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)

Famously, Kant is a transcendental idealist. Yet he also endorses empirical realism, and even boasts that only the transcendental idealist can be an empirical realist. The difficulty of making sense of those commitments together leads many interpreters to begin by attributing to Kant some variant of conventional, subjective idealism. That in turn requires that Kant's empirical realism be at best a merely ersatz or quasi-realism. But that drains Kant's boast of its significance. For any idealist can be a realist if (...) the 'realism' in question is defined in terms of a prior commitment to idealism. Thus I argue, on the contrary, that we must begin the interpretation of Kant's Critical philosophy by taking his empirical realism to be a genuine, common-sense realism about empirical things. That approach yields a consistent, satisfying, and novel reading of the Critical enterprise, including transcendental idealism, as explaining how empirical realism is possible. Along the way I show, among other things, (1) how to make systematic sense of Kant's controversial theory of meaning, which is standardly either downplayed or regarded as grossly inconsistent with his other core commitments; (2) how to dispense with the centuries-old Neglected Alternative objection; and (3) how to account for the syntheticity of the moral law and its role in conferring experience-immanent meaning on the practical postulates (e.g., of the existence of God). (shrink)

In this paper, we will discuss what is called the “Manifestation Challenge” to semantic realism, which was originally developed by Michael Dummett and has been further refined by Crispin Wright. According to this challenge, semantic realism has to meet the requirement that knowledge of meaning must be publically manifested in linguistic behaviour. In this regard, we will introduce and evaluate John McDowell’s response to this anti-realistic challenge, which was put forward to show that the challenge cannot undermine realism. According to (...) McDowell, knowledge of undecidable sentences’ truth-conditions can be properly manifested in our ordinary practice of asserting such sentences under certain circumstances, and any further requirement will be redundant. Wright’s further objection to McDowell’s response will be also discussed and it will be argued that this objection fails to raise any serious problem for McDowell’s response and that it is an implausible objection in general. (shrink)