 See Whitehead 1919: 101; 1920: 76). GEM is compatible with the former possibility, and ÃGEM makes it into a universal necessity. But neither has room for the latter. Indeed, the possibility of junk might be attractive also from an atomist perspective. After all, already Theophilus thought that even though everything is composed of monads, “there is never an infinite whole in the world, though there are always wholes greater than others ad infinitum” (Leibniz, New Essays, I-xiii-21). Is this a serious limitation of GEM? More generally, is this a serious limitation of any theory in which the existence of U is a theorem—effectively, any theory endorsing at least the unrestricted version of (P.14ψ)? (In the absence of Antisymmetry, one may want to consider this question by understanding the predicate ‘PP’ in (P.19) in terms of the stronger definition given in (20′); see above, ad (P.8′).) Some authors have argued that it is (Bohn 2009a, 2009b, 2010), given that junk is at least conceivable (see also Tallant 2013) and admits of plausible cosmological and mathematical models (Morganti 2009, Mormann 2014). Others have argued that it isn't, because junk is metaphysically impossible (Schaffer 2010, Watson 2010). Others still are openly dismissive about the question (Simons 1987: 83). One may also take the issue to be symptomatic of the sorts of trouble that affect any theory that involves quantification over absolutely everything, as the Unrestricted Sum principles in (P.15i) obviously do (see Spencer 2012, though his remarks focus on mereological theories formulated in terms of plural quantification). One way or the other, from a formal perspective the incompatibility with Ascent may be viewed as an unpleasant consequence of (P.15i), and a reason to go for weaker theories. In particular, it may be viewed as a reason to endorse only finitary sums, which is to say only instances of (P.12ξ,i), or perhaps its unrestricted version: