A standard story about what happened with our views on concepts and categorization is broadly accepted in cognitive science circles. The crucial role in this story is played by the notion of the so-called classical view as far as all other views have been conceived as either alternatives, or improvements of that view. The notion of the classical view that supports the standard story is based on three main assumptions: (1) The classical view is a descriptive theory: it is about what concepts are, not about what concepts should be. (2) The classical view presupposes that concepts are mental representations and its main claims are about the structure of the conceptual mental representations. (3) The basic statement of the classical view is that concepts are represented by means of a set of individually necessary and jointly sufficient defining features. This paper will show that the three assumptions listed above are not true for most of the theories to which the notion of the classical view is intended to refer. As a result, the standard story is a source of unsound criticism having far-reaching negative effects: underestimation of the status of well-defined concepts in science, misunderstanding of the relations between the classical theories of concepts and categorization and their alleged alternatives.