I think most of the debate on interpretation of Islam has to do with Sharia law, and ironically both IS and the conservative right pretty much align with and use the most extreme interpretation of it in their respective agendas. Where the disagreement comes from among Muslims and people who argue that the most rigid interpretation of Islamic Law is incorrect, is that it's not a rigid and static belief. The rules are rigid, the interpretation and application are not. Often overlooked in discussion of this is the role of the Sunna and Hadith as supplements to the Qur'an. I find these two passages to be very useful when people try to claim "correct" interpretation. It's pretty clear that the interpretations by IS and the Right are archaic interpretations, no longer in step with current times, and having not evolved, are no longer valid. Wrong? No. Invalid? Yes. This is a pretty good example as to why Muslim world was considered to be so advanced and progressive at one time. "The Qur'an contains a variety of law-making provisions and legal proscriptions interspersed throughout its chapters (suwar) and verses (ayat). A number of rules exist for interpreting these provisions, such as the position of a given ayah within the context of the surah, which in turn is interpreted in accordance with its place in the sequence of revelations, its reference to other revelations, and its historical context in relation to particular conditions which existed at the time of the given revelation. These and other rules are known as the science of interpretation (ilm usul aI-fiqh). According to these rules, for example, one initially is to refer to a specific provision and then to a general provision dealing with a particular situation. No general provision can be interpreted to contradict a specific provision, and a specific rule will supersede a general proposition. A general provision, however, is always interpreted in the broadest manner, while a specific provision is interpreted in the narrowest manner. Reasoning by analogy is permitted, as are applications by analogy, except where expressly prohibited. Simplicity and clear language are always preferred. Similarly, the clear spirit of certain prescriptions cannot be altered by inconsistent interpretations. A policy-oriented interpretation within the confines of the rules of jurisprudence is permissible and even recommended, as is the case with the doctrine of ijtihad (progressive reasoning by analogy)." "Muslim scholars do not consider Islam to be an evolving religion, but rather a religion and legal system which applies to all times. It is, therefore, the application that is susceptible to evolution. Indeed, the provisions of the Qur'an are such that by their disciplined interpretation, with the aid of the Hadith and Sunna and other sources of interpretation, Islam can, as intended, provide the solution to contemporary social problems."