Leibniz's King of China thought experiment

Leibniz famously offers this thought experiment:

Supposing that an individual were to instantly become King of China, but on the condition of forgetting what he has been, as if he was completely born again—isn’t that practically, with regard to perceivable effects, as if he were to be annihilated and a King of China were to be created in the same moment in his place? This the individual has no reason to desire. (Gerhardt IV, p. 460)

The context is that Leibniz isn’t doing metaphysics here, but supporting an ethical point that memory is needed for one to be a fit subject for reward and punishment and a theological point that eternal life requires more than mere eternal existence without the psychological features of human life. Nonetheless, some have thought that thought experiments like Leibniz’s offer support for memory theories of personal identity. I will argue that tweaking Leibniz’s thought experiment in two ways shows that this employment would be mistaken. In fact, I think the second tweak will offer an argument against memory theories.

Tweak 1: Memory theories of personal identity require a chain of memories, but not a chain of personally important memories. So all we need to ensure identity of the earlier individual with the later King of China is that the King of China remembers something really minor from the hour before the transformation, say seeing a fly buzzing around. Allowing the memory of a fly to survive the enthronement does not affect the intuition that the process is one that “the individual has no reason to desire.” The loss of personally important memories—especially of interpersonal relationships—is too high a price for the alleged benefit of ruling a great nation. Hence the intuition is not about personal identity, but—as Leibniz himself thinks—about prudential connections in a person’s life. Nor should we modify memory theories of personal identity to require the memories to be personally important, since that would make personal identity too fragile.

Tweak 2: First, suppose that in addition to the individual’s memories being wiped, the individual gets a new set of memories implanted, copied from some other living person. That so far does not affect the intuition that the process is one that one has “no reason to desire.” Second, add that the other living person happens to be one’s exact duplicate from Duplicate Earth. On memory theories of personal identity, one still perishes—the memories aren’t one’s own, even if they are exactly like one’s own. But a good chunk of the force of the thought experiment evaporates. It is, admittedly, an important thing that one’s apparent memories be real memories, and when they are taken from one’s exact duplicate, they are not. If one’s apparent memories are from one’s duplicate, then one isn’t remembering one’s friends and family, but instead is having quasi-memories of the duplicate’s friends and family, who happen to be exactly like one’s own. That is a real loss objectively speaking. But it is a much lesser loss than if one’s memories are simply wiped or replaced by those of a non-duplicate.

Note further that in the case where one’s memories are replaced by those of a duplicate, if enough benefits are thrown into the King of China scenario, the whole thing might actually become positively worthwhile. Suppose you are a lonely individual without significant personal relationships, but as King of China you would have a fuller and more interpersonally fulfilling life, despite the inevitable presence of flatterers and the mind-numbing work of ruling a vast empire. Or suppose creditors are hounding you night and day. Or you have a disease that can only be cured with the resources of a vast empire. When we note this, we see that the modified thought experiment provides evidence against the memory theory. For on the memory theory, it makes no difference to one’s identity whether the memories will come from a duplicate or not, as long as they don’t come from oneself, and what benefits the King of China will receive is largely prudentially irrelevant.

Objection 1: If the King of China gets memories from your duplicate, then the King of China will have your values and will promote your goals with all of the power of an empire. That could be prudentially worth it and provides some noise for the tweaked thought experiment.

Response: We can control for this noise. Distinguish your goals into two classes: those where your existence is essential to the goal and those where your existence is at most incidental to the goal. We can now suppose that you are a selfish individual who has no goals of the second type. Or we can suppose that all your goals of the second type are such that you think that being King of China will not actually help with them. (Perhaps world peace is a goal of yours, but like Tolstoy you think individuals, including emperors, are irrelevant to such goals.)

Objection 2: If you know that the duplicate has the exact same memories as you do, then copying memories from the duplicate at your behest maintains a counterfactual connection between the final memory state and your pre-transformation memories. If the latter were different from what they are, you wouldn’t have agreed to the copying.

Response: There is nothing in Leibniz’s thought experiment about your consent. We can suppose this just happens to you. And that it is a complete coincidence that the subject from whom memories are taken and put into you is your duplicate.

Do particles have a self-concept?

Of course not.

But consider this. A negatively charged substance has the power to attract other substances to itslf. Its causal power thus seems to have a centeredness, a de se character. The substance’s power somehow distinguishes between the substance itself and other things.

Put this way, Leibniz's (proto?)panpsychism doesn’t seem that far a departure from a more sedate commitment to causal powers.

Panteleology: A few preliminary notes

Panteleology holds that teleology is ubiquitous. Every substance aims at
some end.

