An Aristotelian account of proper parthood (for integral parts)

Here it is: x is a proper part of y iff x is informed by a form that informs y and x's being informed by that form is derivative from y's being informed by it.

Shape and parts

Alice is a two-dimensional object. Suppose Alice’s simple parts fill a round region of space. Then Alice is round, right?

Perhaps not! Imagine that Alice started out as an extended simple in the shape of a solid square and inside the space occupied by her there was an extended simple, Barbara, in the shape of a circle. (This requires there to be two things in the same place: that’s not a serious difficulty.) But now suppose that Alice metaphysically ingested Barbara, i.e., a parthood relation came into existence between Barbara and Alice, but without any other changes in Alice or Barbara.

Now Alice has one simple part, Barbara (or a descendant of Barbara, if objects “lose their identity” upon becoming parts—but for simplicity, I will just call that part Barbara), who is circular. So, Alice’s simple parts fill a circular region of space. But Alice is square: the total region occupied by her is a square. So, it is possible to have one’s simple parts fill a circular region of space without being circular.

It is tempting to say that Alice has two simple parts: a smaller circular one and a larger square one that encompasses the circular one. But that is mistaken. For where would the “larger square part” come from? Alice had no proper parts, being an extended simple, before ingesting Barbara, and the only part she acquired was Barbara.

Maybe the way to describe the story is this: Alice is square directly, in her own right. But she is circular in respect of her proper parts. Maybe Alice is the closest we can have to a square circle?
Here is another apparent possibility. Imagine that Alice started as an immaterial object with no shape. But she acquired a circular part, and came to be circular in respect of her proper parts. So, now, Alice is circular in respect of her proper parts, but has no shape directly, in her own right.

Once these distinctions have been made, we can ask this interesting question:

• Do we human beings have shape directly or merely in respect of our proper parts?

If the answer is “merely in respect of our proper parts”, that would suggest a view on which we are both immaterial and material, a kind of Hegelian synthesis of materialism and simple dualism.

Classical probability theory is not enough

Here’s a quick argument that classical probability cannot capture all probabilistic phenomena even if we restrict our attention to phenomena where numbers should be assigned. Consider a nonmeasurable event E, maybe a dart hitting a nonmeasurable subset of the target, and consider a fair coin flip that is causally isolated from E. Let H and T be the heads and tails results of the flip. Then let A be this disjunctive event:

• (E and H) or (not-E and T).

Intuitively, event A clearly has probability 1. If E happens, the probability of A is 1/2 (heads) and if E doesn’t happen, it’s also 1/2 (tails). (The argument uses finite conglomerability, but it is also highly intuitive.)

So a precise number should be assigned to A, namely 1/2. And ditto to H. But we cannot have these assignments in classical probability theory. For if we did that, then we would also have to assign a probability to the conjunction of H and A, which is equivalent to the conjunction of E and H. But we cannot assign a probability to the conjunction of E and H, because E and H are independent, and so we would have a precise probability for E, namely P(E)P(H)/P(H)=P(E&H)/P(H), contrary to the nonmeasurability of E.

Simple dualism and animals

According to simple dualism, our immaterial souls are the bearers of our mental states and we are these souls. We have bodies, but the bodies are not parts of us. We are wholly immaterial.

If the motivation for simple dualism is that only an immaterial soul can have mental states, then we should think something similar about higher animals like dogs and octopuses. Thus, in Rover the dog just as in Alice the human, the soul is the bearer of mental states, and the body is not a part of the soul. Now, the name “Alice” on simple dualism refers to the soul, so that “Alice is in pain” means that she is the bearer of the pain and “Alice has a broken leg” means that the leg associated with Alice is broken (compare: “Alice has a broken bicycle”) rather than that a part of Alice is broken. Surely, “Rover is in pain” and “Rover has a broken leg” mean something very close to “Alice is in pain” and “Alice has a broken leg”, respectively. Thus, “Rover” on simple dualism also refers to the soul.

Furthermore, Rover might be Alice’s pet. And the kind of interspecies affection that might exist between Rover and Alice requires that Rover be the right kind of thing to have affections and other mental states, and so, once again, “Rover” must refer to the soul.

But of course we also say that Rover is a dog. The simple dualist now has two options. The first is to take literally the statement that Rover is a dog, and conclude that dogs—and presumably other higher animals—are immaterial souls (if Rover is immaterial and Rover is a dog, then Rover is an immaterial dog; and Rover surely does not differ radically from other higher animals). Thus, strictly speaking, biologists don’t primarily study dogs and octopuses but rather their bodies, and we have never seen any higher animal.

