Brains and animalism

Animalists hold that we are animals. It is widely accepted by animalists that if a brain were removed from a body, and the body kept alive, the person would stay with the bulk of the body rather than go with the brain.

I wonder how much of the intuition is based on irrelevant questions of physical bulk. Imagine aliens who are giant brains with tiny support organs—lungs, heart, legs, etc.—dwarfed by the brain. I think we might have the intuition that if the brain were disconnected from the support organs, the animal would go with the brain. In the case of beings that dwarf their brains, it feels natural to talk of a certain operation as a brain transplant. But in the case of beings that are almost all brain, the analogous operation would probably be referred to as a support-system transplant. Yet surely we should say exactly the same thing metaphysically about us and the aliens, assuming that the functional roles of the brains and the other organs are sufficiently similar.

This isn't a positive argument that we'd go with our brains. It's just an argument to defuse the intuition that we wouldn't.

What about cerebra? Here's a widely shared intuition. If the cerebrum is removed from the skull of an animal and placed in a life-support vat, the animal stays with the rest of the body.

But now suppose that we granted that the animal goes with the whole brain. Let's say, then, that I am an animal and sadly become a brain in a life-support vat, losing the rest of my body. Suppose that next my brain is cut and the upper and lower brains are placed in separate life-support vats. It does not seem particularly plausible to think that the animal goes with the lower brain. (Maybe the animal dies, or maybe it goes with the upper brain.) So once we've granted that the animal would go with the brain, the primacy of the lower brain for animal identity seems somewhat undermined.

Maybe, though, one could accept both (a) the common intuition that if the cerebrum were removed the human animal would go with the rest of its body, and (b) my intuition that if the human animal were first reduced to a brain, and the brain then cut into the cerebrum and lower brain, the animal would go with the cerebrum. There is no logical contradiction between these two intuitions. Compare this. I have a loaf of bread. Imagine the loaf marked off into five equally sized segments A, B, C, D and E. If I first cut off the 2/5 of the loaf marked D and E, it's plausible that the loaf shrinks to the ABC part, and DE is a new thing. And then if I cut off C, the same loaf shrinks once again, to AB. On the other hand if I start off by cutting off the AB chunk, the loaf shrinks to CDE. So the order of cutting determines whether the original loaf ends up being identical to AB or to something else. (We can also make a similar example using some plant or fungus if we prefer a living example.) Likewise, the order of cutting could determine whether the animal ends up being just a cerebrum (first remove brain, then cut brain into upper and lower parts) or whether it ends up being a cerebrumless body.

We might have a rough general principle: The animal when cut in two tends to go with the functionally more important part. Thus, perhaps, when the human animal is cut into a brain and a rest-of-body, it goes with the brain, as the brain is functionally more important in the brainier animals. When that brain is subsequently cut into upper and lower brains, the brainy animal goes with the upper brain, as that's functionally more important given its distinctively brainy methods for survival. On the other hand, if the human animal is cut into a cerebrum and a cerebrumless-rest-of-body, perhaps (I am actually far from sure about this) the animal goes with the cerebrumless-rest-of-body, because although the upper brain is more important functionally than a lower brain, the lower brain plus the rest of the body are collectively more important than the upper brain by itself. So the order of surgery matters to identity.

Self-ownership and organ sale

1. Things owned can be permissibly traded, barring special circumstances.
2. Trade in persons is never permissible.
3. Thus, no one owns a person. (By 1-3)
4. Thus, no person owns herself. (By 4)

(By the same argument, God doesn't own us, either. We belong to God, of course, but not by way of ownership.)

Let's continue thinking about self-ownership:

5. If x is not simple and I own every proper part of x, I own x.
6. I don't own myself. (By 4 and as I am a person)
7. I am not simple.
8. So, there is a proper part of me that I don't own. (By 5-7)
9. All my proper parts are on par with respect to my ownership of them.
10. So, I don't own any of my proper parts. (By 8-9)

While I think the conclusion of this argument is true, I am less convinced by it than by the earlier argument. I think 9 is not completely convincing given dualism: spiritual parts perhaps aren't on par with physical. I am far from sure about 7. And I could see ways of questioning 5. Still, it's an argument worth thinking about.