The main objection to panteleology is the same as that to panpsychism: the incredulous stare. I think a part of the puzzlement comes from the thought that things that are neither biological nor artifactual “just do what they do”, and there is no such thing as failure. But this seems to me to be a mistake. Imagine a miracle where a rock fails to fall down, despite being unsupported and in a gravitational field. It seems very natural to say that in that case the rock failed to do what rocks should do! So it may be that away from the biological realm (namely organisms and stuff made by organisms) failure takes a miracle, but the logical possibility of such a miracle makes it not implausible to think that there really is a directedness.

That said, I think the quantum realm provides room for saying that things don’t “just do what they do”. If an electron is in a mixed spin up/down state, it seems right to think about it as having a directedness at a pure spin-up state and a directedness at a pure spin-down state, and only one of these directednesses will succeed.

Panteleology seems to be exactly what we would expect in a world created by God. Everything should glorify God.

Panteleology is also entailed by a panpsychism that follows Leibniz in including the ubiquity of “appetitions” and not just perceptions. And it seems to me that if we think through the kinds of reasons people have for panpsychism, these reasons extend to appetitions—just as a discontinuity in perception is mysterious, a discontinuity in action-driving is mysterious.

Motivating panpsychism

There is something attractive about an ontology where all the properties are powers, but it seems objectionable.

First, a power is partly defined by the properties it can produce. But if these in turn are powers, then we have a vicious regress or circularity.

At the same time, mental properties do not seem to be purely powers: they seem to have a categorical qualitative character that is not captured by the power to produce something else.

What is attractive about a pure powers ontology is the conceptual simplicity, and the fact that categorical properties seem really mysterious.

There is, however, a modification we can make to a pure powers ontology that gets us out of the problem. There are two kinds of properties: powers and qualia. The mysteriousness objection does not apply to qualia, because we experience them. On this ontology, powers bottom out in the ability to produce qualia.

For this to avoid implausible anthropocentrism, we need panpsychism—only then will there be enough qualia outside of living things for the powers of fundamental physics to bottom out in. So we have an interesting motivation for panpsychism: it yields an attractive ontology for reasons that have nothing to do with the usual concerns in the philosophy of mind.

It’s worth noting that this ontology is similar to Leibniz’s. Leibniz had two kinds of properties: appetitions and perceptions. The appetitions are (deterministic) powers. Perceptions are similar to qualia, but not quite the same, because (a) perceptions need not be conscious, and (b) perceptions are always representational. Unfortunately, the representational aspect leads to a regress or circularity problem, much as the power powers ontology did, since representationality will define a perception in terms of other appetitions and perceptions.

Leibniz on the PSR

According to the Principle of Sufficient Reason (PSR), every contingent fact has a sufficient reason. What does “sufficient” mean here? A natural thought is that it means that the reason is logically sufficient for the fact. My own work on the PSR rejects this natural thought. I say that a sufficient reason is one that suffices to explain the fact, not necessarily one that suffices for the fact to be true. I occasionally worry that this is too wimpy a take on the PSR, indeed a kind of bait-and-switch.

When I worry about this, it helps me to come back to Leibniz, whom nobody considers a wimp with respect to the PSR. How does Leibniz understand “sufficient”?

In the Principles of Nature and Grace, Leibniz talks of the

grand principe … qui porte que rien ne se fait sans raison suffisante; c’est-à-dire que rien n’arrive sans qu’il soit possible à celui qui connaîtrait assez les choses de rendre une raison qui suffise pour déterminer pourquoi il en est ainsi, et non pas autrement [great principle … which holds that nothing happens without sufficient reason; that is to say, that nothing happens without its being possible for someone who knows enough about how things are to give a reason that suffices to determine why it is so and not otherwise]. (my italics)

Leibniz does not say that the reason is sufficient to determine the fact. Rather, Leibniz carefully says that the reason is sufficient to determine why the fact occurred. You can read off the explanation, the answer to the why question, from the reason, but no claim is made that you can read the explained fact off from it.

Indeed, the only necessitation in the paragraph is hypothetical:

De plus, supposé que des choses doivent exister, il faut qu’on puisse rendre raison pourquoi elles doivent exister ainsi, et non autrement. [Further, supposing things must exist, it has to be possible to give a reason why they must exist so and not otherwise.] (my italics)

I wish Leibniz had this weaker picture of sufficient reason consistently. Sadly for me, he does not. In a 1716 letter to Bourguet he writes:

Mr. Clark … n’a pas bien compris la force de cette maxime, que rien n’arrive sans une raison suffisante pour le determiner. [Mr. Clark … has not understood well the force of the maxim that nothing happens without a reason sufficing to determine it.]

Oh well.

I comfort myself, however, that my philosophical hero does, after all, have two kinds of necessity, and hopefully the determination in the PSR involves the weaker one.

Gunk, etc.

