Paradoxes, Contradictions and Circularity

Abstract

Paradoxes make us reflect on our assumptions and intuitions linked to many central notions that we thought were clear and precise. They provoke us to the point of having to abandon basic beliefs about vast areas of our knowledge. Notions such as infinity, truth, knowledge, justification and rationality have been victims of this challenge. In this article we will challenge a widespread view about paradoxes claiming that all of them involve circularity and that their problem is they lead to contradictions. For the former we will employ Yablo’s paradox. Against the latter, we will argue that the key notion is not that of consistency or contradiction, but that of non-triviality. In addition, we will briefly review some nontrivial but inconsistent theories of truth, and argue that ω-consistency is a requirement for consistent theories of truth, but that inconsistent and non-trivial theories of truth can retain intended models. Finally, we will introduce and defend what we think is the right way of solving semantic paradoxes based on the BA-Plan. In this framework, it is possible to define a naive truth theory avoiding triviality, without abandoning any classical principle, inferential or metainferential.