This is some further reflection on my use of the term Wesleyan Quadrilateral in my writing, A Wesleyan Quadrilateral Bibliography. Some argue that Wesley intended and used the Quadrilateral to understand scripture, not ethics or theology. I believe that this framework is indeed useful for these two areas, in addition to understanding scripture. But note that the whole debate over sexuality and "homosexuality" is usually rationalized by reference to six or seven isolated scripture passages as is amply illustrated by the sources in that bibliography. Furthermore, the methods used in this rationalization are not based in modern biblical scholarship, to say nothing about scientific discoveries about the manuscripts, the cultures, and the history behind the writings. So, in this instance in particular, the sources I note are all related to what I and many others see as a misunderstanding or misreading (either consciously or not) of scripture. Finally, if scripture is indeed "primary" for Methodist Christians, then these sources are right on point to understand the biblical worldview and how it is different from 21st century human existence. As some of the resources argue, there are other Biblical concepts and passages more relevant to the situation of sexuality in the 21st Century.
The resources below bear further study.
Other perspectives:
Change the Name If We Must, But Keep the Method, by Philip Brooks, May 29, 2015. An overview of the debate.
The 'Wesleyan Quadrilateral': The Story of a Modern Methodist Myth, by Ted Campbell, a survey and critique of the development of this concept.
...since the adoption of a new theological statement in 1972 which held up scripture, tradition, reason, and experience as "Doctrinal Guidelines in The United Methodist Church," this fourfold locus of religious authority has gained remarkable acceptance as a tool for theological analysis and as a starting point for the recovery of the Wesleyan theological tradition in a modern ecumenical context...
...here we have an instance of the development of a modern version of the traditioning process....The notion of the "Wesleyan Quadrilateral," then, would be an intricate composite of these sources, formed under the crucible of Methodist involvement in the ecumenical movement, and then found almost indispensable by Methodists themselves in their defense of a progressive attitude towards biblical authority.
Albert Outler, The Wesleyan Quadrilateral In John Wesley, 1985. The classical answer to the debate, from the famous professor and editor.
The term “quadrilateral” does not occur in the Wesley corpus—and more than once, I have regretted having coined it for contemporary use, since it has been so widely misconstrued. But if we are to accept our responsibility for seeking intellecta for our faith, in any other fashion than a “theological system” or, alternatively, a juridical statement of “doctrinal standards,” then this method of a conjoint recourse to the fourfold guidelines of Scripture, tradition, reason and experience, may hold more promise for an evangelical and ecumenical future than we have realized as yet—by comparison, for example, with biblicism, or traditionalism, or, rationalism, or empiricism.
Finally, an interesting story about Wesley's use of the process, from the point of view of the oppressed: As Methodists Unravel, Remember: John Wesley Disregarded His Own Quadrilateral When He Changed His Mind on Slavery, by Ken Wilson, 2018.