 The algebraic strength of GEM, and of its weaker finitary and infinitary variants, is worth emphasizing, but it also reflects substantive mereological postulates whose philosophical underpinnings leave room for considerable controversy well beyond the gunk/junk dispute. Indeed, all composition principles turn out to be controversial, just as the decomposition principles examined in Section 3. For, on the one hand, it appears that the weaker, restricted formulations, from (P.11ξ) to (P.15ψ,i), are just not doing enough work: not only do they depend on the specification of the relevant limiting conditions, as expressed by the predicates ‘ξ’ and ‘ψ’; they also treat such conditions as merely sufficient for the existence of bounds and sums, whereas ideally we are interested in an account of conditions that are both sufficient and necessary. On the other hand, the stronger, unrestricted formulations appear to go too far, for while they rule out the possibility of junky worlds, they also commit the theory to the existence of a large variety of prima facie implausible, unheard-of mereological composites—a large variety of “junk” in the good old sense of the word.