This summer, I worked on an ARIA research project titled “Early Wittgenstein on Notations” under the supervision of Professor Dirk Schlimm. As part of Professor Schlimm’s broader focus on the history and philosophy of mathematical and logical notations, my project centered on the philosopher Ludwig Wittgenstein’s philosophy as it pertains to the status and nature of logical notations—particularly in his Tractatus Logico-Philosophicus (1921). In essence, the project hinges on the question of “what does Wittgenstein say about notations?” and provides an answer to said question while also evaluating his positions. By the end of the summer, I produced a c. 30-page paper, alongside the ARIA-required poster.
I was drawn to this project due to my broader interest in the history and philosophy of logic, as well as my interest in my professor’s work on notations. Given that the philosophy curriculum at 51łÔąĎÍřoffers relatively little exposure to the philosophy of logic beyond introductory courses and lacks a specific class on Wittgenstein’s philosophy, my professor and I agreed that this topic would provide me with a unique opportunity to learn and engage with this interesting subset of philosophy.
The learning objective was twofold: first, the goal was to gain a deeper understanding of Wittgenstein's philosophy as it pertains to syntactical analysis and notations, more broadly. Secondly, this summer research was intended to provide me with the basis to pursue further, publishable research. The focus on Wittgenstein is key, as academia is particularly concerned with his work, which in turn places my research at the center of an active, routinely publishing field of philosophy.
Highlights include pursuing various, fun tangents that I discovered while working on the project. Three examples include:
(1) Learning parsing algorithms in the context of computational linguistics in a (half-successful) attempt to construct parsers for the Tractatus’s notations in order to analyze their computational complexity.
(2) Reading about the application of Tractarian logical methods in American constitutional law by analyzing “meaningless expression” in the context of free speech.
(3) Going to the Library of Congress in Washington D.C. to get a rare copy of the Principia Mathematica from the 1910s during the literature review phase of my project!
The key challenge of this project was working with Wittgenstein’s work. As a philosopher, Wittgenstein was well known for being highly cryptic and non-substantive in his remarks, and often reading his excerpts resulted in zero understanding at all. This was a major hindrance, as it took me over two months to fully work through the Tractatus, despite the work being only around 70 pages long. To overcome this, I adopted a new strategy by focusing more on secondary material, which provided plain-language explanations of the key ideas, allowing me to refocus on the more nuanced aspects of Wittgenstein’s claims. Moreover, there were sometimes knowledge gaps; some of the literature I reviewed presumed a relatively advanced level of theoretical computer science and mathematical background, which required me to spend more time understanding examples and illustrations that utilized these topics.
ARIA is already demonstrably impacting my future path. After my summer research, my professor and I agreed to continue our partnership into the school year, where we will continue Wittgenstein-relevant research in the field of philosophy of logic and notation. The goal is to co-author a paper and submit it to journals and conferences, to secure publication. More generally, I think this summer has been instructive in showing me what research in philosophy looks like.Â
The funding provided by ARIA was particularly important in helping me support myself over the summer. I would like to thank the generous donor for the Undergraduate Experiential Learning Support Fund. Had ARIA funding not helped me with the cost of rent, groceries, and other everyday expenses, I wouldn’t have been able to dedicate time to this interesting research project instead of working another job.
