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Buridan's Theory of Logical Consequence

In this thesis we develop a proof-theoretic formalization for John Buridan’s theory of modal propositions. This thesis provides a complete exegesis of the second chapter of De Consequentia and develops the system G3syl which we show is an adequate formalization of Buridan’s theory. Coming to the end of writing this thesis leaves me with far too many people I would like to thank. To my fellow students who helped deepen my understanding of logic and philosophy as well as keeping me sane throughout this process, you have my deepest thanks. I would like to especially thank, Hanne Berg, Lorenz Demey, David Fiske, Kian Mintz-Woo and Matthew Wampler-Doty. Their patience, willingness to help me and kindness cannot be repaid. Likewise, to the church community that essentially adopted me and helped me through my two years of living in the Netherlands, I want to offer my deepest thanks. I would like to especially thank: Jolanda Dane, Alastair and Sophie MacDonald, Matthijs van Engelen,Bert de Jong, Marco Klaue, and Thomas and Miriam Jones. Your friendship was a source of great encouragement to me. Special thanks go to my supervisor Catarina Dutilh-Novaes, who was a wonderful and patient guide through this entire writing process. Her constant wisdom and guidance was tremendous through this entire process, as was her patience for working through half a dozen different versions of the G3syl rule systems, often where the only difference was a change in the world label. I would like to thank Sara Uckelman for sparking my interest in medieval logic and supervising two of the January projects on various historical topics in logic. I owe a profound debt of gratitude to Stephen Read, my current PhD supervisor in St. Andrews, for providing me with a draft of his excellent translation of Buridan’s De Consequentia. I would like to thank Dick de Jongh for his mentoring of me for my time with the ILLC. In addition I would like to thank him and Benedikt Lwe for sitting on my thesis committee. I am very grateful and pleased to thank the University of Amsterdam for the financial support they provided for me during my two years in Amsterdam. I would never have become interested in Logic if it had not been for the encouragement of my philosophy professors during my undergraduate. I would like to particularly thank Dr. Davis for introducing me to symbolic logic, encouraging my study of logic and introducing me to modal logic. I would like to thank Dr. Weed for encouraging me to study at the ILLC. I would also like to thank Dr. Urqhart for introducing me to meta-logic, and allowing me to attempt the graduate level logic course at the University of Toronto. Finally, I would like to thank my parents, Gordon and Charlene Johnston, whose constant love, encouragement and support for me has been amazing and a source of great strength to me. It is to them I dedicate this thesis. Fides quaerens intellectum.