If Christmas cake is homeomerous, then any part, or area, of a quantity of Christmas cake is itself a quantity of Christmas cake. The grain of Christmas cake—the fact that Christmas cake stuff is lumpy—has lead many thinkers to deny that it is a homeomerous stuff. For, they argue, some sufficiently small areas of Christmas cake contain, not Christmas cake, but rather, for example, contain only sultana.
Now it’s clearly true that there are bounded areas of Christmas cake that contain sultanas without containing other cake stuff. It’s also true that no sultana is, per se, a quantity of Christmas cake. However, it would follow that Christmas cake is not homeomerous only if it were also true that no sultana constitutes a quantity of Christmas cake. That is, the failure of homeomerousness would depend on the claim that areas of Christmas cake stuff whose boundaries coincide with the boundaries of a sultana do not contain, in addition to sultana, a quantity of cake. And that doesn’t follow just from the fact that the boundaries of a detached sultana—a sultana surrounded by air rather than, for example, cake—would contain no cake.
The suggestion, then, is that the claim that Christmas cake is homeomerous might be defensible if we were willing to accept two general claims about stuffs: (1) the contents of an area of stuff can depend upon the contents of more extensive areas of stuff including that area—so that, for example, whether a sultana constitutes a quantity of cake may depend upon whether it is attached to surrounding cake; (2) an area can contain a plurality of fundamental kinds of stuff, including, for example, both sultana and Christmas cake.
The present discussion may also bear on questions about the metaphysical nature of the holes in certain cheeses.