But once on the team, it doesn’t seem to matter much.

The map from axiology to moral reasons is quite complex, contextual, and heavily agent-centered. The hope of reducing moral reasons to axiology is very slim indeed.

Two different ways of non-instrumentally pursuing a good

Suppose Alice is blind to the intrinsic value of friendship and Bob can see the intrinsic value of friendship. Bob then told Alice that friendship is intrinsically valuable. Alice justifiedly trusts Bob in moral matters, and so Alice concludes that friendship has intrinsic value, even though she can’t “see” it. Alice and Bob then both pursue friendship for its own sake.

But there is a difference: Bob pursues friendship because of the particular ineffable “thick” kind of value that friendship has. Alice doesn’t know what “thick” kind of value friendship has, but on the basis of Bob’s testimony, she knows that it has some such value or other, and that it is a great and significant value. As long as Alice knows what kinds of actions friendship requires, she can pursue friendship without that knowledge, though it’s probably more difficult for her, perhaps in the way that it is more difficult for a tone-deaf person to play the piano, though in practice the tone-deaf person could learn what kinds of finger movements result in aesthetically valuable music without grasping that aesthetic value.

The Aristotelian tradition makes the grasp of the particular thick kind of value involved in a virtuous activity be a part of the full possession of that virtue. On that view, Alice cannot have the full virtue of friendship. There is something she is missing out on, just as the tone-deaf pianist is missing out on something. But she is not, I think, less praiseworthy than Bob. In fact Alice’s pursuit of friendship involves the exercise of a virtue which Bob’s does not: the virtue of faith, as exhibited in Alice’s trust in Bob’s testimony about the value of friendship.

Pursuing a thing for its own sake

Suppose you pursue truth for its own sake. As we learn from Aristotle, it does not follow that you don’t pursue truth for the sake of something else. For the most valuable things are both intrinsically and instrumentally valuable, and so they are typically pursued both for their own sake and for the sake of something else.

What if you pursue something, but not for the sake of something else. Does it follow that you pursue the thing for its own sake? Maybe, but it’s not as clear as it might seem. Imagine that you eat fiber for the sake of preventing colon cancer. Then you hear a study that says that fiber doesn’t prevent colon cancer. But you continue to eat fiber, out of a kind of volitional inertia, without any reason to do so. Then you are pursuing the consumption of fiber not for the sake of anything else. But merely losing the instrumental reason for eating fiber doesn’t give you a non-instrumentally reason. Rather, you are now eating fiber irrationally, for no reason.

Perhaps it is impossible to do something for no reason. But even if it is impossible to do something for no reason, it is incorrect to define pursuing something for its own sake as pursuing it not for the sake of something else. For that you pursue something for its own sake states something positive about your pursuit, while that you don’t pursue it for the sake of anything else states something negative about your pursuit. There is a kind of valuing of the thing for its own sake that is needed to pursue the thing for its own sake.

It is tempting to say that you pursue a thing for its own sake provided that you pursue it because of the intrinsic value you take it to have. But that, too, is incorrect. For suppose that a rich benefactor tells you that they will give you a ton of money if you gain something of intrinsic value today. You know that truth is valuable for its own sake, so you find out something. In doing so, you find out the truth because the truth is intrinsically valuable. But your pursuit of that truth is entirely instrumental, despite your reason being the intrinsic value.

Hence, to pursue a thing for its own sake is not the same as to pursue it because it has intrinsic value. Nor is it to pursue it not for the sake of something else.

I suspect that pursuing a thing for its own sake is a primitive concept.

Human worth and materialism

1. A typical human being has much more intrinsic value than any 80 kg arrangement of atoms.

2. If materialism is true, a typical human being is an 80 kg arrangement of atoms.

3. So, materialism is not true.

An analogy for divine infinity

Here’s an analogy I’ve been thinking about. God’s value is related to other infinities like (except with a reversal of order) zero is related other infinitesimals. Just as zero is infinitely many times smaller than any other infinitesimal (technically, zero is an infinitesimal—an infinitesimal being a quantity x such that |x| < 1/n for every natural number n), and in an important sense is radically different from them, so too the infinity of God’s value is infinitely many times greater than any other infinity, and in an important sense is radically different from them.