The second option is to deny that Rover is literally a dog. This presumably requires denying that we are literally homo sapiens. Rather, “Rover is a dog” is to be understood as shorthand for “Rover ensouls a dog.”

Neither option looks attractive. I conclude that Rover is not a soul, and neither is Alice.

Shuffling an infinite deck of cards

Suppose I have an infinitely deep deck of cards, numbered with the positive integers. Can I shuffle it?

Given an infinite past, here is a procedure: n days ago, I perfectly fairly shuffle the top n cards in the deck.

When one reshuffles a portion of an already perfectly shuffled finite deck of cards, the full deck remains perfectly shuffled. So, the top n cards in the infinitely deep deck are perfectly shuffled for every finite n.

Can we argue that the thus-shuffled deck generates a countably infinite fair lottery, i.e., that if we pick cards off the top of the deck, all card numbers will be equally likely? At the moment I don’t know how to argue for that. But I can say that we get what I have called a countably infinite paradoxical lottery, i.e., one when any particular outcome has zero or infinitesimal probability.

For simplicity, let’s just consider picking the top card off the deck and consider a particular card number, say 100. For card 100 to be at the top of the deck, it had to be in the top n cards prior to the shuffling on day −n for each n. For instance, on day −1000, it had to to be in the top 1000 cards prior to the shuffling. The subsequent 1000 shufflings together perfectly shuffle the top 1000 cards. Thus, the probability that card 100 would end up at the top is 1/1000, given that it was in the top 1000 cards on day −1000. But it may not have been. So, all in all, the probability that card 100 would end up at the top is at most 1/1000. But the argument generalizes: for any n, the probability that card 100 would end up at the top is at most 1/n. Hence, the probability that card 100 would end up at the top is zero or infinitesimal.

If taking an infinite amount of time to shuffle is too boring, you can also do this with a supertask: one minute ago you shuffle the top card, 1.5 minutes ago you shuffle the top two cards, 1.75 minutes ago you shuffled the top three cards, and so on. Then you did the whole process in two minutes.

All the paradoxes of fair countably infinite lotteries reappear for any paradoxical countably infinite lottery. So, the above simple procedure is guaranteed to generate lots of fun paradoxes.

Here is a fun one. Carl shuffles the infinite deck. He now offers to pay Alice and Bob $20 each to play this game: they each take a card off the top of the deck, and the one with the smaller number has to pay $100 to the one with the bigger number. Alice and Bob happily agree to play the game. After all, they know the top two cards of the deck are perfectly shuffled, so they think it’s equally likely that each will win, and hence each calculates their expected payoff at 0.5×$100 − 0.5×$100 + $20 = $20. He puts them in separate rooms. As soon as each sees their own card (but not the other's), he now offers a new deal to them: if they each agree to pay him $80, he’ll broker a deal letting them swap their cards before determining who is the winner. Alice sees her card, and knows there are only finitely many cards with a smaller number, so she estimates her probability of being a winner at zero or infinitesimal. So she is nearly sure that if she doesn’t swap, she’ll be out $100, and hence it’s obviously worth swapping, even if it costs $80 to swap. Bob reasons the same way. So they each pay Carl $80 to swap. As a result, Carl makes $80+$80−$20−$20=$120 in each round of the game.

Causal Finitism, of course, says that you can’t have an infinite causal history, so you can’t have done the infinite number of shufflings.

Fulfilling requests

One of the most moving stories in Rosenbaum’s deeply moving Holocaust and the Halakhah tells of how one can be a great moral hero even when acting out of mistaken conscience. A man in a concentration camp comes to his rabbi with a problem. His son has been scheduled to be executed. But it is possible to bribe the kapo to get him off the death list. However, the kapo have a quota to fill, and if they let off his son, they will kill another child. Is it permissible to bribe the kapo knowing that this will result in the death of another child? The rabbi answers that, of course, it is permissible. The man goes away, but he is not convinced. He does not bribe the kapo. Instead, he concludes that God has called him to the great sacrifice of not shifting his son’s death onto another. The father finds a joy in the sacrifice amidst his mourning.

