 It seems legitimate to call this puzzle a ‘problem of transworld identity’, for it turns partly on the transitivity of identity, and can be avoided by interpreting claims about how bicycles could have been different (de re modal claims about bicycles) in terms of a counterpart relation that is not transitive (Chandler 1976). Thus a counterpart theorist may admit that the bicycle could have been originally composed of A1 + B1 + C2 rather than A1 + B1 + C1, on the grounds that (according to the tolerance principle) it has a counterpart (in w2) that is originally so composed. And the counterpart theorist may admit that a bicycle (such as the one in w2) that is originally composed of A1 + B1 + C2 could have been originally composed of A1 + B2 + C2, since (by the tolerance principle) it has a counterpart (in w3) that is originally so composed. However, since the counterpart relation (unlike identity) is not transitive, the counterpart theorist need not say that the bicycle in w3 that is originally composed of A1 + B2 + C2 is a counterpart of the bicycle in the actual world (w1) originally composed of A1 + B1 + C1, for its similarity to the bicycle in w1 may be insufficient to allow it to be that bicycle’s counterpart. Thus the non-transitivity of the counterpart relation (a relation based on resemblance) appears neatly to allow the counterpart theorist to respect both the tolerance principle and the restriction principle, without falling into contradiction.