Suppose we think with the medievals that value and being are correlative. Then zero value corresponds to complete non-being. There isn’t anything that has that. Between ordinary non-divine things like people and oak trees and non-being we have a radical ontological difference: there are people and oak trees, but there is no non-being. Suppose we push the analogy on the side of God. Then between ordinary non-divine things like people and oak trees and God we will have a radical ontological difference, too. Some theologians have infamously tried to mark this difference by saying that people and oak trees are but God is not. That way of marking the difference is misleading by making God seem like non-being instead of like its opposite. A better way to mark the difference is to say that in an important sense God is and people and oak trees are not (compare what Jesus is said to have have said to St Catherine of Siena: “I am who I am and you are she who is not”). In any case, the gap between God’s “is” and our “is” is at least as radical as the gap between our “is” and the “is not” of non-being.

In fact, I think the gap is more radical: we and all other creatures are closer to non-being than to God. So the analogy I’ve been thinking about, that God’s value is related to other infinities like zero to other infinitesimals (but in reverse order) is misleading: God’s value is in a sense further from other infinities than zero is from other infinitesimals. (And not just because all infinitesimals are infinitesimally close to zero. The relevant scale should not be arithmetic but logarithmic, so that the gap between zero and anything—even an infinitesimal—bigger than zero is in an important sense infinite.)

Don’t take this too seriously. Remember this.

Megavalue

In my previous post, I glibly talked of the infinite value of persons. I forgot that such talk was discredited by this argument. Instead, one should talk of relatively infinite value: being infinitely more times valuable than.

I think the argument of that post can be rescued. And while I am at it, I can modify the argument to avoid another objection, that higher animals like dogs and dolphins are not infinitely less valuable than persons. I do not know if the objection is sound, but it won't matter.

1. Definition: A thing has megavalue if and only if it is infinitely more times valuable than every portion of non-living reality in the universe.

2. The sum total of life in the universe has megavalue.

3. Nothing can cause something that has infinitely more value than itself.

4. If the sum total of life in the universe has a cause and that cause is wholly within the universe, then the cause is a portion of the non-living reality in the universe.

5. There is a cause of the sum total of life in the universe.

6. A cause of the sum total of life in the universe is not wholly within the universe.

Infinite value

1. All persons have infinite value.
2. Nothing in the universe other than persons has infinite value.
3. There was a first person in the universe.
4. Everything in the universe has a cause.
5. The first person in the universe wasn’t caused by a person in the universe.
6. Nothing with finite value can cause something with infinite value.
7. So, something not in the universe and with infinite value caused the first person in the universe.

I am not confident of premise (1).

Yet another account of life

I think a really interesting philosophical question is the definition of life. Standard biological accounts fail to work for God and angels.

Here is a suggestion:

• x has life if and only if it has a well-being.

For living things, one can talk meaningfully of how well or poorly off they are. And that’s what makes them be living.

I think this is a simple and attractive account. I don’t like it myself, because I am inclined to think that everything has a well-being—even fundamental particles. But for those who do not have such a crazy view, I think it is an attractively simple solution to a deep philosophical puzzle.

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.

The Fourth Way, remixed

I’m playing with a reading—or perhaps remix—of Aquinas’ Fourth and Fifth Ways as giving a theistic solution to a problem that non-theistic Aristotelianism has no solution to. In this post, I will discuss the Fourth Way, and in the next, the Fifth.

The Fourth Way starts with the principle that degreed predicates, predicates where it makes sense to talk of “more” and “less”, are predicated in comparison to a maximal case. Infamously, however, given modern science, Aquinas’ down-to-earth illustration of that principle, namely that heat is predicated in comparison to the maximal case—allegedly, fire—is not not an example of the principle, but is actually a counterexample to it. There just is no such thing as maximum heat.

But nevermind heat. Aquinas wants to apply the Fourth Way to goodness. Now, the Aristotelian system that he has adopted already has an account of the good: a thing is good to the extent that it fulfills its proper function, a proper function that is defined by the thing’s form. Note that this account, too, does not match Aquinas’ gradation principle: unlike in Plato, forms are not self-predicating, so rather than the Form of the Sheep being the most ovine thing possible, the Aristotelian form of the sheep is immanent in each sheep, directing each sheep to an ovine perfection that no object actually meets.