The rabbi was certainly right. The father’s conscience presumably was mistaken (unless God specifically spoke to him and required the sacrifice). Yet the father is a moral hero in acting from this mistaken conscience. (Here are two relevant features of this case. First, while he was mistaken, he was not mistaken in a way that shows moral callousness—on the contrary, he is obviously a man of moral sensitivity. Second, while he was mistaken in thinking the sacrifice was morally required, nonetheless the sacrifice was—I think—at least permissible.)

The analytic philosopher will see this as a variant of a trolley case (with some complications, such as that the deaths were mediated by the free agency of the kapo). It is permissible to redirect the trolley away from one’s child and towards a stranger’s child. This is another way in which the proportionality condition in the Principle of Double Effect is not a utilitarian calculation: the agent has a proportional reason to save their own child even when it is foreseen (but not intended) to cost another’s their life.

But at the same time it would not be permissible to redirect the trolley away from one stranger’s child towards another stranger’s child. Such redirection would be a grotesque toying with lives. It would be a needless and callous making of oneself into a cause of another’s death, even if unintentionally.

Here, however, is a case that puzzles me. Suppose Alice’s child is on the track the trolley is speeding towards, and a stranger’s child is on another track. Alice is physically incapable of redirecting the trolley but Bob is capable of it. Alice and both children are strangers to Bob. Would it be permissible for Alice to ask Bob to redirect the trolley?

Here is an argument to the contrary. It is impermissible for Bob to redirect the trolley from one stranger to another: that is just playing with lives. But it is impermissible to request someone to perform an impermissible action. Hence, it is impermissible to ask Bob to redirect the trolley.

That seems mistaken. The case of asking Bob to redirect the trolley need not be that different from begging the kapo to take one’s child off the death list, depending on the details of the latter story. So what is going on?

I think there are at least two ways to justify Bob’s acquiescence to the request and hence Alice’s making of the request:

1. Once Alice asks Bob to redirect the trolley, Alice is no longer a stranger to Bob. There is a way in which Bob in receiving her request can become an agent of Alice’s, and hence those that Alice cares for become ones that he has a special reason to care for.

2. On receipt of the request, Bob has two options coming with distinctive incommensurable reasons. The first is not to redirected, with the reason being promote equality, in this case equality between children who don’t have a parent in place to speak up for them and ones who do. The second is to fulfill the request of an anguished parent to save their child. Both reasons are grave, and it is permissible for him (other things being equal) to act on either reason. Requests really do add weight to reasons.

There is another complicating factor. I do have the intuition that if Bob is an employee in charge of the trolley, he should do nothing. The reason is this. Insofar as he is in charge of the trolley, Bob has a role duty of mitigating damage done by the trolley. It is generally good policy that such a role come along with a significant independence from outside influences, such as bribes or even requests. So, in that case, Bob should act as if he did not receive the request. But if he did not receive any request, he shouldn’t do anything, for it is better not to become the cause of the child’s death—as one would if one redirected.

Here is a variant case. There are three tracks. The trolley is on track A with five people. The other two tracks, B and C, have one person each, and Alice is asking Bob not to redirect to track B, as her child is there. Bob has to redirect to either track B or C, but everything other than Alice’s request is equal between these tracks. Here it seems to me that Bob should flip a coin (if there is time; if not, just act as randomly as he can) if he is an employee. And if he is not an employee, then he has a choice to accede to Alice’s request or flip a coin.

Three versions of proportionality in Double Effect

Bob sees a trolley speeding towards five strangers on a track and can redirect the trolley towards another track which has one stranger on it. Alice, who is herself unable to redirect the trolley, offers Bob a dollar to redirect it. Suppose Bob redirects the trolley solely for the sake of dollar. Bob is clearly a callous individual. But has Bob violated the strictures of the Principle of Double Effect?

Well, Bob has done an action that’s intrinsically good or neutral (redirecting a trolley). The bad effect—the death of the one stranger—was not intended either as an end or as a means, and indeed does not in any way (we assume) contribute to the intended good effect, which is getting a dollar. What remains to check is the proportionality condition.

Here it depends on exactly how the proportionality condition is formulated. There are at least three formulations:

1. The bad effects are not disproportionate to the intended good effects.

2. The bad effects are not disproportionate to the good effects.

3. The bad effects are not disproportionate to those good effects that are not themselves the outcomes of bad effects.

On formulation (1), Bob has violated Double Effect: the death of the one stranger is disproportionate to the sole intended good, namely Bob getting a dollar. On formulations (2) and (3), Bob has not violated Double Effect, since the good effect—the saving of the five—is proportionate (and is not the outcome of a bad effect).

