This chapter contrasts the theory of singular compositional abduction with the “matched interlevel experiments” approach by Carl Craver, Stuart Glennan, and Mark Povich. The Craver, Glennan, and Povich account does not apply to the interpretation cases of “intralevel” experiments. It only applies to “interlevel” experiments. Further, it does not leave room for the scientific use of combinations of interlevel and intralevel experiments in support of compositional hypotheses. The chapter also sketches an account of “interlevel abduction” that might serve as a rival to the matched interlevel experiments interpretation. The chapter also reviews suggestions that the matched interlevel experiments approach is not meant to be an account of how scientists actually confirm compositional hypotheses. A challenge for these suggestions is why a historian and philosopher of science should care about a method that is not used by scientists.

This chapter provides the second case study of the use of singular compositional abduction based on scientific attempts to determine the biological basis of the Hermann grid illusion. First reported by Ludimar Hermann in 1872, the illusion was first explained in terms of local points of simultaneous contrast. In 1961, Gűnter Baumgartner fleshed out the proposal arguing that the illusion might be explained in terms of activity instances of retinal ganglion cell firings. Further, Lothar Spillman performed experiments intended to support this proposal, whereas Jeremy Wolfe, Peter Schiller, and Christina Carvey described experiments meant to challenge it.