 To complete the argument it only remains to show that Tractarian commitments extrinsic to the argument for substance rule out contingent  simples.[7]  Suppose a is a contingent simple. Then “a exists” must be a contingent proposition. But it cannot be an elementary proposition because it will be entailed by any elementary proposition containing ‘a,’ and elementary propositions are logically independent (4.211). So “a exists” must be non-elementary, and so further analyzable. And yet there would seem to be no satisfactory analysis of this proposition on the assumption that ‘a’ names a contingent simple — no analysis, that is to say, that is both intrinsically plausible and compatible with Tractarian principles. Wittgenstein cannot analyse “a exists” as the proposition “∃x(x = a)” for two reasons. First, he would reject this analysis on the grounds that it makes an ineliminable use of the identity sign (5.534). Second, given his analysis of existential quantifications as disjunctions, the proposition “∃x(x = a)” would be further analysed as the non-contingent proposition “a = a ∨ a = b ∨ a = c…”. Nor can he analyse “a exists” as “~[ ~Fa &amp; ~Ga &amp; ~Ha…]” — that is, as the negation of the conjunction of the negations of every elementary proposition involving “a.” To suppose that it could, is to suppose that the proposition “~Fa &amp; ~Ga &amp; ~Ha…” means “a does not exist,” and yet by the lights of the Tractatus this proposition would show a’s existence — or, more correctly, it would show something that one tries to put into words by saying “a exists” (cf. 5.535, Corr, 126)). So, pending an unforeseen satisfactory analysis of “a exists,” this proposition will have to be analysed as a complex of propositions not involving a. In other words, ‘a’ will have to be treated as an incomplete symbol and the fact of a’s existence will have to be taken to consist in the fact that objects other than a stand configured thus and so. But that would seem to entail that a is not simple.