Jean-Yves Beziau

We analyse the behaviour of definite descriptions and proper names terms in mathematical logic. We show that in formal arithmetic, wether some axioms are fixed or not, proper names cannot be considered rigid designators and have the same behaviour as definite descriptions. In set theory, sometimes two names for the same object are introduced. It seems that this can be explained by the notion of meaning. The meaning of such proper names can be considered as fuzzy sets of equivalent co-designative definite descriptions and their references as sets of all equivalent co-designative definite descriptions

After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical pluralism, non-classical logics and cognitive science.