Suppose the argument is correct. Then we have a further interesting argument:

11. My organs are proper parts of me.
12. It's wrong or impossible for me to sell what I don't own.
13. So it's wrong or impossible for me to sell my organs. (By 10-12)

While I am sympathetic to the conclusion, I worry that this argument may equivocate on "organs". Aristotle says that a severed finger is a finger in name alone. Perhaps 11 is true of a kidney as it is found in me, but once the kidney is removed from me, the kidney perishes and a new kidney-like object—a kidney only in name—comes into existence. The kidney-like object is not a part of me, and it is this kidney-like object that is being sold, not the kidney that was a part of me. Still, this isn't clear: maybe the kidney that was a part of me is what is sold, since it is for the loss of it that I am being compensated if "I sell my kidney."

More worryingly, if the above argument were sound, it seems it would be sound with "organs" replaced by "hair". But it doesn't seem wrong or impossible for me to sell my hair. Perhaps, though, we should modify 9 to read:

9*. If I own any one of my living proper parts, I own all my living proper parts and a fortiori all my non-living proper parts.

Then the conclusion is weaker than 10:

10*. I don't own any of my living parts.

This could allow me to sell my hair and some gold atoms in my body, but not my kidney.

Convincing

Free will is incompatible with (causal) determinism, and I know it. I know it because I have sound arguments for it, with compelling premises. It is good for people to know the truth about things that matter, and this is one of them. So I should be glad, for your sake and not just out of vanity, if I convinced you by one of these compelling arguments. And I would be glad.

But perhaps I shouldn't be glad if I convinced everyone, and that's for two reasons. First, there actually being compatibilists helps keep incompatibilist investigators honest and leads to a deeper understanding of the ways in which determinism precludes free will. Second, while I know that freedom is incompatible with determinism, I might be wrong. That chance is sufficiently small that it's safe for me and you to risk the cost of being wrong. But the cost of everyone getting this wrong is more than the sum of the costs of the individuals getting it wrong. Once something becomes near universally accepted, it is much harder for humankind to retreat from it.

Thus, while I want to convince you of incompatibilism, I also want there to be dissent in the epistemic community. This is something like a tragedy of the commons in the epistemic sphere.

Fortunately, human nature is such that I run only an insignificant risk of getting everyone to agree with me when I offer an argument for incompatibilism. So I can offer the arguments safely.

I chose the example of incompatibilism carefully. I wouldn't say the same thing about things that I am much more confident of, say that there is a physical world or that 2+2=4. There the risk of being wrong is so small and the level of unreasonableness in denying the claim are sufficiently high that it would be good for the epistemic community to have universal agreement. On the other hand, there are philosophical doctrines which I think are likely to be true, but where I am sufficiently unsure that I would cringe if I convinced someone.

A quick argument for the bijection principle

The bijection principle says that if we have two sets A and B and we can pair up all the objects of the two sets, then the the sets have the same number of members.

Some people don't like the bijection principle because it leads to the counterintuitive conclusion that there are as many primes as natural numbers.

Here's an argument for the bijection principle. Let's run the argument directly for the above controversial case—that should be enough of an intuition pump to get the general principle. Take infinitely many pieces of paper that are red on one side and blue on the other. Number the pieces of paper 1,2,3,..., putting the numerals down on the red sides. Then on the piece of paper numbered n on the red side, write down the nth prime on the blue side. Then:

1. There are just as many natural numbers as red sides.
2. There are just as many red sides as blue sides.
3. There are just as many blue sides as prime numbers.
4. So, there are just as many natural numbers as prime numbers.

It's very hard to deny that 4 follows from 1-3, and it's very hard to deny any of 1-3.

Two kinds of authority

A president exercises authority with respect to a group that includes herself. She is included in two ways. First, the common good that her authority promotes is a good of a group that includes herself. Second, her legal enactments bind her just as much as they bind other citizens.

