This essay is a study of Haspelmath’s conception of ‘comparative concepts’ vs. ‘descriptive categories’ from a new angle: a study concentrating on questions of logical form and formal explicitness rather than on linguistic adequacy; it is suggested that the inconclusiveness of previous discussion of the conception is mainly due to formal flaws hidden in Haspelmath’s account by its informality. Three major flaws of the conception are identified: (i) a failure to explicitly relativize comparative-concept terms to languages: to construe the terms as relational, as denoting relations between linguistic items, or constructions, and languages; (ii) misconstruing empirical statements on descriptive categories as definitions of the category terms; and (iii) a failure to recognize the importance of theories of language in dealing with ‘comparative concepts’ vs. ‘descriptive categories’. There are serious consequences of these flaws, which are pointed out in detail. The conception as such is not rejected: ten revisions are proposed for an improved version. An attempt is made throughout to actually settle matters, which requires going into details rather deeply. The essay proceeds in three steps, using background notions from logic and the philosophy of science: after the introductory Part A (§§ 1 and 2), Haspelmath’s definition of “serial verb construction” is carefully analysed in Part B (§§ 3 to 10) as the most elaborate example of how he wishes to deal with comparative concepts; in Part C (§§ 11 to 19), the conception of ‘comparative concepts’ vs. ‘descriptive categories’ is modified by introducing the revisions, first with respect to comparative concepts (§§ 11 to 13), then with respect to descriptive categories (§§ 14 to 16), resulting in a different view of their interrelations (§§ 17 and 18) and in a more adequate conception of the relations between general linguistics, comparative linguistics, and descriptive linguistics (§ 19).