Abstract
A guiding theme in analytic philosophy is the hope of achieving philosophical progress by means of clear questions and statements put in the service of rigorous argument. This article explores both historical-cum-exegetical and (meta-)philosophical aspects of this aspiration. Building on propaedeutic clarifications of the notions of clarity and rigour, it disputes that analytic philosophy is inherently clearer than alternative ways of philosophizing, and considers a defence according to which inaccessibilty is a price to be paid for rigour. It then explores a previously unnoticed conflict between these two ideals that emerges from comparing methodological ideas in Frege, Wittgenstein and Carnap. What sets the three apart are their views concerning the role of formal logic in the pursuit of clarity and rigour, which are in turn linked to distinct conceptions of philosophical progress. Nevertheless, there remain surprising affinities between them, which point to the need for balancing the demands of clarity and rigour.