But the Aristotelian account of the good is incomplete. While it allows us to compare the goodness of things within a kind—the four-legged sheep better fulfills its form than a three-legged one—there are also meaningful value comparisons between kinds. When Jesus says that we are “worth more than many sparrows” (Mt. 10:31), what he is saying is entirely commonsense. The human has much more good than the sparrow. The sparrow has more good than the worm. And the worm has more good than a mushroom. There really is a something like a great chain of being in reality. These comparisons, however, are not simply grounded in the immanent forms of things. The form of the worm need make no reference to mushrooms, nor that of a mushroom to worms.

Note that these interspecies value comparisons not only cannot be read off from the immanent forms, but sometimes they are in a kind of tension with the immanent forms. An earthworm’s form limits the neural development of the worm. Were the worm to grow a brain as big as a dog’s, it wouldn’t be able to burrow as well. And a mushroom that walked around would fail to be properly rooted as a mushroom ought.

Interspecies value comparison is a genuine problem that Aristotelianism faces, though some Aristotelians are willing to bite the bullet and deny the meaningfulness of such comparisons. Platonism did not face this problem—it could just talk of varying degrees of participation in the Form fo the Good—but Platonism lacked a satisfactory solution to the problem of intraspecies comparisons (Platonism’s solution would be to posit a self-exemplified Form for each species, which would involve the absurd idea that there is a perfect Sheep, which somehow manages to be both a sheep and immaterial, and we have all sorts of silly questions about whether it is male or female, what color it is, whether it has an even or an odd number of hairs, etc.)

A theistic Aristotelianism, however, has a solution to the problem of interspecies value comparison, in addition to non-theistic Aristotelianism’s solution to the intraspecies’ problem. There is a great chain of being defined by the ways in which the various species participate in the being that has all perfections. The human exemplifies intellection, the sparrow approximates omnipresence through rapid movement and exemplifies a significant degree of intelligence, the worm approximates omnipresence less well and has a lower degree of intelligence, while the mushroom at least exemplifies life. What grounds the goodness of these qualities independently of the forms of the things they are found in, and what makes for their axiological directionality (more intelligence is better than less), is then comparison to the maximal case, namely God.

Note that while this gives something like a great chain of being, it need not exactly be a great chain of being. We should not seek after a strictly total ordering—a partial ordering matches intuition better.

I don’t have a knock-down argument that theistic Aristotelianism is the only good Aristotelian solution to the problem of interspecies comparison. But it is a very good solution, and so once we have accepted basic Aristotelianism, it gives us significant reason to adopt the theistic version.

An earlier, more compact, version of this argument is here.

What does it mean for persons to have infinite value?

It is intuitive to say that persons have infinite value, and recently Rasmussen and Bailey have given some cool arguments for this thesis.

But what does it mean to say that humans have infinite value? If we think of values as something very much like numbers, then I guess it just means that humans have the value +∞. But we shouldn’t think of values as numbers. For instance, to do that loses sight of incommensurability.

We probably should think of value-comparison as more fundamental than “having value z”. Thus, there is a relation of being at least as valuable as on possible items of evaluation (substances, properties, pluralities, whatever). This relation is reflexive and at least arguably transitive.

We can now define:

1. x is more valuable than y if and only if x is at least as valuable as y but y is not at least as valuable as x.

Next we can try to define a relation of being infinitely more valuable than. One approach is:

2. x is infinitely more valuable than y if and only if x is more valuable than any finite plurality of duplicates of y.

I am not quite sure this works, given that sometimes the value of an item rests in the fact that it is the only one of its kind, and then a plurality of duplicates might lose out on an aspect of the value. If we focus on intrinsic value, perhaps we don’t need to worry about this. Or maybe we can proceed probabilistically:

3. x is infinitely more valuable than y if and only if for every natural number n, a 1/n chance of x is more valuable than certainty of y.

Or perhaps we can take being infinitely more valuable than as a primitive transitive and irreflexive relation.

