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February 2025 (Timetable slot is just a placeholder! Please see eCampus for updates on the time.)
In this course, we provide an overview of the (historical) foundations of logic and mathematics, starting from the era of Russell, Hilbert and Brouwer. We aim for an understanding of the associated foundational philosophies (intuitionism, finitism, predicativism) along with a hint at the underlying mathematics and logic. The (rather direct) connection to Turing’s computability theory and Goedel’s incompleteness theorems is discussed. An outgrowth of all the aforementioned is the (more philosophically neutral) program of ‘reverse mathematics’. We introduce the latter, discuss some examples, and provide a detailed study of recent applications in the philosophy of mathematics.