About My Studies
Many businesses hire consultants to examine various programs to determine if they are doing what they claim to be doing, doing these tasks efficiently and effectively. Likewise, my studies in logic run similar analytics on the formal systems adopted by various disciplines. Often times, logic is brought up in a class under the context of "This is not a logic class, per se, but our discipline uses logic to better understand a concept in our field." I designed my major to learn what it means to solve a problem, or if the methods we had to solve problems were effective. Originally, I wondered what it meant to solve a problem, and what the limits of the capabilities we had were. As I have gotten deeper into my studies, these questions have become more focused, but I have not necessarily found answers. Rather than deterring me from the content, this has increased my interest in topics I accidentally stumbled upon in an introductory philosophy course my freshman year, which happened to be my first logic course.
I designed my curriculum with the help of two professors, Andreas Blass in the mathematics department and James Tappenden in the philosophy department. I originally saw logic as a spectrum from the most formal, mathematical logic to the less formal arguments of natural language, but more recently my studies have explored the connections among language, mathematics, and philosophy, in order to better understand how we formally solve problems. When I first took my intro logic courses, I liked the puzzles and the mechanics of deriving complex formulae with different sets of axioms. However, in upper-level classes, I realized that even the most basic ways we reason raised important questions and demanded further explanation. For instance, Robert Stalnaker provided solutions to the many counterexamples to transitivity in conditionals, which highlighted the necessity of differentiating approaches to mathematics versus natural language parsing. In math, you can have a scenario in which a situation A implies B, and that situation B implies C, and it is perfectly valid to conclude that situation A implies situation C. But for language, this breaks down in instances where people are speaking about events that did not happen or will possibly happen in the future. My own research thus far has interacted with Stalnakerian views of context sets, which are responsible for this breakdown of transitivity in natural language, but I apply them to models that philosophers have used to examine the relation between language and belief. I hope to expand my research and knowledge starting this fall by attending Carnegie Mellon University's M.S. program in Logic, Computation, and Methodology.