But now, if what we have are the above ingredients, what does it mean to say that something has infinite value? Here are two options, a maximal and a minimal one:

4. Maximal: x has infinite value if and only if x is infinitely more valuable than everything else.

5. Minimal: x has infinite value if and only if x is infinitely more valuable than something else that has positive value.

On the maximal option 4, you and I do not have infinite value, since you are not infinitely more valuable than I and I am not infinitely more valuable than you. Indeed, only a being like God is a plausible candidate for having infinite value in the maximal sense.

In the minimal option 5, “has positive value” is added to avoid the potential problem that literally everything that has positive value has infinite value, because anything with positive value is infinitely more valuable than something with no value or with negative value. What does it mean for something to have positive value? I guess it’s for it to be more valuable than nothing. (I am using a very broad sense of “item”, including such “items” as “nothing”, when I talk of value in this post.)

But option 5 probably doesn’t capture the intuition that infinite value distinguishes persons from, say, trees. For while arguably a person is infinitely more valuable than a tree, it is also quite plausible to me that a tree is infinitely more valuable than some non-living things like fundamental particles. Or if you don’t share that intuition, suppose eternalism. Then a tree that exists for a year could be infinitely more valuable than a tree that exists for an instant, since there could turn out to be infinitely many instants in a year.

In any case, whether these speculations about the value of trees are right, the important point is that the intuition we were trying to capture with the statement that persons have infinite value was that persons have a lot of value. But having infinitely more value than something of positive value could just mean that you have infinitely more value than something of infinitesimally positive value, which is compatible with not having much value at all.

If the above is right, then it’s false or unhelpful to talk of persons having infinite value simpliciter. What may make sense, however, are specific comparisons such as:

6. A person has infinitely more value than a dollar

or:

7. A person has infinitely more value than a tree.

We might try for something more daring, though:

8. A person has infinitely more value than any non-person.

I think (8) if true would capture a fair amount of the original intuition, and do so without any arbitrary singling out of a unit of comparison like a dollar or a tree. But I do not know if (8) is true. There could be kinds of good that we have no concept of, and those kinds of good could be at least incommensurable with the goods of persons. Something with such a good need not be infinitely less valuable than a person—they might be mutually incommensurable.

So, speaking for myself, I am happy with sticking to a fairly arbitrary unit, and going for something like (6) or (7).

Learning whether p by bringing it about that p

Alice is driving to an appointment she doesn’t care much about. She is, however, curious whether she will arrive on time. To satisfy her curiosity, she stops driving, since she knows that if she stops driving, she won’t arrive on time.

It seems a bit perverse to bring it about that p in order to know whether p. Yet there are cases where people do that.

A straightforward family of cases is very pragmatic. You can only make preparations for something if you know what will happen, so you force a particular thing to happen. For instance, you can only book vacation travel when you know where you will decide to go—so, you decide where to go.

One family of cases is linked to anxiety. Not knowing whether p can induce a lot of anxiety, and knowing for sure can relieve that anxiety. This is, presumably, one of the reasons why peopel turn themselves in for crimes: to relieve the anxiety of not knowing whether one will be arrested today, one ensures that one is arrested today.

Another family is scientific. One arranges a laboratory setup in part precisely to know what the experimental setup is like.

But the Alice case is different from all these. In all of the above cases, you seek knowledge whether p for the sake of something other than knowledge whether p: to buy plane tickets, to relieve anxiety, or to learn some other scientific facts.

What seems perverse, then, is to bring it about that p for the sake of knowing whether p for the sake of knowing (“[t]o satisfy her curiosity”, I said of Alice).

I wonder, now, whether Alice is really being perverse. Maybe it’s just this: there are very few things that we can bring about where there is significant non-instrumental value in knowing them. There is very little value in knowing whether one will arrive on time to the appointment apart from instrumental considerations. Most of the things knowledge of which has significant non-instrumental value are out of our hands: theological, philosophical and scientific facts. But if there is very little value, it’s not worth much trouble. If an appointment is of so little value that it’s worth missing it to know whether one will make it on time to it, it’s probably not worth going to in the first place!