Feyerabend's ideas to me see to be a little scattered. On pg. 114 GS states that Feyerabend claims we should ignore principles or rules that may go wrong. We also learn on pg. 115 that for Feyerabend, science benefits from the presence of a range of alternative ideas and perspectives. So wouldn't ignoring ideas that may go wrong inhibit this "marketplace of ideas" (pg. 116)? GS also states that Feyerabend never gives an answer on how to reject or eliminate ideas, which confused me even more. Can someone shed some light on Feyerabend's views on how his "anything goes" view works within his views of ignoring possibilities of being wrong?
Not knowing what GS is, as Conrad points out, I cannot yet make a definitive answer, but it is possible that Feyerabend is drawing a distinction between principles-and-rules which can go wrong and principles-and-rules which have been rewritten in a form which allows doubt.
"What goes up must go down" fails remarkably if someone holds the object at its apex
"What goes up must go down unless someone opposes it" fails remarkably once you exceed escape velocity.
"'What goes up must go down' has a remarkable track record of being useful" can no longer "go wrong" because the fuzzy words "remarkable" and "useful" temper it, without losing sight of the value of the original rule.
It appears Feyerabend is arguing that we should ignore rules given to us until they are in such a form, because rules which are not in that from have a tendency to squelch contrary ideas (which may be true, but you'd never know it if you squelched them)
We also learn on pg. 115 that for Feyerabend, science benefits from the presence of a range of alternative ideas and perspectives
I don't think that Feyerabend is wrong; after all even at MIT they had a lecture on Aristotle and Physics for a 'bigger Physics'.
Feyerabend was arguing against methodological dogmatism
I suggest a look at Richard J. Bernstein's Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis. His core thesis is that the dichotomy between 'Objectivism' and 'Relativism' is false. See what he has to say about Kuhn:
Kuhn's persistent attacks on the idea of an algorithm for theory-choice, his criticism of the idea of a permanent, neutral observation language, and his undermining of the notion of a determinate set of scientific criteria that can serve as rules or necessary and sufficient conditions for resolving scientific disputes can all be interpreted as calling into question the Cartesian Anxiety. (60)
Feyerabend could be said to have taken Kuhn's claims even further. He is purposely polemical, intentionally a grouch who does not "fit in". However, he's really making the same objection: there is no One Method to Rule Them All:
Feyerabend (almost inadvertently) displays a remarkable perspicacity about his own polemical stance when he writes:
A society that is based on a set of well-defined and restrictive rules so that being a man becomes synonymous with obeying these rules, forces the dissenter into a no-man’s-land of no rules at all and thus robs him of his reason and his humanity. It is the paradox of modern irrationalism that its proponents silently identify rationalism with order and articulate speech and thus see themselves forced to promote stammering and absurdity. . . . Remove the principles, admit the possibility of many different forms of life, and such phenomena will disappear like a bad dream. (pp. 218–19)
The passage is revealing because it not only characterizes the “no-man’s-land” into which Feyerabend has wandered but also underscores the rationale for his polemical stance. At times it does seem as if Feyerabend is promoting “stammering and absurdity” and is forced to take extreme positions of “irrationalism,” because he implicitly accepts the characterization of reason and rationality that he ostensibly seeks to overthrow. (63)
The irony is that those who believe in Objectivism actually coerce their opponents into seeming like they are Relativists, and irrational at that! After all, if you disagree with The Powers That Be, surely there is something wrong with you. For more, see Foucault's Madness and Civilization (from the Wiki page):
He argues that in the Renaissance the mad were portrayed in art as possessing a kind of wisdom – a knowledge of the limits of our world – and portrayed in literature as revealing the distinction between what men are and what they pretend to be. [...]
Foucault contends that in the mid-seventeenth century, in the depths of the age of reason, the rational response to the mad, who until then had been consigned to society's margins, was to separate them completely from society by confining them, along with prostitutes, vagrants, blasphemers and the like, in newly created institutions all over Europe – a process he calls "the Great Confinement.
Who is "rational" and who is "mad" is decided by the powers that be; it is not decided based on 'Reason' or anything like that. Part of Feyerabend's response to philosophers and scientists attempting to declare him mad was to write The Tyranny of Science. The editor introduces the work:
His approach to knowledge and epistemology tries explicitly to take something positive from every experience. He draws from a great variety of courses, arguing that there is no idea, however ancient or absurd, that is incapable of contributing to the improvement of knowledge. He insisted that developing divergent points of view promotes progress better than sticking to just one perspective, no matter how successful it may seem. On this account, scientific progress is not some linear progression towards truth, or a process that converges towards an ideal view. It is rather an ever 'expanding ocean of alternatives', each of which forces the others into greater articulation; all of them contributing through the process of competition to the development of our understanding. (x)
In Anglo-American Postmodernity, Nancey Murphy argues (in the realm of mental illness) that it is only by heeding Feyerabend's advice that the 'psychosocial' school of psychologists were allowed to continue research, given the greater (and increasing) success of the 'medical' school. She argues that the 'psychosocial' school proved beyond a doubt that the placebo effect itself is not a medical phenomenon, but a psychological one. Had the 'medical' school been allowed to win, it would not have known what to do with this phenomenon which did not fit inside their categories of thought. They might not even have seen it, for it had already gone unnoticed for a long time.
P.S. I'm not sure Feyerabend could have foreseen what Murphy claims to have observed. So, what I have provided is not argumentation by Feyerabend, but evidence that he was right, based on his predictions.