My intuition is that the case supports (1). But I worry that this rides on our desire to get the obviously vicious Bob on some charge or other, and violating Double Effect is the obvious one. But there may be another charge. Bob had a moral duty to the do the following: to redirect the trolley in order to save five lives. He failed to do that. His failure to do that is a morally wrong abstension. So even if (2) or (3) are the right story, we can still get Bob on some moral charge or other.

So I am not sure how far the case helps adjudicate between (1)–(3).

Note one nice thing about (1), though. If we go for (1), we automatically filter out any good effects that are the outcomes of bad effects, since if we intended such good effects, we would be intending a bad means and violating the means condition of Double Effected. So (1) implicitly contains the same restriction as is found in (3).

Cupcakes and trolleys

A trolley is heading towards a person lying on the tracks. Also lying on the tracks is a delicious cupcake. You could redirect the trolley to a second track where there is a different person lying on the tracks, but no cupcake.

Utilitarianism suggests that, as long as you are able to enjoy the cupcake under the circumstances and not feel bad about the whole affair, you have a moral duty to redirect the trolley in order to save the cupcake for yourself. This is morally perverse.

Besides showing that utilitarianism is false, this example shows that the proportionality condition in the Principle of Double Effect cannot simply consist in a simple calculation comparing the goods and bads resulting from the action. For there is something morally disproportionate in choosing who lives and dies for the sake of a cupcake.

What needs a cause

Suppose Alice has existed for an infinite amount of time and now time 0 (in some unit system) has just come. Imagine that between time −1 and time 0, Barbara lived internally a life just like Alice did between time −1 and time 0. But between time −1.5 and −1, Barbara lived a life sped up by a factor of two, exactly like Alice’s life between time −2 and time −1. And between time −1.75 and −1.5, Barbara lived a life sped up by a factor of two, exactly like Alice’s life between time −3 and time −2. And so on, with Barbara coming into existence right after time −2.

Some people think that the principle:

1. Everything that has a beginning has a cause

is significantly more plausible than the principle:

2. Everything contingent has a cause.

Now, (1) requires Barbara to have a cause but does not require this of Alice, while (2) requires both Barbara and Alice to have causes. But internally, there is really no significant difference between Alice’s life and Barbara’s. Thus, someone who thinks that (1) is significantly more plausible than (2) needs to think that external differences—such as Barbara’s past life being metrically finite with respect to external time—might make a difference as to what needs and what does not need a cause.

If, however, we think that external differences do not make a difference with respect to what needs a cause, we should judge Barbara and Alice the same way. And if we judge Barbara and Alice the same way, then it seems that we should not think (1) is significantly more plausible than (2).

There are other minds

Suppose there are n (physically, including neurally) healthy mature humans on earth. Let Q₁, ..., Q_n be their non-mental qualitative profiles: complete descriptions of their non-mental life in qualitative terms. Let H_i be the hypothesis that everything with profile Q_i is conscious. Now, consider the hypotheses:

• M: All healthy mature humans have a mental life.

• N: Exactly one healthy mature human has a mental life.

• Z: No healthy mature human has a mental life.

Assume our background information contains the that there are at least two healthy mature humans. Given that background, the hypotheses are mutually exclusive. Now add that there are n healthy mature humans on earth, where n is in the billions, and that they have profiles Q₁, ..., Q_n, which are all different. What’s a reasonable thing to think now? Well, N is no more likely than M or Z. Conservatively, let’s just suppose they are all equally likely, and hence all have probability 1/3. Furthermore, if N is true, exactly one H_i is true. Moreover all the H_i are just about on par given N, so P(H_i|N)≈1/n for all i, and hence P(H_i&N) is at most about 1/(3n). On the other hand, P(H_i|Z)=0 and P(H_i|M)=1.

Now suppose I learn that Q_m is my profile. Then I learn that H_m is true. That rules out the all-zombie hypothesis Z, and most of the H_i&N conjunctions. What is compatible with my data are two mutually exclusive hypotheses: H_m&N as well as M. It’s easy to check (e.g., with Bayes’ theorem) that my posterior probability for H_m&N will then be approximately at most 1/(n + 1). Thus, the probability that there is another mind is bigger than 0.999999999.

Whether we can argue for M in this way depends on how the priors for M compare to the priors of hypotheses in between M and N, such as the hypothesis that all but seven healthy mature humans have consciousness.

Antisolipsism

I never heard anyone defend this view: "Billions of people exist but I don't."

