 Another argument on behalf of impossible worlds, quite pervasive in the literature, comes from counterpossible reasoning (e.g. Beall &amp; van Fraassen 2003, Chapter 4; Nolan 1997; Restall 1997; Brogaard &amp; Salerno 2013). This is reasoning from suppositions, assumptions, or conditional antecedents which are not only false, but impossible. We can reason non-trivially from impossible suppositions, by asking what would be the case, were (say) the Law of Excluded Middle false. To say that we reason non-trivially from an assumption means just that we accept some conclusions but reject others on the basis of that assumption. If we hypothetically suppose the Law of Excluded Middle to be false, for example, then we would likely conclude that intuitionistic logic would be preferable to classical logic, given that supposition. We are unlikely to conclude that classical logic would be a satisfactory logic, or that scarlet would be a shade of green, given that supposition. The point readily generalizes to reasoning about entire theories and to serious philosophical and logical debates. We often reason from suppositions about the truth of certain logical, mathematical, or metaphysical theories which, if in fact false, are necessarily false, because of the very nature of their subject matter.