The tendency to attribute foundationalist ambitions to the Vienna Circle has long obscured our view of its attempted revolution in philosophy. The present paper makes the case for a consistently epistemologically anti-foundationalist interpretation of all three of the Circle's main protagonists: Schlick, Carnap, and Neurath. Corresponding to the intellectual fault lines within the Circle, two ways of going about the radical reorientation of the pursuit of philosophy will then be distinguished and the contemporary potential of Carnap's and Neurath's project explored.

Rudolf Carnap’s principle of tolerance states that there is no need to justify the adoption of a logic by philosophical means. Carnap uses the freedom provided by this principle in his philosophy of mathematics: he wants to capture the idea that mathematical truth is a matter of linguistic rules by relying on a strong metalanguage with infinitary inference rules. In this paper, I give a new interpretation of an argument by E. W. Beth, which shows that the principle of tolerance (...) does not suffice to remove all obstacles to the employment of infinitary rules. (shrink)