Van Inwagen's ear

Van Inwagen holds that:

1. All and only things whose activity constitutes a life (properly) compose a whole.

2. Whether a plurality of things composes a whole depends only on their internal relations.

He considers a counterexample to (1) and (2) of the following sort. Let the xs be the particles in van Inwagen outside the right ear.

3. If van Inwagen were to have lost the right ear, the activity of the xs would have constituted a life (his life) and composed a whole (namely, van Inwagen).

4. But in fact, the activity of the xs does not constitute a life, but only partly does so, along with the activity of the right ear particles.

5. However, the internal relations between the xs were he to have lost his right ear would have been the same as they are now.

This is a problem: for by (4) and (1), the xs do not compose a whole, but by (3) they would have had he lost his right ear, and by (5) they would have had the same internal relations then, which contradicts (2).

Van Inwagen attempts to escape this problem by denying (5), saying that the internal relations between the particles in his body in the vicinity of the right ear would be affected by the ear not being there. For they would no longer experience forces from the ear particles.

But let d be the closest distance between a right-ear particle and a van Inwagen particle not in the right ear (i.e., one of the xs). But now if God were to suddenly annihilate the right ear, then it seems that none of the xs would be in any way affected until influences traveling at the speed of light could bridge the distance d. I.e., until d/c (where c is the speed of light) had passed, the xs would be without the ear just as they are with the ear. Hence, if we specify that the time of severance in (3) is less than d/c ago, van Inwagen’s response seems to fail.

One might try to get out of this by invoking (non-Bohmian) quantum mechanics, and saying that all particles have fuzzy positions, and the ear particles overlap positionally with the non-ear particles, so that the disappearance of the ear particles affects the non-ear particles instantly. But the instant part of the effect is slight. We can imagine that the disappearance of the ear is so orchestrated as to never split any molecules or atoms. But particles in different molecules are fairly localized to their respective molecules, and the effect of the tails of the wavefunction on what is going on in a neighboring molecule will presumably be negligible.

Of course, a negligible effect is still an effect. But we could imagine a third scenario: van Inwagen loses his ear, and God miraculously tweaks the movements of the xs in a slight and biologically negligible way during the d/c period so that they behave just as they do in the actual world where the ear is attached. In that scenario, the xs would compose van Inwagen, but they would have exactly the same internal relations as they do in the actual world.

Artifacts and non-naturalism

One of the reasons to be suspicious of artifacts is that it seems magical to think we have the power to create a new object just by thinking about things a certain way while manipulating stuff. If Bob gets some clay and exercise his fingers by randomly kneading it, he doesn’t make a sculpture or any other new object out of it. But if his identical twin Carl intends to shape the clay into a sculpture, and in doing so moves his fingers in exactly the same way that Bob did, and produces exactly the same shape, then—assuming artifacts exist—he creates a new object, a sculpture. It seems magical that our thoughts should affect what object exists in the world, even when the thoughts make no difference to our manipulation of the world.

When I discussed arguments with this in my Mid-Sized Objects graduate seminar, I found, however, that there was a lot of friendliness towards the view that, yes, we are capable of this magic, though some demurred at the word “magic”. And in particular, a student pointed out that we are in the image of a God who can create.

This has made me think that a non-naturalist can think that our thoughts have effects that are not screened by the movements of our bodies. Thus, it could well be that Carl’s thoughts causes the world to be different. For instance, on a hylomorphic view, Carl could have the power to create a scu;tural form for a piece of clay by his thoughts. Or on a variant of Markosian’s brute composition view, Carl could have the power simply to cause a new object composed of the clay.

In fact, this suggests an interesting new argument against physicalism, where physicalism is understood as the claim that all causal powers reduce to those of physics. Intuitively, the correct ontology includes more things than van Inwagen’s ontology of particles and organisms and but not all the things from the mereological universalist’s bloated ontology. In particular, intuitively, the correct ontology does include Carl’s new sculpture, but Bob hasn’t produced anything new, and hence the correct ontology seems to require a non-natural “magical” power over composition facts to be found in Carl’s (and presumably, albeit in this context unexercised, Bob’s) mind. And if our ontology is to include, as common-sense would suggest, galaxies, planets, mountains and rocks, we need powers in things to produce such objects—i.e., to ensure that their particulate parts do compose something—and these powers are not to be found in physics.