Not all authority is like this. A Dean of Students, for instance, exercises authority over students and for the sake of their good, and typically is not a student herself.

Sometimes authority of the second sort derives from authority of the first sort. The Dean of Students has an authority deriving from the consent of the students, and the students have an authority of the first sort over themselves. The general has an authority of the second sort (I think), deriving from that of the president.

An interesting hypothesis is that the second sort of authority always derives from the first. There are two nice test cases: parental and divine authority.

Parental authority is of the second sort. Is it derivative? If not, then the hypothesis is false. Maybe parental authority derives from the authority of one or both parents over the whole family, which would be of the first type? Or from God's authority?

God's authority is surely non-derivative and yet seems to be of the second type, yielding a counterexample. But maybe God's authority is of the second type: God is trying to put together a kingdom of ends that he is head of.

Or maybe the first sort of authority derives from the second? That could make for a neat story, with divine authority on top.

Or maybe there is no interesting derivation relationship.

Blackmail, promises and self-punishment

I was reading this interesting paper which comes up with "blackmail" stories against both evidential and causal decision theory (CDT). I'll focus on the causal case. The paper talks about an Artificial Intelligence context, but we can transpose the stories into something more interpersonal. John blackmails Patrick in such a way that it's guaranteed that if Patrick pays up there will be no more blackmail. As a good CDT agent, Patrick pays up, since it pays. However, Patrick would have been better off if he were the sort of person who refuses to pay off blackmailers. For John is a very good predictor of Patrick's behavior, and if John foresaw that Patrick would be unlikely to pay him off, then John wouldn't have taken the risk of blackmailing Patrick. So CDT agents are subject to blackmail.

One solution is to add to the agent's capabilities the ability to adopt a policy of behavior. Then it would have paid for Patrick to have adopted a policy of refusing to pay off blackmailers and he would have adopted that policy. One problem with this, though, is that the agent could drop the policy afterwards, and in the blackmail situation it would pay to drop the policy. And that makes one subject to blackmail once again. (This is basically the retro-blackmail story in the paper.)

Anyway, thinking about these sorts of cases, I've been playing with a simplistic decision-theoretic model of promises and weak promises—or, more generally, commitments. When one makes a commitment, then on this model one changes one's utility function. The scenarios where one fails to fulfill the commitment get a lower utility, while scenarios where one succeeds in fulfilling the commitment are unchanged in utility. You might think that you get a utility bonus for fulfilling a commitment. That's mistaken. For if we got a utility bonus for fulfilling commitments, then we would have reason to promise to do all sorts of everyday things that we would do anyway, like eat breakfast.

This made me think about agents who have a special normative power: the power to lower their utility function in any way that they like. But they lack the power to raise it. In other words, they have the power to replace their utility function by a lower one. This can be thought of in terms of commitments—lowering the utility value of a scenario by some amount is equivalent to making a commitment of corresponding strength to ensure that scenario isn't actualized—or in terms of mechanisms for self-punishment. Imagine an agent who can make robots that will zap him in various scenarios.

Now, it would be stupid for an agent simply to lower his utility function by a constant amount everywhere. That wouldn't change the agent's behavior at all, but would make sure that the agent is less well off no matter what happens. However, it wouldn't be stupid for the agent to lower his utility function for scenarios where he gives in to blackmail by agents who can make good predictions of his behavior and who wouldn't have blackmailed him if they thought he wouldn't give in. If he lowers that utility enough—say, by making a promise not to negotiate with blackmailers or by generating a robot that zaps him painfully if he gives in—then a blackmailer like John will know that he is unlikely to give in to blackmail, and hence won't risk blackmailing him.

The worry about the agent changing policies and thereby opening oneself to blackmail does not apply on this story. For the agent in my model has only been given the power to lower his utility function at will. He doesn't have the power to raise it. If the agent were blackmailed, he could lower his utility function for the scenarios where he doesn't give in, and thereby get himself to give in. But it doesn't pay to do that, as is easy to confirm. It would pay for him to raise his utility function for the scenarios where he gives in, but he can't do that.

