My question is quite specific as it refers to this article but I hope that someone here could help me. I cite the relevant part of the article:
... The second example consists of gravitational attraction of a configuration of material points on a particular material point. For convenience, we place the particular material point, whose motion is observed, at the center of a system of spherical coordinates $(r, \theta, \varphi)$. The configuration $a$ in $A$ is a function that assigns to each triple $(r, \theta, \varphi)$ either zero or a mass point $a(r, \theta, \varphi)$. If the function $a$ is nonzero at $n-1$ points, then the total system, involving the configuration and the observed point, is an $n$-body system. If $a$ consists of $n-1$ points and $b$ of $m$ points, then $a\oplus b$, defined in the obvious way, consists of $n+m-1$ points, yielding and $(n+m)$-body system. The exception occurs when $a$ and $b$ are nonzero at some common coordinate $(r, \theta, \varphi)$; we then need a method whereby two material points combine to yield a third [...] In this example, if $A$ is taken to be the set of configurations actually occuring in some empirically realizable celestial system, then of course, $\oplus$ and $*$ cannot be defined.
Why could the "addition" (i.e. superposition) of two configurations not defined? Maybe because two point masses (or bodies) could "physically" not be at the same position in space. But then we could simply define the "addition" as a configuration where at the common point of two point masses a new point is put with the mass of the two other point masses. This would be a valid configuration in my opinion, so where is the problem?