Do the roots of conflicts of opinions lie in the variability and non-identity of people's views or in the variability and non-identity of people themselves as cognitive agents? There are two ways to answer this question, functional and ontological approaches. The first of them leads to the special regulative protocols of interaction which will be sufficient for modeling and resolution of the conflicts of opinions. The second suggests creating formal ontologies and constitutive theories. In our talk we discuss the advantages and limitations of these approaches in regarding argumentation studies.