 Concerning the second worry, to the effect that the unrestricted sum principles in (P.15i) would go too far, its earliest formulations are almost as old as the principles themselves (see e.g. V. Lowe 1953 and Rescher 1955 on the calculus of individuals, with replies in Goodman 1956, 1958). Here one popular line of response, inspired by Quine (1981: 10), is simply to insist that the pattern in (P.15i) is the only plausible option, disturbing as this might sound. Granted, common sense and intuition dictate that some and only some mereological composites exist, but we have just seen that it is hard to draw a principled line. On pain of accepting brute facts, it would appear that any attempt to do away with queer sums by restricting composition would have to do away with too much else besides the queer entities; for queerness comes in degrees whereas parthood and existence cannot be a matter of degree (though we shall return to this issue in Section 5). As Lewis (1986b: 213) puts it, no restriction on composition can be vague, but unless it is vague, it cannot fit the intuitive desiderata. Thus, no restriction on composition could serve the intuitions that motivate it; any restriction would be arbitrary, hence gratuitous. And if that is the case, then either mereological composition never obtains or else the only non-arbitrary, non-brutal answer to the question, Under what conditions does a set have a sumi?, would be the radical one afforded by (P.15i): Under any condition whatsoever. (This line of reasoning is further elaborated in Lewis 1991: 79ff as well as in Heller 1990: 49f, Jubien 1993: 83ff; Sider 2001: 121ff, Hudson 2001: 99ff, and Van Cleve 2008: §3; for reservations and critical discussion, see Merricks 2005, D. Smith 2006, Nolan 2006, Korman 2008, 2010, Wake 2011, Carmichael 2011, and Effingham 2009, 2011a, 2011c.) Besides, it might be observed that any complaints about the counterintuitiveness of unrestricted composition rest on psychological biases that should have no bearing on the question of how the world is actually structured. Granted, we may feel uneasy about treating shoe-umbrellas and trout-turkeys as bona fide entities, but that is no ground for doing away with them altogether. We may ignore such entities when we tally up the things we care about in ordinary contexts, but that is not to say they do not exist. Even if one came up “with a formula that jibed with all ordinary judgments about what counts as a unit and what does not” (Van Cleve 1986: 145), what would that show? The psychological factors that guide our judgments of unity simply do not have the sort of ontological significance that should be guiding our construction of a good mereological theory, short of thinking that composition itself is merely a secondary quality (as in Kriegel 2008). In the words of Thomson (1998: 167): reality is like “an over-crowded attic”, with some interesting contents and a lot of junk, in the ordinary sense of the term. We can ignore the junk and leave it to gather dust; but it is there and it won't go away. (One residual problem, that such observations do not quite address, concerns the status of cross-categorial sums. Absent any restriction, a pluralist ontology might involve trout-turkeys and shoe-umbrellas along with trout-promenades, shoe-virtues, color-numbers, and what not. It is certainly possible to conceive of some such things, as in the theory of structured propositions mentioned in Section 2.1, or in certain neo-Aristotelian metaphysics that construe objects as mereological sums of a “material” and a “formal” part; see e.g. Fine 1999, 2010, Koslicki 2007, 2008, and Toner 2012. There are also theories that allow for composite objects consisting of both “positive” and “negative” parts, e.g., a donut, as in Hoffman and Richards 1985. At the limit, however, the universal entity U would involve parts of all ontological kinds. And there would seem to be nothing arbitrary, let alone any psychological biases, in the thought that at least such monsters should be banned. For a statement of this view, see Simons 2003, 2006; for a reply, see Varzi 2006b.)