 Three themes predominated Churchland’s philosophical discussion: developing an alternative to the logical empiricist theory of intertheoretic reduction; responding to property-dualistic arguments based on subjectivity and sensory qualia; and responding to anti-reductionist multiple realizability arguments. These projects remained central to neurophilosophy for more than a decade after Churchland’s book appeared. John Bickle (1998) extended the principal insight of Clifford Hooker’s (1981a,b,c) post-empiricist theory of intertheoretic reduction. He quantified key notions using a model-theoretic account of theory structure adapted from the structuralist program in philosophy of science (Balzer, Moulines, and Sneed 1987). He also made explicit a form of argument to draw ontological conclusions (cross-theoretic identities, revisions, or eliminations) from the nature of the intertheoretic reduction relations obtaining in specific cases. For example, it is routinely concluded that visible light, a theoretical posit of optics, is electromagnetic radiation within specified wavelengths, a theoretical posit of electromagnetism; in this case, a cross-theoretic ontological identity. It is also routine to conclude that phlogiston does not exist: an elimination of a kind from our scientific ontology. Bickle explicated the nature of the reduction relation in a specific case using a semi-formal account of “intertheoretic approximation” inspired by structuralist results.