An agent like this would likewise give himself a penalty for two-boxing in Newcomb cases.

So it's actually good for agents to be able to lower their utility function. Setting up self-punishments can make perfect rational sense, even in the case of a perfect rational agent, so as to avoid blackmail.

System-relativity of proofs

There is a generally familiar way in which the question whether a mathematical statement has a proof is relative to a deductive system: for a proof is a proof in some system L, i.e., the proof starts with the axioms of L and proceeds by the rules of L. Something can be provable in one system—say, Euclidean geometry—but not provable in another—say, Riemannian geometry.

But there is a less familiar way in which the provability of a statement is relative. The question whether a sentence p is provable in a system L is itself a mathematical question. Proofs are themselves mathematical objects—they are directly the objects in a mathematical theory of strings of symbols and indirectly they are the objects of arithmetic when we encode them using something like Goedel numbering. The question whether there exists a proof of p in L is itself a mathematical question, and thus it makes sense to ask this question in different mathematical systems, including L itself.

If we want to make explicit both sorts of relativity, we can say things like:

1. p has (does not have) a proof in a system L according to M.

Here, M might itself be a deductive system, in which case the claim is that the sentence "p has (does not have) a proof in L" can itself be proved in M (or else we can talk of the Goedel number translation of this), or M might be a model in which case the claim is that "p has a proof in L" is true in that model.

This is not just pedantry. Assume Peano Arithmetic (PA) is consistent. Goedel's second incompleteness theorem then tells us that the consistency of PA cannot be proved in PA. Skipping over the distinction between a sentence and its Goedel number, let "Con(PA)" say that PA is consistent. Then what we learn from the second incompleteness theorem is that:

2. Con(PA) has no proof in PA.

Now, statement (2), while true, is itself not provable in PA.[note 1] Hence there are non-standard models of PA according to which (2) is false. But there are also models of PA according to which (2) is true, since (2) is in fact true. Thus, there are models of PA according to which Con(PA) has no proof and there are models of PA according to which Con(PA) has a proof.

This has an important consequence for philosophy of mathematics. Suppose we want to de-metaphysicalize mathematics, move us away from questions about which axioms are and are not actually true. Then we are apt to say something like this: mathematics is not about discovering which mathematical claims are true, but about discovering which mathematical claims can be proved in which systems. However, what we learn from the second incompleteness theorem is that the notion of provability carries the same kind of exposure to mathematical metaphysics, to questions about the truth of axioms, as naively looking for mathematical truths did.

And if one tries to de-metaphysicalize provability by saying that what we are after in the end is not the question whether p is provable in L, but whether p is provable in L according to M, then that simply leads to a regress. For the question whether p is provable in L according to M is in turn a mathematical question, and then it makes sense to ask according which system we are asking it. The only way to arrest the regress seems to be to suppose that at some level that we simply are talking of how things really are, rather than how they are in or according to a system.

Maybe, though, one could say the following to limit one's metaphysical exposure: Mathematics is about discovering proofs rather than about discovering what has a proof. However, this is a false dichotomy, since by discovering a proof of p, one discovers that p has a proof.

Deep Space Nine in Minecraft

My big kids and I are Deep Space 9 fans. Here's a Deep Space 9 station rendered in Minecraft using our modifications to Martin O'Hanlon's rendering script from a mesh by Joerg Gerlach. For more on python and Minecraft, see here.

Escaping infinitely many arrows

Suppose infinitely many thin arrows are independently shot at a continuous target, with hitting points uniformly distributed over the target. How many arrows would we need to shoot to make it likely that the center of the target has been hit?

Given finitely or countably infinitely many arrows, the probability that the center will be hit is zero. But what if there are as many arrows as points in the continuum? And what if there are more?

