Why should we act morally? This question regarding justification has like no other occupied moral philosophy since the Second World War. Eventually, a perspective has prevailed that has abandoned traditional models of justification in favour of ethical pluralism and moral progress. Since there should no longer be any external reasons, only that which can be thought without contradiction can be considered generally binding. But what does contradiction mean here? This study brings Wittgenstein's philosophy of language into constellation with critical theory in order to show that modern moral philosophy must fail because of its claim. The starting point is Wittgenstein's private language argument and in particular §125 of the Philosophical Investigations, in which he describes contradiction as the central philosophical problem of bourgeois society. It becomes clear that neither freedom from contradiction nor moral justification precede social practice. On the contrary, the supposed rationality of modern moral philosophy reflects the contradictions of our society. The task of philosophy is therefore not to resolve these contradictions, but to expose them through critical linguistic analysis. By bringing Wittgenstein into dialogue with Marx, Adorno and Horkheimer, a new approach to moral philosophy emerges - a critique that is both linguistic and social.