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.

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 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.)

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.

Leibniz, bodies and phenomena

Leibniz tells us that bodies are phenomena. He also tells us that phenomena are modes of monads. Now, the modes of monads are appetites and perceptions. But appetites and perceptions are identity-dependent on the monad that they are appetites and perceptions of. Your appetite or perception may be very much like mine, but it is numerically distinct from mine. But this seems to imply that the moon you see and the moon I see are numerically distinct. For the moon you see is a mode of you, and hence identity-dependent on you, while the moon I see is a mode of me, and hence not numerically distinct with the moon that is identity-dependent on you.

Something must go. The identity dependence of modes on the monad is central to Leibniz's argument against inter-modal causation: he insists that the same mode cannot have a leg in each of two monads. My suggestion is that what Leibniz should say, and maybe what he really thinks, is that real phenomena, like the moon, aren't modes of monads in the narrow sense that implies identity dependence, but are grounded in monads, and in that sense are modes of monads in the broad sense. Consider "the committee's opinion." This is grounded in the committee members' minds, but it is not identity-dependent on any one committee member: individual committee members can change their view while the committee is still "of the same mind."

Here is one way to make this go. The moon is a phenomenon and it has a two-fold ground. One part of the ground are monads having "lunar perceivings", like the one I had last night when looking through the telescope, and like the one I am now, according to Leibniz, unconsciously having. But the moon isn't just a lunar perceivings, because your lunar perceiving is distinct from my lunar perceiving. The other part of the ground is what unifies the lunar perceivings in different monads, and that is the monads that are elements (in Robert Adams' phraseology) of the moon. Your lunar perceiving represents the same lunar monads as my lunar perceiving does.

For Leibniz, as for Aristotle, being and unity are interchangeable. To have being, bodies need a source of unity. On this reading, there are two sources of unity in the moon: first, the perception of a monad, say you or me, unifies the many lunar monads that are being perceived; second, the lunar monads unify the perceptions of the many monads. There is no vicious circularity here.

This significantly qualifies Leibniz's alleged idealism. It sounds idealist to say that bodies are phenomena. But they aren't just any phenomena, they are "well founded" phenomena (to use Leibniz's phrase), and a part of what constitutes them into the self-identical phenomena that they are is the monads that are appearing in the appearance.

The above brings together ideas I got from at least two of our graduate students. Another move suggested by one of them is to take the unification of the lunar perceivings to happen through the complete individual concept of the moon which is confusedly found in all of the lunar perceivings. I think this, too, is a possible reading of Leibniz, but I think it makes for poorer philosophy, since I don't think there is any complete individual concept of the moon found in all lunar perceivings, except in the way that the concepts of causes are, by essentiality of origins, found in the effects.

Leibniz's doctrine of mirroring

Leibniz held that each monad mirrored all the others, namely that by knowing all there is to know about each, you knew all there was to know about all. If essentiality of origins holds, then we get Leibniz-like theses quite easily.

1. If essentiality of origins holds, then each thing mirrors everything in its causal history in the strong sense that the proposition that x exists entails the whole causal history of x's coming into existence.

2. If essentiality of origins and determinism holds, and if we add the further postulate that all of the initial conditions for the whole universe are a part of the causal history of every item in the universe's coming into existence, then for every item x in the universe, the proposition that x exists conjoined with the laws entails the whole past, present and future history of the universe.

3. If to the assumptions in (2) we add the postulate that no item in the universe could have existed with the laws being different, then we get the stronger claim that no item in the universe could have existed in any other world—i.e., that the items in the universe are world-bound individuals.

This might make Leibniz's doctrine of mirroring more plausible to some. But I am not a determinist myself.