This paper portrays the later Wittgenstein’s conception of contradictions and his therapeutic approach to them. I will focus on and give relevance to the Lectures on the Foundations of Mathematics, plus the Remarks on the Foundations of Mathematics. First, I will explain why Wittgenstein’s attitude towards contradictions is rooted in: a rejection of the debate about realism and anti-realism in mathematics; and Wittgenstein’s endorsement of logical pluralism. Then, I will explain Wittgenstein’s therapeutic approach towards contradictions, and why it means that (...) a contradiction is not a problem for logic and mathematics. Rather, contradictions are problematic when we do not know what to infer from them. Once a meaning is established through a new rule of inference, the contradiction becomes a usable expression like many others in our inferential apparatus. Thus, the apparent problem is dissolved. Finally, I will take three examples of dissolved contradictions from Wittgenstein to clarify further his notion. I will conclude considering why his position on contradictions led him to clash with Alan Turing, and whether the latter was convinced by the Wittgensteinian proposal. (shrink)

The lingering mystery of John Rawls’s reflective equilibrium is that its nature is unclear. Rawls at times suggests he is merely describing people’s conceptions of justice, whereas at other times he implies that his reflective equilibrium is a way to justify his conception of justice. Faced with seemingly conflictual passages, most scholars privilege the justificatory ones. However, I argue that this is not an effective strategy because understanding how the descriptive and justificatory aspects of reflective equilibrium fit together is the (...) key to unlocking its nature and actual force. This paper compares Rawls’s method to the philosophical method of later Wittgenstein in his so-called private language argument to argue how the descriptive and justificatory aspects of Rawls’s reflective equilibrium fit together. In my view, both philosophers’ methods are descriptive clarifications of our unclear conceptions. However, their clarification is not just descriptive; they also aim at their readers achieving enlightenment. Importantly, I argue, that enlightenment offers us justification of the conception resulting from their clarification. Hence, their methods are justificatory as well. Finally, I claim that this way of understanding reflective equilibrium makes us realise how Rawls could respond to a prominent objection to it. (shrink)