If we think parts are explanatorily prior to wholes, then gunky objects—objects which have parts but no smallest parts—involve a vicious explanatory regress. But if one takes the Aristotelian view that wholes are prior to parts, then the regress involved in gunky objects doesn’t look vicious at all: the whole is prior to some parts, these parts are prior to others, and so on ad infinitum. It’s just like a forward causal regress: today’s state causes tomorrow, tomorrow’s causes the next day’s, and so on ad infinitum.

On the other hand, on the view that parts are explanatorily prior to wholes, upward compositional regresses are unproblematic: the head is a part of the cow, the cow is a part of the earth, the earth is a part of the solar system, the solar system is a part of the Orion arm, the Orion arm is a part of the Milky Way, the Milky Way is a part of the Local Group, and this could go on forever. The Aristotelian, on the other hand, has to halt upward regresses at substances, say, cows.

This suggests that nobody should accept an ontologically serious version of the Leibniz story on which composition goes infinitely far both downward and upward, and that it is fortunate that Leibniz doesn’t accept an ontologically serious version of that story, because only the monads and their inner states are to be taken ontologically seriously. But that's not quite right. For there is a third view, namely that parthood does not involve either direction of dependence: neither do parts depend on wholes nor do wholes depend on parts. I haven't met this view in practice, though.

Leibniz on infinite downward complexity

Leibniz famously thinks that ordinary material objects like trees and cats have parts, and these parts have parts, and so on ad infinitum. But he also thinks this is all made up of monads. Here is a tempting mental picture to have of this:

• Monads, …, submicroscopic parts, microscopic parts, macroscopic parts, ordinary objects.

with the “…” indicating infinitely many steps.

This is not Leibniz’s picture. The quickest way to see that it’s not is that organic objects at each level immediately have primary governing monads. There isn’t an infinite sequence of steps between the cat and the cat’s primary monad. The cat’s primary monad is just that, the cat’s primary monad. The cat is made up of, say, cells. Each cell has a primary monad. Again, there isn’t an infinite sequence of steps between the cat and the primary monads of the cells: there might turn out to be just two steps.

In fact, although I haven’t come across texts of Leibniz that speak to this question, I suspect that the best way to take his view is to say that for each monad and each object partly constituted by that monad, the “compositional distance” between the monad and the object is finite. And there is a good mathematical reason for this: There are no infinite chains with two ends.

If this is right, then the right way to express Leibniz’s infinite depth of complexity idea is not that there is infinite compositional distance between an ordinary object and its monads, but rather than there is no upper bound on the compositional distance between an ordinary object and its monads. For each ordinary object o and each natural number N, there is a monad m which is more than N compositional steps away from o.

Two kinds of occasionalism

Suppose a burner is turned on, a pot is heated, and the water in the pot is boiled. On occasionalism, the heating of the pot is caused only by God, and the same is true for the boiling of the water.

But there are two ways of understanding this:

1. God causes the water to boil because the pot is being heated. God causes the pot to be heated because the burner is on. God causes the burner to be on because….

2. God causes the water to boil just because God causes the pot to be heated. God causes the pot to be heated just because God causes the burner to be turned on. God causes the burner to be on just because God causes…

On type 1 occasionalism, God reacts to events in the world, and one has real but non-causal explanatory connections in the world: the water boils because the burner is on. On type 2 occasionalism, there are no real explanatory connections between events in the world: they are all just the effects of God’s plan. Leibniz has type 2 occasionalism in intermonadic causation. And that’s a problem.

I am not saying that type 1 occasionalism has no problems. But at least it makes for real explanatory connections between events in the world, even if these are not causal.

Wishful thinking

Start with this observation:

1. Commonly used forms of fallacious reasoning are typically distortions of good forms of reasoning.

For instance, affirming the consequent is a distortion of the probabilistic fact that if we are sure that if p then q, then learning q is some evidence for p (unless q already had probability 1 or p had probability 0 or 1). The ad hominem fallacy of appeal to irrelevant features in an arguer is a distortion of a reasonable questioning of a person’s reliability on the basis of relevant features. Begging the question is, I suspect, a distortion of an appeal to the obviousness of the conclusion: “Murder is wrong. Look: it’s clear that it is!”

Now:

2. Wishful thinking is a commonly used form of fallacious reasoning.

3. So, wishful thinking is probably a distortion of a good form of reasoning.

I suppose one could think that wishful thinking is one of the exceptions to rule (1). But to be honest, I am far from sure there are any exceptions to rule (1), despite my cautious use of “typically”. And we should avoid positing exceptions to generally correct rules unless we have to.

So, if wishful thinking is a distortion of a good form of reasoning, what is that good form of reasoning?

