Don’t imagine junk! Positive conceivability and modal illusion in mereology

There is a widespread practice of using evidence obtained from conceiving/imagining for establishing possibility claims. As a case study. I offer a critical reconstruction of an influential conceivability argument, Bohn’s (Philosophical Quarterly 59:193-201, 2009a, Analysis 70:296–298, 2009b, Analysis 70:296-298, 2010) argument for junk (there are proper parts forming wholes, but there is no whole that is not a proper part itself). The most influential scenario used by Bohn and his successors is purported to be junk but not ensured to be junk. This finding calls for an explanation. I distinguish ways of conceiving/imagining that are insufficient to establish modal claims from positive conceiving/imagining, which is more promising. Positive conceiving/imagining often works by a partial structural isomorphy to its target, and it is sufficiently detailed. In order to be sufficiently detailed, it has to properly integrate theoretical considerations. I outline a concern about extant ways of conceiving/imagining junk: they do not yet include a metaphysical understanding of what it takes for there to be proper parts and wholes without a whole that is not a proper part itself, for instance in terms of a non-gerrymandered principle of composition.