This fall the Department of Philosophy welcomed professor Paul Tran-Hoang to our faculty as an assistant professor. Previously, he was a visiting assistant professor at Vassar College. Tran-Hoang's research focuses on logic, philosophy of logic, and philosophy of mathematics. He's also interested in the history of science and 19th and 20th century philosophy. Read on for a Q&A to learn more about his research.
What are your research interests and why are you passionate about these areas of study?
Much of my research interests are in the philosophy of mathematics and logic. In particular, I am interested in questions concerning the nature of mathematical truth and mathematical knowledge. Mathematics is philosophically puzzling for a variety of reasons: the truths of mathematics seem to be such that they couldn’t be otherwise, mathematical truths are knowable without appealing to sense experience, and mathematical objects, such as numbers, don’t seem like the kind of things we can encounter in physical reality. A lot of my work seeks to make sense of these puzzling features of mathematics by incorporating insights from formal logic and by considering how mathematics has developed historically.
I first became passionate about the philosophy of mathematics and logic when I was an undergraduate student at UC Irvine. I initially started as a math major, but once I took my first philosophy class, I was immediately hooked, and shortly thereafter, I declared a second major in philosophy. As luck would have it, UC Irvine was the perfect place to develop an interest in philosophy of mathematics and logic. UC Irvine is well-known for having a dedicated Logic and Philosophy of Science department, where I took many of my major courses. For my PhD, I decided to go to the University of Notre Dame, which, like UC Irvine, has a large and thriving philosophy of mathematics and logic community.
Why did you decide to join the Department of Philosophy at the University of Illinois?
I decided to join the Department of Philosophy at the University of Illinois because of its faculty and its existing research strengths in mathematical philosophy. When I interviewed, I received some of the most engaged and probing feedback on my research that I had ever received. I was also very excited about how the department had been undergoing so much growth over the past few years. In light of all of this, I felt that the Philosophy department at University of Illinois would be the perfect place for someone like me to thrive.
What research projects are you working on right now?
I am currently focusing on two research projects. The first concerns a view in the philosophy of mathematics known as logicism, which was pursued by various philosophers in the 19th century. According to logicism, our knowledge of mathematics ultimately stems from our knowledge of logic. However, due to a number of philosophical and technical reasons, logicism is widely regarded as untenable. My project aims to articulate and defend a novel approach to thinking about logicism that is informed by recent work in a field of mathematical logic known as model theory. As a result, this work seeks to shed light on how modern developments in mathematics can be brought to bear on traditional philosophical questions.
My second project examines the relationship between the philosophical movement known as phenomenology and developments in physics and mathematics at the turn of the 20th century. Broadly, phenomenology is a philosophical methodology that examines what is given in experience as it is experienced from the first-person perspective. This project examines how ideas from physics and scientific-philosophy informed the ideas of the 20th century German philosopher Martin Heidegger.
What classes will you teach?
This academic year I am scheduled to teach undergraduate classes on formal logic, the philosophy of language, and connections between philosophy and formal logic. I am also currently teaching a first graduate seminar on the philosophy of logic. It has been such a delight getting to know both the undergraduate and graduate students at the University of Illinois. In the future, I hope to teach classes on Asian philosophy, 20th century philosophy, and the philosophy of mathematics.
What key ideas or lessons do you hope to impart to your students?
An important lesson I try to instill in my students is how philosophy can benefit from engaging with other disciplines, especially, the mathematical sciences. Some of the greatest philosophers in history such as Descartes, Leibniz, and Newton were also some of the most innovative scientists. I also try to instill in my students an appreciation of the multicultural nature of philosophy. My goal is to demonstrate to students that philosophy can be successfully practiced by anyone regardless of their cultural or socio-economic background. To achieve this, I make sure to forefront thinkers from underrepresented backgrounds and traditions alongside Western ones.