 Suppose, however, that we replace our criterion of identity by the following more complicated rule: \(x\) and \(y\) are the same relative to z, if both \(x\) and \(y\) differ from \(z\) at most by a single part. (This relation is transitive, and is in fact an equivalence relation.) For example, relative to \(P\), \(P, P^1, Q^2\), and \(Q^3\) are the same, but \(Q, Q^1, P^2\) and \(P^3\), are not. Of course, replacement by a single part is an artificial criterion of identity. In actual cases, it will be a matter of the degree or kind of deviation from the original (represented by the third parameter, \(z)\). The basic idea is that identity through change is not a matter of identity through successive, accumulated changes — that notion conflicts with both intuition (e.g., the sandals example) and the Kripkean argument: Through successive changes objects can evolve into other objects. The three-place relation of identity does not satisfy LL and is consistent with the outlook of the relativist. Gupta (1980) develops a somewhat similar idea in detail. Williamson (1990) suggests a rather different approach, but one that, like the above, treats identity through change as an equivalence relation that does not satisfy LL.