 To see the motivation for AV6, notice that if the handle and head do compose something then there are three things: the handle, the head, and a hammer. If they don’t, then there are only two things: the handle and head. And if it is vague whether they do, then it will be vague whether there are two things or three. As for AV7, notice that one can specify how many objects there are using what would seem to be entirely precise vocabulary. For any finite number, one can produce a “numerical sentence” saying that there are exactly that many concrete objects. Here, for instance, is the numerical sentence for two: ‘∃x∃y(x≠y &amp; Cx &amp; Cy &amp; ∀z(Cz→(x=z ∨ y=z)))’. (The restriction to concreta ensures that numerical sentences aren’t trivially false simply on account of there being infinitely many numbers, sets, and so forth.) And since these numerical sentences contain no vague vocabulary, it would seem to follow that it cannot be indeterminate how many objects there are.