The history of the foundations of mathematics in the XXth century lead to a revision of the meaning of traditional philosophical notions such as "evidence", "existence", or "rationality". This paper focuses on the influence of Gonseth's "Open philosophy" on Bernays' philosophical interpretations of the technical results in the foundations. Familiar with the ideas of Fries and Nelson, the logician Bernays turns at the mid of the century more and more towards Gonseth's ideas. Quite before Kuhn, Bernays considers the revisions under consideration not simply as a problem of truth and falsehood, but as a task requiring the introduction of a new conceptual system. Indeed, in opposite to Kuhn, according to Bernays, the necessary change is less the consequence from a change of paradigm and methodological incommensurability as a epistemological necessity.
