This paper revisits a well-known rebuttal of Peter van Inwagen’s consequence argument. This CS-rebuttal, as I shall call it, focuses on the counterfactual structure of alternative possibilities. It shows that the ability to do otherwise is such that if the agent had exercised it, the distant past and/or the laws of nature would have been different. On the counterfactual scenario, there is, therefore, no need for the agent to exercise an ability to change the past or the laws of nature. (...) I first present van Inwagen’s original version of the consequence argument. After exposing some difficulties with Lewis’ famous version of the CS-rebuttal, I proceed by explaining and defending an older and, in my view, superior version. I subsequently discuss a traditional incompatibilist rejoinder, which insists that the past and the laws of nature are fixed. Although this rejoinder delivers a valid argument against the existence of alternative possibilities, it relies on premises the compatibilist explicitly rejects. The outcome of the debate is therefore properly characterized as a genuine dialectical stalemate between compatibilists and incompatibilists. In the final sections of the paper, I demonstrate that attempts by Fischer, Holliday and Fischer and Pendergraft to move beyond the stalemate in favor of the incompatibilist position all fail. I thereby show that the debate is marred by a misunderstanding of the semantics underlying the backtracking conditionals sometimes associated with the compatibilist position. In view of my arguments, the dialectical stalemate between compatibilists and incompatibilists regarding the counterfactual structure of the ability to do otherwise remains fully intact. (shrink)