 Expectedly, proponents of multiple realizability quickly responded to the myriad challenges outlined in  section 2  above. Carl Gillett and Ken Aizawa were perhaps the most vocal defenders of multiple realizability against a number of them. Gillett (2003) develops a precise framework for understanding compositionality relations in science generally, and uses this framework to define property realization and multiple realization, and to distinguish further “flat” from “dimensioned” realization. Recall from  section 2.4  above that “flat” realization involves both realized and realizing properties inhering in a single object. “Dimensioned” realization involves realized and realizing properties inhering in distinct individuals that stand in a compositional relationship to one another. For Gillett (2002, 2003), this distinction is important for two reasons. First, scientific explanations employ dimensioned realizations, because inter-level mechanistic explanations relate distinct individuals. Second, Fodor and other proponents of the standard multiple realizability arguments were assuming a dimensioned account, while the arguments of Shapiro and other recent critics (see  §2  above) challenge the existence of multiple realizability only by assuming a flat realization. According to Gillett, no recent proponent of multiple realizability has assumed or defended flat realization as the correct account involved in any of the scientific cases at issue.