Feyerabend commenced an eclectic intellectual life reading history, sociology and then theoretical physics. He appears to have followed the logical positivism of the Vienna School, then coming under the influence of Ludwig Wittgenstein and Karl Popper. He was accepted as a student by Wittgenstein, who died before Feyerabend moved to England. Feyerabend then studied under Popper. It was at the LSU that he met another of Popper’s students, Imre Lakatos.
Lakatos' sudden death put an end to a planed joint publication, but Feyerabend went on to write his most famous criticism of methodology, first as an article and then as a book entitled ''Against Method'.
Feyerabend’s critique of science takes place on two fronts. Having been influenced By Popper, he examines in detail the logic of scientific method, as well as making a detailed, if unconventional, study of key episodes in the history of science.
Feyerabend argued that adherence to any strict method would in the long run be counterproductive for the progress of science. He points out that to insist that new theories be consistent with old theories gives an unreasonable advantage to the older theory. He also argues that no interesting theory is ever consistent with all the relevant facts. Together these remarks sanction the introduction of theories that are inconsistent with well-established facts. Furthermore, a pluralistic methodology that involves making comparisons between any theories at all forces defendants to improve the articulation of each theory. Thus Feyerabend proposes that science might proceed best not by induction, but by counterinduction.
Feyerabend examines in detail crucial events in the history of science, arguing that that provide examples of counterinduction at work. For instance, from the point of view of an Aristotelian, that a ball dropped from a tower lands directly under the point from which it was dropped, and not to one side or the other, is a falsification of the hypothesis that the earth moves. Feyerabend argues that in order to progress beyond Aristotelianism, Galileo had to make use of ad hoc hypothesis and alterations to the very language in which observations are made. For Feyerabend, Galileo proceeds counterinductively, and against the rational principles of scientific method.
Feyerabend objected to any single prescriptive scientific method on the grounds that any such method would limit the activities of scientists, and hence restrict scientific progress. New theories came to be accepted not because of their accord with scientific method, but because their supporters made use of any trick- rational, rhetorical or ribald, in order to advance their cause. Without a fixed ideology, or the introduction of religious tendencies, the only approach which does not inhibit progress (using whichever definition of progress you see fit) is "anything goes": "'anything goes' is not a 'principle' I hold... but the terrified exclamation of a rationalist who takes a closer look at history." (Feyerabend, 1975).
Feyerabend enjoyed using inflammatory and direct language. He described science as being essentially anarchistic, of being obsessed with its own mythology, and of making claims to truth well beyond its actual capacity. He called for a separation of the state and science for much the same reasons that are used to justify the separation of state and church.
There is passion and energy in Feyerabend's writings unequaled by other philosophers of science. In his autobiography Killing Time he reveals that this came at great cost to himself. Following the initial reviews of Against Method, which were overwhelmingly negative, he fell into a deep depression.