My research project was undertaken as part of a larger project by Prof. Dirk Schlimm about documenting and studying the history and philosophy of notations in mathematics and logic. Particularly, my research aims to investigate how “dot notation” was developed and gradually replaced by other notations in 20th century logic. This notation was introduced by Peano in the 1890s and popularized in Whitehead and Russell’s groundbreaking Prinicipia Mathematica (1910-1913), which became the standard reference book in symbolic logic in the first half of the 20th century. I was tasked with conducting a literature review, synthesizing and recording the usage of dot notation on a) few logic textbooks published by Quine as an individual logician b) the Journals of Symbolic Logic as a logic community.
As a math and philosophy major, logic seems destined to attract me. I took Prof. Schlimm’s class and really enjoyed the magical feeling when I study into it. I’m an intrinsically deductive person, who tend to “collect some data” by experiencing firsthand about one direction I’d like to pursue, then make an informed decision. So I’d like to see first if I truly love it, and secondly what research about it is really like. But this direction is not that popular, also there is not that many opportunities, especially for undergraduate students. ARIA filled this gap for me, since it gave undergraduate students a chance to “get our hands wet” about research and be supervised by an expert in this field.
One of the main ideas that math and philosophy attracts me is, they both tend to describe the underlying principles and patterns of different entities in a deductive way. This magical connection portraits the most in their fundamental core: logic. My research was about notations, which the study of it is a category of “principles” about formats of how humans convey messages. Consequently, my learning objectives within this are twofold: a) Expand my knowledge about logic and notation beyond what I’ve learned in class, at the same time meta-think if my understanding about this field fits its intrinsic traits, b) immerse in firsthand research to see if I’d like to pursue this direction.
One interesting fact is, the most surprising moments of my research are all not directly related to the very content I’m looking for, instead they come as serendipities when I searched and read some articles as background knowledge. For example, I’ve learned Gödel’s Incompleteness Theorem in class, but I didn’t realize how complex and metatheoretical it was until I saw tons of articles published in the Journals discussed it (though not quite understand but at least I see how deep it could be, which really opens my eyes). Another thing highlights is that I saw how scholars interact and influence one another both academically and personally, and how they support each other during the war. Reading their biographies-like pieces let me know not only how academics progress, but also how they think and live as a mortal. We are all human beings, after all.
Sometimes understanding the texts is hard, due to my subject's metatheoretical nature. To understand a notation's advantages and disadvantages, I thought I must have understood their usage completely. Gradually I realized, this “perfectionism” stuck me and it’s really important to only focus on what matters the most. Just keep reading and thinking, sometimes just leave the unclear ones there, probably it would be naturally dissolved along the way. Moreover, I felt quite disappointed when couldn't find any resources useful at the beginning. This is one of the main difference I feel about being a student and being a researcher, since there is no longer a clear guide prepared for you to proceed, and no certain outcome is expected firmly, especially for an open-ended research like mine. It’s still acceptable that there is nothing useful within what you have searched, and this discovery is already something new since you kind of “clear an area” for future work. This answer freed me somewhat.
Finally, I’d like to thank Prof. Schlimm for supporting my research this summer. Your generous support and considerate guidance let me take my first step into research field that truly interests me. Under your supervision, my thinking style and working methods transformed a lot. Thanks for upfolding a new world of logic for me, and for this I’m especially grateful.
