This is Chapter 8 of my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.

This essay deals with a connection between a relatively recent (1940s and 1950s) field of mathematics, category theory, and a hitherto vague notion of philosophical logic usually associated with Plato, the self-predicative universal or concrete universal.  Consider the following example of “bad Platonic metaphysics.”

Given all the entities that have a certain property, there is one entity among them that exemplifies the property in an absolutely perfect and universal way.  It is called the “concrete universal.”  There is a relationship of “participation” or “resemblance” so that all the other entities that have the property “participate in” or “resemble” that perfect example, the concrete universal.

All of this and much more “bad metaphysics” turns out to be precisely modeled in category theory.