Wide sets, deep many-valuedness and sorites arguments
Carlos Pelta Resano · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · 2004
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 many-valuedness established by Marraud. It is shown that if the premises of a sorites argument are conceived as a succession of indexed consequence opera-tors (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. Key words: Wide set, consequence operator, sorites argument. 1