In the present paper, we will be examining two closely related issues: the sorites paradox and the so-called phenomenon of vagueness. We will canvass several formulations of the major premise, rejecting the conditional version, to embrace the one in terms of disjunction and weak negation. In order to avoid the absurd conclusion of the paradox, while preserving the truth of the premises, we judge the inference rule (i.e., disjunctive syllogism for weak negation) to be invalid, which entails a change of logic. On the other hand, we discuss a possible way out of the paradox, consisting in disqualifying the words occurring in the argument by reason of their supposedly vicious vagueness, a defect that would prevent logic from being applied to vague words. In fact, we reject the view of vagueness as some sort of indetermination, indecision, or ignorance, demanding instead that vagueness be understood as an inappropriate generality, that is, as a pragmatic issue consisting of a lack of detailed information required in a given communicative context. Therefore, instead of tracing the origins of the sorites paradox to vagueness, we rather prefer to associate it with graduality in the possession of a fuzzy property. We develop our proposal in dialogue with Williamson’s epistemicism and the supervaluationist theory. We start arguing for our way by presenting a particular instance of the paradox.