In this article I show how to obtain a powerful and truthful explanation of the failure of sorites arguments combining an adaptation of the Wide Set Theory formulated by Formato and Gerla and the concept of deep manyvaluedness established by Marraud. It is shown that if the premises of a sorites argument are conceived as a succession of indexed consequence operators (where indices express the accuracy of the inferences) prefixing sentences, the argument fails because the transitive property for the inclusion between wide data sets is not always maintained.