My best answer is that wishful thinking is a distortion of correct probabilistic reasoning on the basis of the true claim that:

4. Typically, things go right.

The distortion consists in the fact that in the fallacy of wishful thinking one is reasoning poorly, likely because one is doing one or more of the following:

1. confusing things going as one wishes them to go with things going right,

2. ignoring defeaters to the particular case, or

3. overestimating the typicality mentioned in (4).

Suppose I am right about (4) being true. Then the truth of (4) calls out for an explanation. I know of four potential explanations of (4):

1. Theism: God creates a good world.

2. Optimalism: everything is for the best.

3. Aristotelianism: rightness is a matter of lining up with the telos, and causal powers normally succeed at getting at what they are aiming at.

4. Statisticalism: norms are defined by what is typically the case.

I think (iv) is untenable, so that leaves (i)-(iii).

Now, optimalism gives strong evidence for theism. First, theism would provide an excellent explanation for optimalism (Leibniz). Second, if optimalism is true, then there is a God, because that’s for the best (Rescher).

Aristotelianism also provides evidence for theism, because it is difficult to explain naturalistically where teleology comes from.

So, thinking through the fallacy of wishful thinking provides some evidence for theism.

Leibniz on PSR and necessary truths

I just came across a quote from Leibniz that I must have read before but it never impressed itself on my mind: “no reason can be given for the ratio of 2 to 4 being the same as that of 4 to 8, not even in the divine will” (letter to Wedderkopf, 1671).

This makes me feel better for defending only a Principle of Sufficient Reason restricted to contingent truths. :-)

Leibniz: a reductionist of the mental?

Leibniz talks about all substances having unconscious perceptions, something that threatens to be nonsense and to make Leibniz into a panpsychist.

I wonder if Leibniz wasn’t being unduly provocative. Let me tell you a story about monads. If Alice is as monad, Alice has a family of possible states, the Ps, such that for each state s among the Ps, Alice’s teleological features make it be the case that there is a state of affairs s^* concerning the monads—Alice and the other monads—such that it is good (or proper) for Alice to have s precisely insofar as s^* obtains.

This seems a sensible story, one that neither threatens to be nonsense nor to make its proponent a panpsychist. It may even be a true story. But now note that it is reasonable to describe the state s of Alice as directly representing the state of affairs s^* around her. Teleological features are apt to be hyperintensional, so the teleological property that it is good for Alice to have s precisely insofar as s^* obtains is apt to be hyperintensional in respect to s^*, which is precisely what we expect of a representation relation.

And it seems not much of a stretch to use the word “perception” for a non-derivative representation (Leibniz indeed expressly connects “perception” with “representation”). But it doesn’t really make for panpsychism. The mental is teleological, but the teleological need not be mental, and on this story perceptions are just a function of teleology pure and simple. In heliotropic plants, it is good for the plant that the state of the petals match the position of the sun, and that’s all that’s needed for the teleological mirroring—while plants might have some properly mental properties, such mirroring is not sufficient for it (cf. this really neat piece that Scott Hill pointed me to).

If we see it this way, and take “perception” to be just a teleological mirroring, then it is only what Leibniz calls apperceptions or conscious perceptions that correspond to what we consider mental properties. But now Leibniz is actually looking anti-Cartesian. For while Descartes thought that mental properties were irreducible, if we take only the conscious perceptions to be mental, Leibniz is actually a reductionist about the mental. In Principles of Nature and Grace 4, Leibniz says that sometimes in animals the unconscious perceptions are developed into more distinct perceptions that are the subject of reflective representation: representation of representation.

Leibniz may thus be the first person to offer the reduction of conscious properties to second-order representations, and if these representations are in fact not mental (except in Leibniz’s misleading vocabulary), then Leibniz is a reductionist about the mental. He isn't a panpsychist, though I suppose he could count as a panprotopsychist. And it would be very odd to call someone who is a reductionist about the mental an idealist.

Of course, Leibniz doesn’t reduce the mental to the physical or the natural as these are understood in contemporary non-teleological materialism. And that’s good: non-teleological naturalist reductions are a hopeless project (cf. this).

Are monads in space?

It is often said that Leibniz’s monads do not literally occupy positions in space. This seems to me to be a mistake, perhaps a mistake Leibniz himself made. Leibnizian space is constituted by the perceptual relations between monads. But if that’s what space is, then the monads do occupy it, because they stand in the perceptual relations that constitute space. And they occupy it literally. There is no other way to occupy space, if Leibniz is right: this is literal occupation of space.

Perhaps the reason it is said that the monads do not literally occupy positions in space is that an account that reduces position to mental properties seems to be a non-realist account of position. This is a bit strange. Suppose we reduce position to gravitational force and mass (“if objects have masses m₁ and m₂ and a gravitational force F between them, then their distance is nothing but (Gm₁m₂/F)^1/2”). That’s a weird theory, but a realist one. Why, then, should a reduction to mental properties not be a realist one?