I don't know of a good mathematical model for these questions. Standard mathematical probability is defined up to sets of measure zero, and this makes it not useful for answering questions like this. Questions like this seem to make sense, nonetheless, thereby indicating a limitation of our mathematical models. But perhaps that is a mere seeming.

Bigger and smaller infinities

Anecdotal data suggests that a number of people find counterintuitive the Cantorian idea that some infinities are bigger than others.

This is curious. After all, the naive thing to say about the prime numbers and the natural numbers is that

1. while there are infinitely many of both, there are more natural numbers than primes.

For the same reason it is also surely the obvious thing to say that

2. while there are infinitely many of both, there are more real numbers than natural numbers.

So there is nothing counterintuitive about different sizes of infinity. Of course, (1) is false. Our untutored intuitions are wrong about that case. And that fact should make us suspicious whether (2) is true; given that the same intuitions led us astray in the case of (1), we shouldn't trust them much in case (2). However, the fact that (1) is false should not switch (2) from being intuitive to being counterintuitive. Moroever, our reasons for thinking (1) to be false—namely, the proof of the existence of a bijection between the primes and the naturals—don't work for (2).

All in all, rather than taking (2) to show us how counterintuitive infinity is, we should take (2) to vindicate our pretheoretic intuition that cardinality comparisons can take us beyond the finite, even though some of our pretheoretic intuitions as to particular cardinality comparisons are wrong.

Living in the moment, literally

Jim lives for a minute. Then he activates the time-and-space machine in his backpack, and travels to position one minute back and one meter back. Then the story repeats, giving Jim a lifespan of 80 internal years, all contained within a single minute of external time.

We could shorten that minute of external time to a second, or to any non-zero length of time, by making him jump back in time even faster.

Bold Hypothesis: We could shorten it to zero.

This works most easily if Jim is made out of ghostly matter that can overlap itself (nothing absurd about this: two photons can be in the same place at the same time), and as we shorten the time interval, we shorten the spatial distance of the jump.

The Bold Hypothesis basically says that just as one can have a time-travel machine, one can have a time-non-travel machine that keeps one in the same place in external time for all one's life.

Given the possibility of time travel, and the possibility of discrete time, it's not hard to argue for the Bold Hypothesis. Suppose at each instant of time, Jim can set the time-machine to determine where he will be in the next internal instant. Then why couldn't he set it so that in the next internal instant he will be at the same external instant as he is now.

Given the Bold Hypothesis, Jim would have a lifespan of 80 internal years, all in one moment.

All this suggests that when thinking about time, we should be careful with moving from our subjective experience of time and change--which Jim would have in his all-at-one-moment life--to claims about what external time is like.

When would a computer feel pain?

Whether a computer could feel pain shouldn't depend on fine detail of how the CPU synchronization works or whether the CPU is implemented with electricity, or light, or gears. It's only the computational characteristics that matter if computers can be conscious.

Let's imagine a simplified picture of a computer's synchronization. There is a synchronizing clock. Each time the clock ticks, the computer very quickly executes the next instruction and enters a new state. Then it stays in its new state until the next clock tick.

Let's imagine that the dynamic stuff that is triggered by each clock tick takes places over a small portion of the time between ticks—most of the time between ticks, the computer is staying in a static state. For instance, if the computer is made up of gears, as a computer could well be (though it would be impractically big), then the picture is this. The computer is still for a while. Then the clock ticks. The gears make a quick movement to a new configuration. And then the computer is still until the next tick.

Suppose the computer feels pain. When does it do that? It is hard to believe that the computer is feeling pain when it is statically maintaining its state in between ticks. Suppose the computer got stuck between ticks—the clock broke down. Would the computer be permanently in pain?! I guess I just find it incredible that a contraption made of gears should feel something when the gears are not even moving.

So I think the best candidate for when the computer would feel pain would be when it is transitioning between states. But remember the intuition that only the computational characteristics matter to things like pain if computers can be conscious—the details as to implementation should be irrelevant. Assuming it's possible for a computer to feel pain, we should thus be able to have a possible world with a computer in pain whose state transitions are instantaneous. For a nanosecond all is still. Then a clock ticks. The computer instantaneously jumps to a new state. Another nanosecond of stillness. And so on.

