RUB Research School

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Author
Name Berwe, Theodor
Research field Philosophy of Mathematics
Career stage doctoral researcher
Home university/institution Ruhr-Universität Bochum (RUB)
Department/Research unit at home university/institution Philosophy and Educational Research
Chair/Working group at home institution Lehrstuhl für Wissenschaftstheorie und Wissenschaftsgeschichte

International activity
Country United States
Location Austin, Texas
University University of Texas at Austin
Fund Research School PR.INT
Type of activity research stay
Period starts 15-01-2024
ends 21-04-2024
Keywords Kant, Philosophy of Mathematics
Report I completed a three-month research stay at the University of Texas at Austin in this PR.INT. The aim of this stay was to complete a core part of my dissertation on the history of genetic definition in the early modern period: Namely, the part on Immanuel Kant.
Kant takes a key role in my project because he rigorously rejects the transfer of genetic definitions to domains outside of mathematics. He bases this rejection on a novel understanding of genetic definition, which he develops in the course of his philosophical re-foundation of mathematics in the Critique of Pure Reason. In this way, Kant arrives at a new view on the construction that underlies the genetic definition (e.g. the construction of rotating a straight line around a center). Kant assumes that such a construction can only take place in what he calls intuition. According to Kant, such a form of construction in intuition is only possible in the case of mathematical concepts and therefore impossible outside of mathematics (e.g. in metaphysics).
Research on Kant's philosophy of mathematics has been heavily influenced by U.S. scholars in recent years (cf. Friedman 2012, Dunlop 2014, Posy & Rechter 2020, Sutherland 2021). It was therefore only natural to combine my own investigation of Kant with a research stay at an American university. The University of Texas at Austin offered ideal conditions for this, not only because it has an excellent Department of Philosophy, but above all because my host Prof. Katherine Dunlop is a renowned expert on the philosophy of mathematics in the 18th century. Prof. Dunlop has written extensively on Kant's understanding of mathematics in numerous publications (e.g. Dunlop 2012; 2014) and has worked in particular on Kant's theory of definition (2005).
I have benefited from the research stay in Austin in two ways: First, I had an intensive exchange of thoughts on Kant's understanding of genetic definitions. For this purpose, Prof. Dunlop was the ideal host and discussion partner. In addition, I was able to present my own view on Kant in the department’s research colloquium and to make my project known to a wider field of researchers.
Second, I spent my time in Austin completing two chapters of my dissertation. First, the chapter on Kant, for which I could make use of the feedback from my exchange with Prof. Dunlop and other scholars for this purpose. Second, I also wrote a chapter on Johann Heinrich Lambert. Lambert has strongly influenced Kant but comes to a completely different conclusion about the possibility of genetic definitions outside of mathematics. Prof. Dunlop has also made crucial research contributions on Lambert's philosophy of mathematics (Dunlop 2007), so I could benefit greatly from an exchange with her in this regard as well.
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