Liars and Circles: essays on truth, self-reference and paradoxes - Abrahão, Fernanda Birolli (2023)
This MA dissertation comprises four chapters that investigate philosophical and logical aspects related to paradoxes, self-reference, and circularity. The first chapter provides possible responses to the question \"What is a paradox?.\" It begins by exploring the etymology of the word \"paradox\" and its potential connection to nonsense, with the aid of the philosophers Wittgenstein and Deleuze in their conception of nonsense. It ends with the examination of arguments and the judgment whether they are paradoxical or not. In the second chapter, I provide a formal study of logical paradoxes, including the Liar, the Heterological, and the Yablo Paradox; in the discussion about the latter paradox, I identify a lack of explicit definitions for self-reference and circularity. This topic is taken up again in third chapter, where I provide precise definitions for the concepts of reference, self-reference and circularity using model-theoretic interpretations and demonstrate properties about well-known paradoxes. The fourth chapter delves into semantically closed languages and theories, presenting a formal definition and a construction of a first-order bisorted semantically closed language. Moreover, it discusses whether everyday languages such as Portuguese or English are semantically closed or not. This dissertation offers an exploration of truth, self-reference, and paradoxes, bridging philosophy and formal logic.