Spinozistic partitionings [sic] Joel Friedman in 1974 invented these things called Spinozistic partitionings [sic] (of a set) where the pieces are all pairwise isomorphic as binary structures (piece, $\in$).  He shows that $V_\omega$ has one. The idea seems to me to hold possibilities for exercises for a set theory course, but beyond that i can't see any real reason why i should care about them.  Is there some model theory angle i'm missing..?
 A: I hope a negative answer isn't inherently rude - that's certainly not my intention - but that does seem to be the situation, as far as I can tell.
Friedman's original paper appears in the journal Synthese, which has a strong philosophical focus. In particular, quoting from Friedman's paper:

In Friedman (1972), it was presented as a
   philosophical thesis that, in general, maximization implies decidability in set theory. ... [I]n this paper, we attempt to support our general thesis by offering still another concrete, and hopefully, non-trivial example, showing that Spinoza's metaphysical system generates some settheoretical concepts and theorems. Conversely, we hope to show that Set Theory sheds light on Spinoza's metaphysics.

So Friedman's paper was not motivated by a particular mathematical relevance of the combinatorial principles involved, but rather the (claimed) connection between them and specific philosophical issues. Obviously I'm not qualified to judge the validity of this connection, but I think this does explain that the notion of Spinozistic partitionings emerged as an attempt to find a mathematical topic corresponding to a philosophical topic rather than as a concept relevant to a specific problem (or similar).
The situation, as far as I can tell, hasn't changed since then. I could only find two follow-up papers (both also published in Synthese, indeed in the same issue): "The universal class has a Spinozistic partitioning" by Friedman and "Spinozistic partitions of classes" by John Lake. The papers address specific mathematical questions appearing in Friedman's original paper. At a quick glance, neither paper appears to give more mathematical motivation for the notion beyond independent interest (or further develop the philosophical angle); between this and the general lack of work on the topic, I think that the answer to your question is no. Of course, it's essentially impossible to prove a negative like this, and I wouldn't be too surprised if there turned out to be a relation between these and some more mainstream notion, but I don't see any at the moment.