Maybe that’s just definitional: a reduction of physical properties to mental ones counts as a non-realism about the physical properties. Still, that’s kind of weird. First, a reduction of mental properties to physical ones doesn’t count as a non-realism about the mental properties. Second, a reduction of some mental properties to other mental properties—say, beliefs to credence assignments—does not count as non-realism about the former. Why, then, is a reduction of physical to mental properties count as a non-realism?

Maybe it is this thought. It seems to be non-realist to reduce some properties to our mental properties, where “our” denotes some small subset of the beings we intuitively think exist. Thus, it seems to be non-realist to reduce aesthetic properties to the desires and beliefs of persons, or to reduce stones to the perceptual properties of animals. But suppose we are panpsychist as Leibniz is, and think there are roughly at least as many beings as we intuitively think there are, and are reducing physical properties to the mental properties of all the beings. Then it’s not clear to me that that is any kind of non-realism.

Leibniz's idealistic transsubstantiation

I’ve been thinking how much nicer Leibnizian idealism is than the Berkeleyan sort, because you get this nice dose of realism from unconscious perception.

For instance, in one of his letters to Des Bosses, Leibniz offers a neat idealistic account of transsubstantiation: the unconscious perception of the micro-structure of the bread and wine perishes and is replaced with the unconscious perception of the micro-structure of Christ’s body, while the conscious perception of the macro-structure of the bread and wine remains. Material substance is better identified with micro-structure than macro-structure, and the macro-structure is more accident-like, so this counts as a replacement of the material substances in the bread and wine with the material substance of Christ’s body and blood.

Clever! But I am not sure what Leibniz can do with issues about size. The phenomenal perception of the micro-structure of Christ’s body presumably covers a larger volume of perceptual space than the macro-structure of the host. But Christ’s body is supposed to be where the host is.

Leibniz doesn’t say that this account of transsubstantiation is good. He suggests it’s the best one that can be adopted by Jesuits who don’t believe in composite substances.

Leibniz and inter-monadic causation

Along with my graduate students, I was trying yesterday to figure out how Leibniz’s argument against inter-monadic causation works. There are two constrants on figuring this out:

1. Leibniz thinks intra-monadic causation happens.

2. Leibniz thinks God can exercise causation on monads.

Here is a somewhat a moderately interesting Aristotelian argument that may or may not be what Leibniz had in mind:

3. Inter-monadic causation is the causation of an accident of one substance by another substance.

4. Accidents are grounded in their substances.

5. If y is grounded in x, and z causes y, then either z causes x or z = x.

6. So, if substance z causes accident y of substance x, then either z causes x or z = x. (by 4, 5)

7. So, a distinct substance can only cause an accident in another substance if it causes that substance. (by 6)

Leibniz thinks that only God causes monads. Given this, it would follow from (7) that only God can cause an accident in a distinct substance.

One controversial premise in the argument is (5). But it seems to me to have some intuitive force. An official’s being elected is grounded in her getting a majority of the votes, say. But then the only way you can cause the official to be elected is by causing her to get a majority of the votes: i.e., you cause the grounded event (election) by causing the ground (majority vote).

Perhaps the big weakness in the argument is that (5) is most plausible for full grounding, while accidents seem to be only partly grounded in their substances. But the best argument that accidents are only partly grounded in their substances seems to be that full grounding necessitates: if x fully grounds y, then x’s existence or occurrence necessitates y’s; but accidents are not in general necessitated to exist by the existence of their substance. However, Leibniz does think that accidents are in general necessitate to exist by the existence of their substance—that is part of the “complete individual concept” idea. So Leibniz may think (4) is true even for full grounding. (Spinoza almost certainly does.)

Good-bye, (Aristotelian) matter

Of course, there are material things like oaks and people, and it’s distinct from immaterial things like angels. But for a long time I’ve been wondering why my fellow Aristotelians think that there is matter, a component of material things. In the process of reflection, I have given up on matter as a fundamental ontological category. Of course, for theological and common-sense purposes, I need to have the concept of a material substance, but here I hope there is some reduction, such as that a material substance is a substance that has at least one geometric property. My Aristotelianism now inclines to be more like Leibniz’s than like the historical Aristotle’s or Aquinas’s. Material substances, on my view, are much like Leibniz’s monads; they are like Aristotle’s gods or Aquinas’s angels, plus whatever properties or causal powers are needed for them to count as material. I am my own form, and in this form there inhere accidents.

What philosophical work does matter play, particularly in Aristotelian theories?

