The Introduction to this chapter raises the problem of how to distinguish between tolerable and intolerable inconsistencies in linguistic theorising. In , Rescher and Brandom’s () logic will be introduced, which differentiates between paraconsistency, allowing for a special kind of inconsistency without ex contradictione quodlibet, and strong inconsistency, which is exposed to logical chaos. The workability of this distinction in theoretical linguistics will be exemplified by two case studies in Sections 4.3 and 4.4, respectively. They will illustrate, first, that tolerable inconsistency can be represented as paraconsistency, while the unavailability of a paraconsistent resolution may leave us with an intolerable strong inconsistency. Second, they will also show that in the cases examined the emergence of inconsistencies is closely related to the data handling techniques applied.summarises the solution to the problem raised in this chapter and highlights that there is a need to re-evaluate the way data are treated in theoretical linguistics; but tackling the question of how this should be done will be postponed to later chapters.