I discuss some difficulties in writings by Imre Lakatos, Larry Laudan and Michael Friedman, where - in efforts to reinstate methodological normativity and the rationality of science - they modify, complicate, and expand Kuhn's conception of the development of science by replacing his concept of paradigm with a more rigorous one, or by supplementing it with various concepts of meta-paradigms. It is not clear that any of their proposed replacements of "paradigm" are more (methodologically) rational, better (logically) designed, and less monopolistic and dogmatic. I also present more broadly Stefan Amsterdamski's conception of the historical ideals of knowledge and my own ideas, elaborated, in some cases many years ago, in order to improve Kuhn's view. I introduce a concept of an "intellectual tradition" as a multi-level structure, containing a metaphysical layer and (several) scientific layers; the idea of a hierarchy of scientific achievements based on their differentiated cognitive significance; and an outline of a narrative of the history of science as a self-constituting process.
Kuhn; Lakatos; Laudan; Friedman; Amsterdamski; Paradigm; Dynamics of science; Scientific rationality; Scientific normativity; Ideals of knowledge