The present paper considers a generalization of the Lockean thesis to a quantitative, many-valued, setting. The aim of such generalization is to handle the conjunctive closure principle, that usually fails in the classical setting, by a gradual approach. Being the Lockean thesis probabilistic in nature, we also show how its quantitative version can be formalized within the language of the probability logic FP(RŁ). Our analysis shows that the belief operator definable in FP(RŁ) recovers the satisfiability of belief sets that might be classically contradictory. In other words, there are belief set whose conjunctive closure is classically unsatisfiable, but whose generalized representation in FP(RŁ) are not contradictory.