The Logic and Metaphysics Workshop will meet on September 22nd from 2:00-4:00 in-person at the Graduate Center (Room TBA) for a talk by Fernando Cano-Jorge (Otago).

Title: The heresies project

Abstract: In the late 90’s, Richard Sylvan and Jack Copeland advanced the idea that computability is logic relative and that the Church-Turing thesis is false. Sylvan called this The Heresies Project and at its core is the idea that couching computability theory on a paraconsistent logic can take us beyond the classically computable. In the first part of this talk, I provide a brief introduction to paraconsistent computability theory, distinguishing non-revisionary approaches vs. Sylvan and Copeland’s more radical proposal. In the second part of this talk, I discuss what is required to pursue The Heresies Project. I will focus on Robinson arithmetic based on Sylvan’s preferred logic, DK, and its ability to both represent all recursive functions and prove Gödel’s first incompleteness theorem. I conclude that one of the keys to The Heresies Project, i.e. using an inconsistent metatheory, seems to clash with the arithmetic’s capacity to capture all recursive functions.