A Comparison between self-Reference and Indefinite Extensibility in Relation to Paradoxes

This article is about the diagnosis of logical paradoxes. That means we are going to examine paradoxes based on the diagnostic aspect. In these type of studies, the main question is that how the paradoxes enter into the inference, and how can they be detected properly. The article concentrates on the structural diagnostic proposals, and studies two kinds of them. First, those which are formed around notions like circularity and impredicativity, which we have studied under the title of “self-reference”. Second, those proposals that are formed based on the assumption of the actual infinite or some kind of indefiniteness and essential extensibility. These are studied under the title of “indefinite extensibility”. The latter group is presented in different versions and here we consider that of Wright and Shapiro. In both cases, the proposal and its conceptual context are surveyed initially. Then, its relation with the paradoxes and the way of inferring the paradoxes from them are explained. Finally, the fact that both proposals can explain common paradoxes leads us to offer an argument which shows that they are somehow identical, and, using a formal semantic mapping, we can adapt each one to the other.