1. Many Aristotelians say that something remains through substantial change, namely matter.

The persistence of matter through substantial change is said to do justice to the intuition that the corpse is the remains of the living creature: that there is something in the corpse that was in the living creature. But it is notoriously difficult to remain faithful to the Aristotelian emphasis that identity always comes from form and allow that anything in the corpse is identical to anything in the prior living body. Absent a solution to this, the Aristotelian has to say that there is one bunch of matter prior to death, a bunch of matter informed by the form of the living body, and a different bunch of matter after death, informed by the forms of the substances making up the corpse. But that does not do justice to the common-sense intuition.

In the vicinity, too, there is the question of why it is that the corpse is physically like the living body. But this is not to be accounted for by matter, but by accidents such as shape, mass and color. Accidents are possessed by substances. Either accidents can or cannot survive the destruction of their underlying substance. If they can, then we have an explanation of why the corpse is physically like the living body. If they cannot, then adding that there is matter in both—and even that it is the same matter—does not help: we simply have to bite the bullet and say that the accidents of the living body have the power to cause similar accidents in the corpse.

2. Matter may play a role in diachronic identity.

But since immaterial substances like angels can persist over time, matter isn’t needed to solve the problem of diachronic identity. Moreover, the problem of diachronic identity seems to me, as a four-dimensionalist, to be a pseudoproblem (see also this]). It is no more a problem how the same thing can exist in 2017 and in 2018 than it is a problem how someone can exist in the room and in the hall—just put a leg in each, and you’ll see how. Matter does nothing to help with the latter problem, since presumably it isn’t the same chunk of matter that’s in the room as in the hall. So, why should matter help with the former?

3. Matter may play a role in problems of material composition.

Matter may also play a role in some specific solutions to the problem of material composition. One might, for instance, identify the lump with the matter and the statue with the substance composed of it, or the lump with one thing made of the matter and the statue with another thing made of the same matter, and then explain away the commonality of many properties, like mass, by the identity of matter. But either the statue and the lump have numerically the same accident of mass or they do not. If they do, then since accidents inhere in substances, not in matter, the commonality of matter doesn’t do any work. If they do not, then the commonality of matter doesn’t seem to have done much—we still have to explain why the two have an exactly similar accident of mass, given that they have numerically distinct ones.

What matter does do, I think, is help differentiate the classic statue–lump case from the horse–ghost case where Bucephalus’s ghost happens to walk right through the living Seabiscuit, in such a way that the ghost horse and the living horse happen to occupy exactly the same space. For we can say that the ghost case is a case of merely spatial colocation, while the statue–lump case is a case of having the same matter. And intuitively there is a difference between the two cases. Interestingly, though, this isn’t the material composition problem that matter usually gets invoked to solve. And since I don’t believe in statues, or in any other entities that could plausibly be thought to make there be two entities of one chunk of matter, this does little for me.

4. Isn’t hylo-morphism the distinctively Aristotelian solution to the mind-body problem?

Sure. But, even more than the classic Aristotelian solution, my view is a dissolution to the mind-body problem rather than a solution. The form of course affects the accidents that constitute and shape our embodiment. All of this is due to the nexus—ontological, teleological and causal—that exists between the substance and its accidents (both substance–accident and accident–accident). It’s not a case of one thing moving another: it is just the common story of the form affecting the accidents and the accidents affecting one another.

And, yes, of course I agree with the Council of Vienne that the soul is the form of the body. On my view, talk of the soul is talk of the substance qua form and apart from the accidents constituting its materiality, and the substance qua form is a base for all the accidents which constitute us as having bodies. So, the soul is the form of the body.

5. Physics talks of matter.

Sure, but physics probably doesn’t have a fundamental distinction between matter and energy, I think.

Anyway, I don’t deny that there is matter in the sense of substances that are so configured as to count as material. Quite possibly, where you have a heap of sand, you have a heap of material substances, and hence matter. (But perhaps not: perhaps fundamental physical reality is just a handful of fields.)

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All in all, I just see little if any benefit to matter. And there is much mystery about it. Ockham’s razor cuts it away.

Unless, of course, we come to some philosophical problem that can’t be solved without matter, or can’t be solved as well without it…

Priors, justification and rationalism

The rationalism of Leibniz and Spinoza worked like this: We figure out fundamental necessary metaphysical principles, and these principles determine everything else of necessity (with some qualifications on the Leibniz side as to the type of necessity).

But another rationalism is possible: We figure out fundamental necessary metaphysical principles, and these principles determine the basic probabilistic structure of reality. In Bayesian terms, the fundamental metaphysical principles yield the prior probabilities. A version of this was Descartes’ project in the Meditations.

