In this paper, I introduce three criteria for the historical assessment of research activities and apply them to mathematical activities, especially research activities in the set-theory. These criteria are accuracy, expressibility, and coherence. According to my proposal, a research tradition is progressive, when it is more accurate, more expressive and more coherent than its predecessors. A research tradition in a crisis is regressive with respect to at least one of these criteria. This approach is based on a nominalistic non-realism that is connected with a metaphysical position, namely the ontological theory of multiple languages.