Taking the classification of certainties or hinges in Wittgenstein’s sense provided by Moyal-Sharrock, (Moyal-Sharrock, Understanding Wittgenstein’s On Certainty, Palgrave Macmillan, 2004) as a reference, Fortney (Fortney, Philosophia 48:967– 979, 2020, this journal) held that certainties can be regarded as universal when they are restricted to those certainties that we should have to be able to participate in complex language-games. In this paper, however, I show that Fortney’s conception of universal certainties is wrong, for it does not allow us to distinguish between local and universal certainties. After this first approach, in which I attempt to clarify what universal certainties are not, I focus on what they are. To this end, I analyze Pleasants’ (Pleasants, Ethical Perspectives 22:197–215, 2015) proposal to consider the certainty of the wrongness of killing innocents as a universal certainty that allows exceptions. Focusing on the mentioned certainty, I explain why a universal certainty that admits exceptions should be regarded as a local certainty. But this analysis also leads me to conclude that universal certainties are those that allow no exception at any time or in any culture.