Abstract Recent work on the epistemology of climate science includes arguments that are against probabilistic representations of uncertainty about climate and for possibilistic ones as well as some development and use of the latter. I reinstate these arguments, partly by rebutting Corey Dethier’s recent challenge to them and partly by arguing that they remain effective against recent improvements to probabilistic representations. Recognising, however, that the case for possibilistic representations can be undermined by problematic interpretations of epistemic possibilities, I set out criteria of adequacy for such interpretations in the climate context while arguing for a preferred interpretation. I criticise the appropriateness of standard interpretations, according to which a proposition is epistemically possible if and only if it is not recognised to be excluded by what is known, as well as some other prominent non-probabilistic interpretations. So too, I criticise interpretations of epistemic possibilities in terms of upper probabilities. I conclude that an interpretation of epistemic possibilities as possibilities that are consistent with knowledge that approximates the basic way things are is preferable to the other available interpretations.