Date of Degree
Logic and Foundations of Mathematics | Philosophy
substructural logic, paradox, metainferences, validity, logic
This thesis consists of three papers on substructural approaches to semantic paradoxes. The first paper introduces a formal system, based on a nontransitive substructural logic, which has exactly the valid and antivalid inferences of classical logic at every level of (meta)inference, but which I argue is still not classical logic. In the second essay, I introduce infinite-premise versions of several semantic paradoxes, and show that noncontractive substructural approaches do not solve these paradoxes. In the third essay, I introduce an infinite metainferential hierarchy of validity curry paradoxes, and argue that providing a uniform solution to the paradoxes in this hierarchy makes substructural approaches less appealing. Together, the three essays in this thesis illustrate a problem for substructural approaches: substructural logics simply do not do everything that we need a logic to do, and so cannot solve semantic paradoxes in every context in which they appear. A new strategy, with a broader conception of what constitutes a uniform solution, is needed.
Porter, Brian C., "Three Essays on Substructural Approaches to Semantic Paradoxes" (2023). CUNY Academic Works.