Markosian’s apparently preferred version of the brute composition view can almost accommodate this. On that version, the composition facts supervene on the arrangement of particles: there are infinitely many necessary truths that specify which arrangements of particles compose. But these necessary truths would include lots of arbitrary parameters (e.g., encoding the difference between some stones that are just lying there and a hillock). We don’t want necessary truths with arbitrary parameters. It is much better if any such arbitrary parameters are relocated to the laws of nature or, better, the causal powers of things.

A gambling puzzle about nonmeasurable events

I have two sealed envelopes, labeled A and B. One contains $3 and the other nothing. You don’t know which is which. I am willing to sell either or both envelopes for $1 each. You have a fixed period of time to inform me whether you are buying neither, both, A, or B, after which time you pay any get to open any envelopes you bought.

Obviously, it makes sense for you to hand me $2 and buy both envelopes and profit by a dollar.

But suppose now that I tell you that I chose which envelope to put the $3 using a saturated nonmeasurable method. For instance, perhaps I chose a subset N of the points on the circumference of a spinner that has the properties that:

1. N is nonmeasurable,

2. the only measurable subsets of N have measure zero, and

3. the only measurable subsets of the complement of N have measure zero,

then I spun the spinner, and if the spinner landed in N, I put the $3 in envelope A, and otherwise in B.

Your purchase options are: Neither, Both, A and B. The probability that the $3 is in A is completely undefined (we should represent the probability as the full interval from 0 to 1) and the probability that the $3 is in B is completely undefined.

It seems then:

1. It’s clearly rationally permissible for you to go for Both.

2. Going for A is neither rationally better nor rationally worse than going for Both. For by going for A, you miss out on B. But the expected utility of purchasing B iscompletely undefined: it is a choice to pay $1 for a gamble that has a completely undefined probability of paying out $3. So, it is completely undefined whether Both is better than A or worse. If Both is permissible, so is A, then.

3. But by similar reasoning it is completely undefined whether going for Neither is better than or worse than going for A. For the expected payoff of A is completely undefined. So, if A is rationally permissible, so is Neither, then.

4. Swapping A and B in the reasoning in (2) shows that B is rationally permissible as well.

So now it seems that all four options are equally permissible. But something has gone wrong here: Clearly, Both beats Neither, and it’s irrational to go for Neither.

I think to get out of the above puzzle, we have to deny the initially plausible principle:

5. If an option is rationally permissible, and another option is neither better nor worse than it, then the latter is also permissible.

Here is another case where this principle needs to be denied. You have a choice between playing Pac Man, or eating one scoop of ice cream, or eating two. Playing Pac Man is neither better nor worse than either one or two scoops of ice cream. Two scoops of ice cream is better than one. It is clearly rationally permissible to play Pac Man. By (5), it’s permissible to eat one scoop of ice cream, then. But that’s not true, since two scoops beats one.

So, let’s deny (5). Now I think the reasonable thing to say is that Neither is irrational, but each of Both, A and B is rationally permissible. But there is still a puzzle in the vicinity. Suppose you are asked about your purchases envelope-by-envelope. First you’re offered the chance to buy A, and then a chance to buy B, and once a deal is declined, it’s gone. You have no rational obligation to buy A. After all, going for B alone is permissible. So, let’s say you decline A. Next you’re asked about B. At this point, A is out of the picture, and the question is whether to pay $1 for a completely undefined probability of getting $3. It’s permissible to decline that. So, you can permissibly decline B as well. So, let’s say you do so. Now by a pair of perfectly rational choices you ended up “doing something stupid”. This is a bit like Satan’s Apple. but with a finite number of choices.

The puzzle above seems familiar. I may have read it somewhere and it stuck in my subconscious.

The great chain of being and the glory of God

There are things with power but no knowledge or moral will: e.g., trees. There are things with power and knowledge but no moral will: e.g., horses. There are things with all three: e.g., human beings.

These fundamental attributes mark radical qualitative differences. I suspect there are infinitely many further possible fundamental attributes besides power, knowledge and moral will. A being that had one more of these attributes would be qualitatively as far above us as we are above horses or as far as horses are above trees. But just as a horse cannot conceive of moral will, and a tree cannot conceive of anything, we cannot conceive of what these further attributes would be. All we can do is speculate that then chain power, knowledge and moral will can be continued indefinitely.

God actually has all three of power, knowledge and moral will, and has each to its maximal perfection. If my suspicion about the chain continuing ad infinitum, then all the further attributes in the chain God also has to an infinite degree. (While remaining simple.) But we have no idea what they are.