I examine the variety of Kuhn’s notions of incommensurability, including methodological, semantic and observational incommensurability as found in the Structure of Scientific Revolutions, and local incommensurability as found in later publications. I argue that through these various presentations, Kuhn establishes reasons to criticize and reject the correspondence theory of truth that is predicated on a mind-independent world. I show that under both observational incommensurability and local incommensurability, Kuhn provides reasons to criticize the epistemic assumptions in truth as correspondence. I maintain that for both semantic incommensurability and local incommensurability, Kuhn assumes the conception of language as the universal medium. I contend that this view of language, together with Kuhn’s rejection of a neutral language, provides reasons to challenge the linguistic assumptions behind the correspondence theory. I suggest that, given the challenges his thesis of incommensurability raises against truth as correspondence, Kuhn rejects the correspondence theory and instead considers alternative theories of truth.