The computer in this story, then, feels pain only during a series of instants. The total amount of time it spends feeling pain is zero. Yet it feels pain. Is that possible? Can there be pains that take no time at all?

Perhaps, though, the computer's subjective time doesn't line up with objective time. Maybe objectively the pains take zero time, but subjectively they take a lot more time? I don't know if this is possible.

There may be an argument against the possibility of computers feeling pain in the vicinity. In any case, there are interesting questions here.

Note: When I talk of a computer feeling pain, I mean a merely material computer. As Swinburne has pointed out to me, God could give a soul to a computer. And then there could be consciousness. But the subject of the pain, I think, wouldn't be the computer. The computer would be like a body. My body never feels pain. It is I (the whole of which the body is a part) who feel the pain.

A paradox about prediction of belief

Sally is perfectly honest, knows for sure whether there has ever been life on Mars (she's just finished an enormous amount of NASA data analysis), and is a perfect predictor of my future beliefs. She then informs me that she knows what I will believe at midnight about whether there was once life on Mars, and she further informs me that:

1. There was once life on Mars if and only at midnight tonight I will fail to believe that there was once life on Mars.

Moreover, I know that:

2. I won't get any other evidence relevant to whether there was once life on Mars.

I'd love to know whether there was once life on Mars. I start off thinking:

Well, right now I have no belief either way, and I am unlikely to get any evidence before midnight. So by midnight I will also have no belief either way. And thus by Sally's information there was once life on Mars.

But of course as soon as I accept this argument, I start to believe that there was life on Mars. And I know that if I keep on believing this until midnight, then my belief is false. I quickly see the pattern, and I realize that I don't know what to think! But when I don't know what to think, I default to suspension of judgment. But this, too, leads me astray: For as soon as I think that the appropriate rational attitude for me is suspension of judgment, then I start thinking I will suspend judgment at midnight, and I then conclude that there was once life on Mars. And the circle starts again.

Now, I know I'm not perfectly rational. So I can get out of the circle by concluding that given how confusing this case is, I am probably not going to act rationally. So something non-rational will affect my beliefs by midnight, and I don't know what that will be, so I might as well not speculate until that happens. Sally knows what it will be, but I don't.

But suppose I am perfectly rational. I shall assume that a part of perfect rationality is knowing for sure you're perfectly rational, knowing for sure what you belief, and drawing all the right conclusions from one's evidence. What should I believe in the above case?

Truth and Dutch Books

Suppose I initially assigned probability 0.5 to p and 0.5 to ~p. Suppose p is in fact true, and my credence in p comes to be magically increased to 0.8 without my credence in ~p being changed. I thus have inconsistent probabilities: 0.8 for p and 0.5 for ~p. This is supposed to be bad: it lays me open to Dutch Books. For instance, I will accept the following pair of options:

1. Pay $0.75 to win $1.00 if p
2. Pay $0.45 to win $1.00 if ~p.

But if I do that, then I will pay $1.20 and get $1.00, for a net loss of $0.20.

Yes, that's an unhappy result. But note that I am actually better off than earlier when my credences were consistent. Earlier I would have rejected (1) since my credence in p was 0.5, but I would have accepted (2). So I would have paid $0.45 and got nothing to show for it. Thus my revision in the direction of truth made me be better off, even though it also led me to accept a Dutch Book.

This suggests that pragmatically and synchronically speaking what matters is truth, not probabilistic consistency. Better be inconsistent and closer to truth than consistent and further from truth.

Diachronically, of course, at least logical inconsistency could be dangerous, as it can lead to lots of absurd conclusions. But in practice we all have inconsistent beliefs and we manage to contain the inconsistency without much in the way of explosion.

