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The criticism of Popper’s work left room for new philosophers of science to build novel interpretations. For instance, Popper is considered by some to be a transitional figure between logical positivism and the Kuhnian tradition. The critical response to Popper’s normative appraisal of falsifiability criteria has placed Popper’s philosophy of science as the progenitor to the Kuhnian relationship between anomalies and paradigms.
Imre Lakatos attempted to save the core rationality of Popper’s methodology, while taking into account the wealth of criticisms it received. For example, Lakatos introduced the concept of ‘progressive and degenerating research programmes’ to resolve the contradistinction between Popper’s normative critical rationalism of science and Thomas Kuhn’s uncritical socio-psychological appraisal in Structure of Scientific Revolutions.
In the wake of Lakatos’ reaction to the Popper and Kuhn debates, another opposition to Popperian interpretation emerged between the more moderate philosophy of Laudan, and the more radical one of Feyerabend. Feyerabend coined the term “anything goes” in an anarchist interpretation that science does not follow, and never has been governed by, a precise method or even rationally defined precept. Feyerabend’s book “Against Method” [[Feyerabend (1975a)|''Against Method'']] (1975) rejected Popper’s original theory, as well as Lakatos’ corrections, with his anarchist opinions on humanity and science. In face of this radical anti-rationalism Larry Laudan reformulated Lakatos’ work on “research programmes” and Khun’s theories of paradigms and normal science with his alternative “research traditions”.
The panorama of influence from Popper’s work is expansive and includes epistemologists such as Agassi, Bartley, Watkins, Musgrave, Albert and Stegmuller. Scientists such as Bondi, Eccles, Medawar and the anthropologist Ian Jarvie, have all paid respect to Popper. Among his critics, Miller, Tichy, Ackermann, and Johannson consider themselves largely in agreement with Popper’s work, especially in contrast to the relativism and irrationalism of Feyerabend and Kuhn.
Popper’s critical rationalism can be seen as a watershed of philosophical thought on the limits of empiricism, rationalism, and positivism, and an opening of the flood-gates for questioning and contemplation within nearly every branch of philosophy.
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