Given that Graham Harman’s form of withdrawal-oriented ontology postulates that objects withdraw from relations, his metaphysics can be seen as one particular model of the more general set-theoretic ontology proposed by Badiou in BEING AND EVENT. This is confirmed by an analysis the naive and surprising use that Harman makes of his pseudo-concepts of undermining and overmining.
Harman seems to think that “physics” reduces objects to , and replaces them by, smaller parts. Atoms and sub-atomic particles would be one possible specification of set-theoretic elements, when considered non-relationally (as Harman does). However if we take into consideration (as we should) relations between the elements then we need the conceptual apparatus of Badiou’s LOGICS OF WORLDS to even begin to deal with them. Harman has no corresponding book.
Harman argues that there exists another form of reduction, this time upwards, dissolving objects into larger entities. This is a bogus concept, and is contradicted by his favorite example from physics. All reduction is “down”, but Harman is looking for a neat binary symmetry to divide and conquer his enemies. His notion of “undermining” as reduction to smaller component particles relies on a pre-quantum vision of atoms. A “particle” is also a field that is much bigger than the object it composes.
A consistent withdrawal-oriented ontology must postulate either that there are as many realities as there are interpretations, none of which can be privileged, and it amounts to relativism, or that there is only one real, and it amounts to reductionism.
Harman’s version of this metaphysics, OOP, combines both these alternatives. He both multiplies the number of realities (talking about the tables of science, of common sense and of the humanities) and misdescribes them in terms of his reductionist “object” vocabulary. That is to say OOP is a contradictory mix of reductionism and relativism.
Note: I am indebted to a facebook discussion with Eric Sapp for helping me to clarify these points.