From everything I have learned about "Aspect-Oriented Programming" or "Aspect-Oriented Software Development," labeling it as a programming paradigm or methodology appears to be inaccurate. From what I can tell it is not a fundamental technique for programming.
To nail down what is meant by "paradigm" and "methodology," please refer to the following definitions from the American Heritage Dictionary. Compare how well or poorly "Object-Oriented Programming" applies to each vs. how well AOP fits.
Paradigm: A set of assumptions, concepts, values, and practices that constitutes a way of viewing reality for the community that shares them, especially in an intellectual discipline.
Methodology: A body of practices, procedures, and rules used by those who work in a discipline or engage in an inquiry; a set of working methods.
"Evidence-based medicine" satisfies the definition of paradigm, but "hysterectomy-based medicine" would be a misnomer because the problem space is too narrow.
I am getting the impression that AOP may be misnamed because based on the "oriented-programming" suffix, AOP is alleging to be both a paradigm and a methodology in the same way "Object-Oriented Programming" is.
Both of these terms (paradigm and methodology) indicate a fundamental technique, where what I understand about aspects is a technology for solving a narrow problem scope, maybe comparable in magnitude to the static variable feature of Java.
If it's true that aspects solve a narrow set of problems, and AOP isn't a misnomer, then why shouldn't all programming techniques be given the "oriented-programming" suffix, such as "inheritance-oriented programming," "dependency-oriented programming," or "scope-oriented programming?"