"Knowledge is not a series of self-consistent theories that converges toward an ideal view; it is rather an ever increasing ocean of mutually incompatible (and perhaps even incommensurable) alternatives, each single theory, each fairy tale, each myth that is part of the collection forcing the others into greater articulation and all of them contributing, via this process of competition, to the development of our consciousness."

      - Paul Feyerabend, "Against Method"

Counterinduction is a measure/tactic for calling something into question/doubt that is the opposite of induction - that is, not so much doing what is illogical, but rather the opposite of what is or appears to be in the concrete instance logical. Not so much an ill-advised choice as one that stands against advice as such. Counterinductive methods were popularized by philosopher and scientific anarchist Paul Feyerabend in his "epistemological anarchism" and promoting of pluralistic methodology (in place of fixed methods and best practice recipes or the privileging of one kind of methodology or type of knowledge over any other, etc.) He sums up the general approach thus: 

"Therefore, the first step in our criticism of customary concepts and customary reactions is to step outside the circle and either to invent a new conceptual system, for example, a new theory, that clashes with the most carefully established observational results and confounds the most plausible theoretical principles, or to import such a system from the outside science, from religion, from mythology, from the ideas of incompetents, or the ramblings of madmen."

Feyerabend really promotes a rather anarchic and ad hoc practice of combinatorial and creative scientific methodology and discourse, where the only real principle that is guaranteed to always apply is "anything goes". Feyerabend also shows/argues that counterinduction can be a much more efficient tool for scientific discovery than usual induction. He also claims that:

"Ideological ingredients of our knowledge and, more especially, of our observations are discovered with the help of theories which are refuted by them. They are discovered counterinductively."

The no less curious/interesting study and practice of ethnomethodology draws a lot of inspiration and influence from Feyerabend in the building of its discipline, its approach and methods to discovering and revealing (also often by proceeding counterinductively to apply/do the opposite of what is allowed or tolerated, seen as socially acceptable, generally accepted as true or validated by, etc.) Choosing to adopt such tactic naturally often yields unexpected and surprising results and consequences given its unpredictability (which is what adds new information).

Feyerabend himself goes as far as suggesting that we deal with empirical "facts" and theories by forming many contradicting and conflicting theories and claims about them that we can then counterinductively analyze to determine their validity as "facts". As he says, we need to make use of an "external measure of comparison, including new ways of relating concepts and percepts." Needless to say, a counterinductive move needs to execute itself from a domain or field or area as different/divergent from that/those that the original claim/theory is grounded/rooted in as possible. And always remind yourself that we only see only part of what we know (or think we know).