And there is reason to engage in this probabilistic rationalist project. We cannot get out of the need to have something like prior probabilities. Moreover, priors need epistemic justification. Consider an empirical claim p that we assign a high enough credence for belief to, say 0.99, on the basis of total evidence e. Thus, P(p|e)=0.99. It follows by the axioms of probability that P(p ∨ ¬e)≥0.99. Hence we have a high enough prior credence for belief in p ∨ ¬e. Surely assigning a credence of 0.99 to something requires epistemic justification. Moreover, surely (though people who don’t like closure arguments may not like it) if we have posterior justification when we believe p, we have posterior justification when we believe the obviously entailed claim p ∨ ¬e. But this justification did not come from e. For P(p ∨ ¬e|e)=P(p|e)=0.99 and we have seen that P(p ∨ ¬e)≥0.99, so e is not evidence for p ∨ ¬e (in face, typically e will be evidence against this disjunction). Since e is our total evidence, the justification had to be there in the first place.

Thus we need epistemic justification for our priors. The priors encode genuine information about our world, information that we are justified in possessing. Where do we justifiedly get this information from? We don’t get it through logic, pace logical probability accounts. Metaphysics is one potential answer to this question and exploring this answer gives us good reason to engage in the probabilistic rationalist project. Another option is that the priors are a kind of innate knowledge built into our nature—my Aristotelian Bayesianism is a version of this.

Against isotropy

We think of Euclidean space as isotropic: any two points in space are exactly alike both intrinsically and relationally, and if we rotated or translated space, the only changes would be to the bare numerical identities to the points—qualitatively everything would stay the same, both at the level of individual points and of larger structures.

But our standard mathematical models of Euclidean space are not like that. For instance, we model Euclidean space on the set of triples (x, y, z) of real numbers. But that model is far from isotropy. For instance, some points, like (2, 2, 2) have the property that all three of their coordinates are the same, while others like (2, 3, 2) have the property that they have exactly two coordinates that are the same, and yet others like (3, 1, 2) have the property that their coordinates are all different.

Even in one-dimension, say that of time, when we represent the dimension by real numbers we do not have isotropy. For instance, if we start with the standard set-theoretic construction of the natural numbers as

0 = ⌀, 1 = {0}, 2 = {0, 1}, 3 = {0, 1, 2}, ...
and ensure that the natural numbers are a subset of the reals, then 0 will be qualitatively very different from, say, 3. For instance, 0 has no members, while 3 has three members. (Perhaps, though, we do not embed the set-theoretic natural numbers into the reals, but make all reals—including those that are natural—into Dedekind cuts. But we will still have qualitative differences, just buried more deeply.)

The way we handle this in practice is that we ignore the mathematical structure that is incompatible with isotropy. We treat the Cartesian coordinate structure of Euclidean space as a mere aid to computation, while the set-theoretic construction of the natural numbers is ignored completely. Imagine the look of incomprehension we’d get from a scientist if one said something like: “At a time t₂, the system behaved thus-and-so, because at a time t₁ that is a proper subset of t₂, it was arranged thus-and-so.” Times, even when represented mathematically as real numbers, just don’t seem the sort of thing to stand in subset relations. But on the Dedekind-cut construction of real numbers, an earlier time is indeed a proper subset of a later time.

But perhaps there is something to learn from the fact that our best mathematical models of isotropic space and time themselves lack true isotropy. Perhaps true isotropy cannot be achieved. And if so, that might be relevant to solving some problems.

First, probabilities. If a particle is on a line, and I have no further information about it except that the line is truly isotropic, so should my probabilities for the particle’s position be. But that cannot be coherently modeled in classical (countably additive and normalized) probabilities. This is just one of many, many puzzles involving isotropy. Well, perhaps there is no isotropy. Perhaps points differ qualitatively. These differences may not be important to the laws of nature, but they may be important to the initial conditions. Perhaps, for instance, nature prefers the particles to start out at coordinates that are natural numbers.

Second, the Principle of Sufficient Reason. Leibniz argued against the substantiality of space on the grounds that there could be no explanation of why things are where they are rather than being shifted or rotated by some distance. But that assumed real isotropy. But if there is deep anisotropy, there could well be reasons for why things are where they are. Perhaps, for instance, there is a God who likes to put particles at coordinates whose binary digits encode his favorite poems. Of course, one can get out of Leibniz’s own problem by supposing with him that space is relational. But if the relation that constitutes space is metric, then the problem of shifts and rotations can be replaced by a problem of dilation—why aren’t objects all 2.7 times as far apart as they are? Again, that problem assumes that there isn’t a deep qualitative structure underneath numbers.

From modal to many-minds interpretations of quantum mechanics

I should warn readers that all my posts on quantum stuff are very, very sketchy. I'm very much learning the material.

In my exploration of many-minds interpretations of quantum mechanics, I’ve been trying to figure out how the many-minds dynamics could work without using problematic notion of a “local” or “effective” wavefunction. Here’s a way I like.

1. Start with a privileged set O of commuting observables whose values would be sufficient to ground the phenomenal states of all minded beings. Perhaps particle positions will do.

