 The general form of Church’s argument has been exploited by others to reach further puzzling conclusions. For example, it has been used to show that there can be no such thing as vague or “indeterminate” identity (Evans 1978; and for discussion, Parsons 2000). For \(x\) is not vaguely identical to \(x\); hence, if \(x\) is assumed to be vaguely identical to \(y\), then by LL, \(x\) and \(y\) are (absolutely) distinct. As it stands, Evans’ argument shows at best that vaguely identical objects must be absolutely distinct, not that there is no such thing as vague identity. But some have tried to amend the argument to get Evans’ conclusion (Parsons 2000; and see the entry on vagueness). In any case, it is useful to see the connection between Evans’ argument and Church’s. If, for example, ‘vaguely identical’ is taken to mean ‘thought to be identical’, then the two arguments collapse into one another. Church’s line of argument would seem to lead ultimately to the extreme antirealist position that any perceived difference among objects is a real difference. If one resolves not to attempt to escape the clutches of LL by some clever dodge — by disallowing straightforward quantifying-in, for example, as with the doctrine of Abelardian predicates — one comes quickly to the absurd conclusion that no statement of the form \(x = y\), where the terms are different, or are just different tokens of the same type, can be true. Yet it might just be that the fault lies not in ourselves, but in LL.