Qualitative cognition and quantitative cognition are different in basis, form, structure and function. In essence, they developed two different research programs and two different epistemological frameworks in the form of methodology. Technically speaking, due to the complexity and diversity of the research objects, different ways to solve the problem are adopted.
Even in natural science, the understanding of some properties of force, electric field and magnetic field and the understanding of atomic structure are qualitative problems, but the conclusions of these properties have to be strictly tested by experiments, and qualitative research is also very important in chemistry, biology and geography. In order to effectively use mathematical methods to engage in scientific research, we must have a certain understanding of the qualitative characteristics of the research object. Without high-level qualitative theory, quantitative research is just a blind number game, that is, in natural science, quantitative analysis methods can only give full play to their functions if they are combined with good qualitative analysis.
In fact, most effective theories can reasonably combine qualitative analysis with quantitative analysis, and the fundamental way to combine quantitative analysis with qualitative analysis is to let researchers know these two methods.