He did not think it was possible to construct a philosophy of science that set out invariable rules for scientific progress. Instead, he argued that the most important scientific revolutions proceeded in violation of standing accepted methodological rules. He believed, for example, that the “consistency criterion,” which posits that new theories not contradict older ones, is not a rational rule but an aesthetic one, insofar as old theories have been falsified.

Feyerabend also argued against Karl Popper’s (1902–1994) idea of falsification on the grounds that interesting theories are not constructed in accordance with all relevant facts. One example of this was how the Renaissance astronomer Galileo Galilei (1564–1642) and his followers disregarded some of their telescopic observations during the construction of their optical theory. Feyerabend claimed that Lakatos’ notion of a research program was a form of his own anarchism in disguise; he dedicated Against Method: Outline of an Anarchistic Theory of Knowledge (1975) to Lakatos as his “fellow-anarchist.”