Eliminativist relational dualism

Here is a combination of views that, as far as I know, is missing from the literature:

• eliminativism about persons

• multigrade relational dualism.

Let me explain the view. There are no people on earth. There are just particles arranged humanwise. No particle by itself has mental properties and there is no whole having mental properties. But there is irreducibly collective activity mental activity. The humanwise-arranged particles responsible for this post stand in non-physical mental relations, such as collectively being aware of the smoothness of the spacebar and collectively intending to communicate a novel philosophy of mind view. These relations are multigrade in the sense that there is no specific number of particles that are needed to stand in such a relation.

There are about 10²⁸ (give or take an order of magnitude, depending on whether we count just the brain or the whole body) particles jointly responsible for this post, but some particles are always flying off and terminating their participation in the relations and others are joining, which is why the mental relation is multigrade.

The availability of the view shows that arguments, like those of van Inwagen and Merricks, for the existence of complex wholes based on our mental function need more work. As does Descartes’ “I think therefore I am”: perhaps all we can say at the outset is is “There is thinking so there is one or more things that individually or jointly engage in thought.”

The view has the very attractive feature that it is compatible with nihilism about parthood: there need be no part-to-whole relation. This allows for a very nice and simple ideology.

The view is a dualist view, and hence puzzles about phenomenal properties, the unity of consciousness and intentionality can be solved much like in property dualism. (E.g., consciousness is unified by joint possession of a consciousness property.)

But the typical property dualist has two things to explain: why a single entity arises from a bunch of particles arranged a certain way and why that entity gains mental properties. The eliminative relational dualist only needs to explain the latter.

At the same time, some of the difficulties with the more normal kinds of eliminativism about persons (think of Unger and the Churchlands) are neatly solved. The idea of thought without any subject of thought is absurd. But we can draw on reflections in social epistemology to get a model for thought with an irreducibly plural subject of thought.

As I think is often the case with metaphysical views, the main difficulties arise in ethics. There is no particular difficulty about being responsible. The particles that engaged in a joint action are jointly responsible. The problem, however, is with holding responsible. Particles are always leaving and entering the mental relations. Many of those particles that were responsible for the robbery last year are now scattered across the city, and while (at least for last year’s robbery) a bunch of them are still clumped together, it’s impossible to punish them without punishing a plurality of particles that includes a number of particles that had nothing to do with the robbery. And this is nothing compared to the difficulty of punishing cannibalism, since we will end up punishing many victimized particles.

Multigrade relations

One strategy for avoiding ontological commitment to sets is to deal with pluralities and multigrade relations. Multigrade relations are relations that can be had by a variable number of things. Instead of, say, saying of the books on my shelf that there is a set of them whose total number of pages is exactly 800, one says that there are xs such that each of them is a book on my shelf and the xs stand in the multigrade relation of jointly having 800 pages. Let’s say these books are x₁, x₂ and x₃. Then we express their jointly having 800 pages as:

• Has800Pages(x₁, x₂, x₃).

We do not need a set of them to express this. And the Has800Pages(x₁, ...) predicate flexibly can take as many arguments as one wishes, corresponding to the multigradeness of the property it expresses.

But now consider a different statement: there are two pluralities of books on my shelf, having no books in common, where each plurality has the same total number of pages as the other. Can we make sense of this using multigrade relations instead of sets?

I don’t see how. Let’s say that the plurality x₁, x₂, x₃ and the plurality y₁, y₂ of my books each have the same total number of pages. So we introduce a predicate with variable arity and say:

• HasSameTotalNumberOfPages(x₁, x₂, x₃, y₁, y₂).

But that doesn’t work! For how can we tell if it is says that x₁, x₂, x₃ have the same number of pages as y₁, y₂ rather than saying that x₁, x₂ have the same number of pages as x₃, y₁, y₃?

We could multiply predicates with fixed arity and say:

• TheFirst3HaveTheSameTotalNumberOfPagesAsTheLast2(x₁, x₂, x₃, y₁, y₂).

But that won’t work with quantification, since we don’t know ahead of time how many xs and how many ys we are dealing with.

Maybe we should do this:

• Count(3,x₁, x₂, x₃) and Count(2,y₁, y₂) and SameNumberOfPages(3,x₁, x₂, x₃,2,y₁, y₂)

where the SameNumberOfPages variable arity predicate takes a number, then a plurality of that number of objects, then another number, and then another plurality of that number of objects.

But these kinds of solutions won’t work for infinite pluralities. For instance, suppose we want to say that the xs cause the ys, where there are ℵ₂ xs and ℵ₃ ys. Then I guess we say something like:

• Cause(ℵ₂, x₁, x₂, ..., ℵ₃, y₁, y₂, ...).

There are serious technical problems here, however. I will leave it to the reader to explore these.