Adams may be interpreted as providing two arguments, the first being the continuity argument used above. The second is a modal argument relying on the Necessity of Identity and a suitably strong modal logic. Suppose there are two objects that are distinguished by accidental features, as it might be one of the spheres, A has a scratch, while the other B does not. Then it is possible that A has no scratch and hence possible that the spheres be indiscernible. If the Principle holds of necessity then that entails that it is possible that A = B. But by the Necessity of Identity that in turn entails that it is possibly necessary that A = B, so in S5 modal logic (or the weaker system B), it follows that A = B, which is absurd given that one has a scratch and the other does not. In this argument any accidental difference would suffice in place of the scratch.