 But our intuitive notion of part does not allow for wholes with only one part: if something x is part of a whole W, there is a remainder of W that is not identical with x. To illustrate: If you tell me that this slice is part of your cake, but there is no distinct, further part of your cake, I will take you to make joke or to be confused. The remainder principle is implied by the supplementation principle of mereology, but not the other way around (see  mereology  entry, sect. 3.2) Hence, we can draw on the remainder principle without endorsing the stronger supplementation principle. Now there seem to be states of affairs that “contain” only one property (see Bynoe 2011 who argues the following point in detail). Bradley’s Regress which was discussed in  section 3.1  seems to show that the state of affairs Socrates’ being wise consists only of Socrates and being wise. There is no relation that ties them to a state of affairs. Otherwise the question would arise what relates this relation to Socrates and being wise. Now some properties instantiate themselves: identity is self-identical. Hence, the state of affairs identity’s being self-identical obtains. But this state of affairs contains only the property of identity. There seems to be no intuitively acceptable sense of “part” in which such states of affairs have parts.