 Van Inwagen’s version of eliminativism is subject to the same objections raised against nihilism, but it also faces problems of its own. Here is one worry. There are borderline cases where it is vague whether or not the activity of some simples constitutes a life (consider, for example, the question of when, exactly, a person’s life comes to an end). But, if it is vague whether the activity of some simples constitutes a life then, according to van Inwagen, it is vague how many objects exist. But it cannot be vague how many objects exist, since cardinality claims can be made in a part of language where nothing is vague. Suppose, for example, that there are exactly one-million simples and that it is vague whether or not the activity of those simples constitutes a life. Now consider the numerical sentence that asserts the existence of (at least) one-million and one objects. (A numerical sentence is a first-order sentence asserting the existence of some objects. For example, the numerical sentence that there exist at least two objects is: ∃x∃y(x ≠ y).) If van Inwagen is correct, then it is indeterminate whether or not the relevant numerical sentence is true, in which case one of the constituent expressions—‘∃’, ‘x’, ‘y’, ‘~’, ‘=’—must be vague. Yet philosophers have claimed that the terms of first-order logic do not admit of borderline cases. (For a more detailed presentation of this argument, see Lewis 1986, pp. 212–213, Sider 2001, pp. 120–132, and section 2.2 of the entry on  ordinary objects.  For potential replies, see Hirsch 2002b, Liebesman and Eklund 2007, and van Inwagen 1990, Chapter 13.)