So what's so bad about Dutch Books? It seems to be this: an opponent who knows (with certainty) your credences and doesn't know (at least with certainty) whether p is true can offer you a series of bets that you are guaranteed to lose money on. This is a big deal if you're playing an adversarial game against such an opponent. But such games are, I think, a special case, and while they do occur in war, business, sport and other competitive pursuits, we should not let competitive pursuits against fellow humans dictate the nature of rationality to us. And note a curious thing: consistency is not the only available strategy against such an opponent—hiding your credences will also help. If you revise your credence in the direction of truth but your opponent doesn't know about your revision, you will do at least as well as before, and quite possibly better.

Particle accretion and excretion in Aristotelian ontology

In Aristotelian ontology the matter and parts of a substance get their being from their substance. But now we have a problem: we constantly accrete (say, when eating) and excrete (say, when sloughing off skin-cells) particles. These particles seem to exist outside of us, then they exist as part of us, and then one day they come to exist outside of us again. How could their being come from our form, when they existed before they joined up with us—sometimes, presumably, even before we existed at all?

But suppose an ontology for physics on which fields are more fundamental than particles, and particles are like a bump or wave-packet in a field. Then we have a very nice solution to the problem of accretion and excretion.

Imagine two ropes. Rope A is tied by one end to a hook on the wall and the other end of rope A is tied to the end of rope B. And you're holding the other end of rope B. You rapidly move your end of the rope up and down. A wave starts traveling along rope B, then over the knot, and finally along rope A. We are quite untroubled by this description of this ordinary phenomenon.

In particular, it is correct to say that the same wave was traveling along rope A as along rope B. Yet surely the being of a wave in a medium comes from the medium and its movement. So we have a very nice model. Rope A has excreted the wave and rope B has accreted the wave. (You might object that in Aristotelian ontology, ropes aren't substances. Very well: replace them with strings of living kelp.) If the knot is negligible enough, then the shape of the wave will seamlessly travel from rope A into rope B.

I think one reason an Aristotelian is apt to be untroubled by the description is because we don't take waves in a rope ontologically very seriously, just as we shouldn't take kings in chess very seriously. They're certainly not fundamental. Perhaps they don't really exist, but we have merely adopted a mode of speech on which it's correct to talk as if they existed.

However, if a field ontology is correct, we shouldn't take particles any more seriously than waves in a rope. And then we can start with the following model. Among the substances in the world, there are fields, gigantic objects that fill much of spacetime, such as the electromagnetic field. And there are also localized substances, which are tiny things like an elephant or a human or a bacterium. The fields have holes in them, holes perfectly filled by the localized substances. The localized substances exist within the fields much like a diver exists in the ocean—the diver exists in a kind of hole in the ocean's water.

Next, pretty much the same kinds of causal powers that are had by the fields are had by the localized substances. Thus, while strictly speaking there is no electromagnetic field where your body is found, you—i.e., the substance that is you—act causally just as the electromagnetic field would. A picture of the field you might have is of a string whose central piece had rotted out and was seamlessly replaced with a piece of living kelp that happened to have the same material properties as the surrounding string. But you don't just do duty for the electromagnetic field. You do duty for all the fundamental fields.

Because you have pretty much the same kinds of causal powers as the fields that surround you, waves can seamlessly pass through you, much as they can through a well-installed patch in a rubber sheet. You accrete the waves and then excrete them. Some wave packets we call "particles".

Objection: When I digest something, it becomes a part of me. But when a radio wave passes through me, it doesn't become a part of me even for a brief period of time.

Response 1: We shouldn't worry about this. In both cases we're talking about non-fundamental entities. There are many ways of talking. For practical reasons, it's useful to distinguish those wave packets that stick around for a long time from those that pass in and out. So we say that the former are denizens of us and the latter are visitors.

Response 2: Perhaps that's right. Maybe we don't exist in holes in the fields, but rather the fields overlap us. However, when the fields are in us, we take over some, but not all, of their causal powers. The radio wave that travels through me does so by virtue of the electromagnetic field's causal powers, while the particles of the piece of cheese that I digest and which eventually slough off with my dead skin travel through me by virtue of my causal powers. The picture now is more complicated.