 There is a potential glitch in the above piece of reasoning. It assumes that when an individual is a teapot in a world, no proper part of that individual is also a teapot in that world. This assumption can be questioned, however. Following Geach 1980 (p. 215; see entries  identity,  problem of many), we might reason as follows: My teapot would remain a teapot if we chipped off a tiny piece. Chipping off pieces from teapots doesn’t create new teapots, so there must have been smaller teapots all along. We might feel that there is just a single teapot sitting on the table, but upon reflection we might have to acknowledge that there are in fact many overlapping entities that all have legitimate claims to teapothood. The unexpected multitude of teapots is a source of headaches when it comes to counting. A fundamental principle of counting says that a domain for counting cannot contain non-identical overlapping individuals (Casati &amp; Varzi 1999, 112):