 Most authors (beginning with Simons himself) would say so. Yet here there is room for genuine disagreement. In fact, it is not difficult to conceive of mereological scenarios that violate not only (P.4), but also (P.4b) and even (P.4a). A case in point would be Brentano's (1933) theory of accidents, according to which a mind is a proper part of a thinking mind even though there is nothing to make up for the difference. (See Chisholm 1978, Baumgartner and Simons 1993.) Similarly, in Fine's (1982) theory of qua-objects, every basic object (John) qualifies as the only proper part of its incarnations (John qua philosopher, John qua husband, etc.). Another interesting example is provided by Whitehead's (1929) theory of extensive connection, where no boundary elements are included in the domain of quantification: on this theory, a topologically closed region includes its open interior as a proper part in spite of there being no boundary elements to distinguish them—the domain only consists of extended regions. (See Clarke 1981 for a rigorous formulation, Randell et al. 1992 for developments.) Finally, consider the view, arguably held by Aquinas, according to which the human person survives physical death along with her soul (see Brown 2005 and Stump 2006, pace Toner 2009). On the understanding that persons are hylomorphic composites, and that two things cannot become one, the view implies that upon losing her body a person will continue to exist, pre-resurrection, with only one proper part—the soul. (This is also the view of some contemporary philosophers; see e.g. Oderberg 2005 and Hershenov and Koch-Hershenov 2006.) Indeed, any case of material coincidence resulting from mereological diminution, as in the Stoic puzzle of Deon and Theon (Sedley 1982) and its modern variant of Tibbles and Tib (Wiggins 1968), would seem to be at odds with Supplementation: after the diminution, there is nothing that makes up for the difference between what was a proper part and the whole with which it comes to coincide, short of holding that the part has become identical to the whole (Gallois 1998), or has ceased to exist (Burke 1994), or did not exist in the first place (van Inwagen 1981). One may rely on the intuitive appeal of (P.4) to discard all of the above theories and scenarios as implausible. But one may as well turn things around and regard the plausibility of such theories as a good reason not to accept (P.4) unrestrictedly, as argued e.g. by D. Smith (2009), Oderberg (2012), and Lowe (2013). As things stand, it therefore seems appropriate to regard such a principle as providing a minimal but substantive addition to (P.1)–(P.3), one that goes beyond the basic characterization of ‘part’ provided by M. We shall label the resulting mereological theory MM, for Minimal Mereology.