2. Now let’s suppose we have a modal interpretation with O as the privileged set of observables and with an appropriate dynamics (like the one here).

3. Attach immaterial minds to the systems described by O, and have them travel along with the systems.

4. But now do a switcheroo: instead of supposing the observables in O to describe physical reality, ground their values in properties of the minds. If O is phenomenally distinguishable, i.e., if any two distinct assignments of values to the observables in O will result in different ensembles of phenomenal states, then we don’t need to posit properties of minds over and beyond the phenomenal ones here. But if O is too rich to be phenomenally distinguishable, we will need to suppose unconscious properties of the minds to ground the values of the observables in O.

This yields something closer to the Squires-Barrett Traveling Minds variant of Albert and Loewer’s Single Mind View, rather than the many-minds view. (In particular, there is no problem of meeting “mindless hulks”.)

If O determines all particle positions, then the result is a Leibnizified Bohm-like theory where particle positions are grounded in the properties of monads (minds).

If we want many-minds, then we just do the above uncountably infinitely often for each different assignment of values to members of O.

Are Leibniz's monads immaterial?

Leibniz says that "souls, like all other Unities of substances, are immaterial, indivisible and imperishable" (Leibniz's letter to Churfuerstin Sophie). These "Unities" are, of course, the monads as Leibniz explicitly notes earlier in the sentence. So Leibniz is claiming that monads are immaterial. I think Leibniz may be making a mistake in exposition of his own view here. It is essential to Leibniz's view that monads are spiritual. But there is a reasonable story to be told on which they are also material.

A plausible story is that to be material is just to have a place in space. But space on Leibniz's picture is just an abstraction from the interrelations of things in space. These interrelations are constituted by the harmoniously ordered interplay of the monads' representations of the universe. But these representations have--Leibniz is explicit about this--have a point of view. We can thus reasonably identify the location of a monad with the location of its point of view. Monads, then, have a place in space. If they have a place in space, then it seems we should say that they are material.

This was a bit too quick, though. First, it might be that some monads--God, for instance (though I don't know that Leibniz ever calls God a monad)--might have a point of view that is non-spatial in nature. Those monads won't be material.

Second, one might think that having a location is insufficient for spatiality. Two examples. First, God is a paradigm of an immaterial being, and yet the tradition holds that God is present everywhere. Second, on dualism, the soul is immaterial, and yet the soul might be said to be located wherever the body is.

The case of God is, I think, easily handled. Maybe materiality involves not just having location, but being locationally limited. Omnipresent beings aren't locationally limited. But those monads that have a single point of view that fits into the spatial order are locationally limited.

The case of the soul is, I think, a bit more difficult. One option is to say that the soul has its location derivatively from the location of something else--viz., the body. So our account of materiality now is: x is material provided that it has a limited location that does not derive from the location of something else.

Leibniz's monads qualify--or at least those that embody a spatially limited point of view. While the monads' location derives from their representations, it does not derive from the location of their representations--it derives from the interrelation of the representations. (Objection: The monad's location derives from the location of its point of view. Response: Leibniz's ontology does not include points of view as entities.)

Perhaps, though, there is something more to materiality than spatiality. Leibniz probably thought that extension is needed. Extension seems to be the occupation of multiple locations. In that case, Leibniz should have said that while individual monads are not material, in aggregate they are material. But I think requiring non-zero extension is a mistake. We might find out that all fundamental particles are unextended, and that shouldn't lead us to hold that they are immaterial.

Here's another move that Leibniz could take, though. He could say that if we try to spell out the definition of materiality, yes the monads do qualify. But it is unhelpful to put the ingredients of Leibniz's quite unique ontology into the straitjacket of other ontologies. Yet if for the sake of exposition we draw analogues, then we can say that Leibniz's monads are more like the immaterial elements of other ontologies than like the material ones.

Uniform motion and relationalism

An old objection to relationalism about space--an objection going back to the Leibniz-Clarke correspondence--is that it seems possible for all things to move together at the same speed in the same direction. But since the relations between things don't change when they all move together, on a relationalist view of space it seems impossible to make sense of global uniform motion.

Here's a solution to the objection: The motion of an object x can be characterized by saying that x at t₂ is at a non-zero spatial distance from x at t₁. This allows one to characterize absolute motion in a relationalist account of space, which has typically been held impossible.

The above story works most neatly if we have eternalism and temporal parts: then x moves provided that it has temporal parts at a spatial distance from each other. But we can also do this with eternalism without temporal parts, provided that we index distance relations to two times. Whether a presentist who is a relationalist about space can make use of the solution depends on how well the presentist can solve the problem of cross-time relations.

I don't personally like this story, because I would prefer a relationalism based on spacetime relations rather than spatial ones.