Wittgenstein and the philosophical significance of not solving the paradoxes

The standard question about the semantic paradoxes is how we should solve them. Wittgenstein raised a different question: whether we should solve them. In this paper, I argue that we have two reasons to take the question raised by Wittgenstein seriously. First, reflecting on the question posed by Wittgenstein might free us from a philosophical ideal, the assumption that we should reason according to strictly valid logical principles, in the sense of Hofweber (2008; 2009). Second, reflecting on Wittgenstein’s question might lead us to realize a possibly obvious, but important, point: the fact that several logical principles are jointly inconsistent does not show that one of them is more problematic than the others, for the same reason why the fact that several plans of action are jointly inconsistent does not show that one of them is more problematic than the others.