Irreducibly joint activity

I’ve long wondered what it means to say that a bunch of things are “irreducibly jointly producing an effect.” One place this comes up in contemporary metaphysics is strongly non-reductivist materialist theories of mind on which the particles of our bodies working together produce thought.

This irreducible production—if there is such a thing—is supposed to be different from the reducible way of how, say, four rocks can depress an analog spring-based scale. Yet I’ve always found it hard to grasp the difference. After all, no single one kilogram rock has the power to depress the scale to the four kilogram point. You need all four. Why is that not an irreducibly joint production of an effect?

A paradigm example of irreducible production would be something like this, however. Suppose the laws of nature ensure that when you arrange four spherical objects of equal size in a tetrahedron, they begin to whistle (I am adapting an example by Trenton Merricks). You arrange three or five or any other number of marbles, nothing like that happens. What’s the difference?

In the case of the rocks and the scale, it is tempting to say that the outcome is just a matter of “summing forces”. But as we learn from Nancy Cartwright and by reflecting on Hume’s insights, summing forces is not as innocent as it sounds. The world could have been so that when multiple forces impinge, they average, or the greatest force carries the day, or the weakest does. Thus the laws of nature seem to have to include some clause like

1. When a number of objects act on an object with forces, the latter accelerates in proportion to the vector sum of the forces.

But now consider.

2. When a number of spherical objects are arranged, whistling results with an intensity equal to one if the objects are four in number, equal in size, and tetrahedrally arranged, and intensity zero otherwise.

The main difference seems to be that “vector sum” is a simpler and more mathematically natural description than “one if the objects are four in number, equal in size, and tetrahedrally arranged, and zero otherwise”. And that’s just a difference of degree, while the difference between reductively and non-reductively joint action is not a difference of degree.

Here is a thought. Perhaps the worry arises out of a mistaken way to think about the case of the scale. The force on the scale’s platform (subsequently transmitted to the spring) is not the sum of the pressures imposed by the four rocks. In the Newtonian setting, each particle of the platform is affected by gravitational attraction to every other particle with mass in the universe, as well as affected by interaction via other forces (e.g., electromagnetic) with countless particles. There are no small closed systems. Perhaps, then, we should rethink the ordinary case: it isn’t a case of reducibility either. On the contrary, it is a case of an irreducible interaction with, basically, everything else—or, in a relativistic context, everything else in its past light cone.

The difference between the whistling tetrahedron of balls and the scale’s depression then isn’t that the whistling is irreducibly jointly effected by multiple things and the scale’s depression isn’t. It is, rather, that the scale’s depression is jointly effected by vastly more things, most of which have only a slight effect, while the magical-seeming whistling is produced only by the four things.

On this picture, what would reducible joint influence be like? It would have to be a case of independent production, where maybe object x produces property P in object z while object y independently produces property Q in z, so that x and z reducibly jointly produce P ∧ Q in z. But it’s not clear that this ever actually happens in our world—all we have are better and worse approximations to such causally independent production.

Some non-reductivist materialists will want to say that our particles, through irreducibly joint activity, produce mental states. Can we accommodate this in the above story? Yes, but only if we suppose that the mental states are in no way directly affected by anything outside our body.

Here is a worry about what I said. Suppose that the four rocks are sufficient to push the scale to a position where the indicator needle is right around the middle of the 4 kg dashmark, while the sum total of the other forces in the universe is insufficient to shift the needle to the outside of the 4 kg dashmark. Then while the exact position of the needle isn’t effected by the four rocks alone, the fact that the needle points somewhere within the 4 kg dashmark on the scale seems to be accounted for by the four rocks alone. Thus, with respect to the coarse grained event of the needle being within the 4 kg dashmark, the four rocks are sufficient to produce the effect. And if that’s right, then we’ve lost the distinction between the four rocks depressing the scale and four marbles causing whistling.

Conjecturally, I answer as follows. The coarse-grained event of a needle’s being in some range (given by the thickness of the 4 kg dashmark) has an identity dependence on fine-grained event of the needle’s being exactly where it is. Thus, had the fine-grained event been different, the coarse-grained event would have been a numerically different event. Hence the coarse-grained event does actually depend on vast numbers of things.