 A third solution to the transitivity problem has been proposed (by Chandler, followed by Salmon) which apparently allows us to reconcile all three of the transitivity of identity, the tolerance principle, and the restriction principle. This is to say that although there are possible worlds (such as w3) in which the bicycle is originally composed of only a small proportion of its actual original parts, such worlds are not possible relative to (not ‘accessible to’) the initial world w1. From the standpoint of w1, such an original composition for the bicycle is only possibly possible: something that would have been possible, had things been different in some possible way, but is not, as things are, possible (Chandler 1976; Salmon 1979; Salmon 1982, 238–240). Whether this solution is satisfactory is disputed. (See, for example, Dorr, Hawthorne, and Yli-Vakkuri 2021, Chs 7–8.) Admittedly, there are some contexts in which we talk of possibility in a way that may suggest that the ‘accessibility relation’ between possible worlds is non-transitive: that not everything that would have been possible, had things been different in some possible way, is possible simpliciter. (If Ann had started writing her paper earlier, it would have been possible for her to finish it today. And she could have started writing her paper earlier. But, as things are, it is not possible for her to finish it today.) Nevertheless, the idea that, as regards the type of metaphysical possibility that is involved in puzzles such as that of the bicycle, there might be states of affairs that are possibly possible and yet not possible (and hence that de re metaphysical possibility and necessity do not obey the system of modal logic known as S4) is regarded with suspicion by many philosophers.