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What are the limits of mathematical explanation? An interview with David Charles McCarty

Professor David Charles McCarty interviewed by Piotr Urbańczyk. Professor McCarty conducts research on the foundations of mathematics and logic, early analytical philosophy, and on the history of mathematics and logic, especially the late 19th and early 20th Centuries. Concerning the foundations of mathematics and logic, he has published on intuitionism, antirealism, realizability, potentially infinite sets, denotational semantics, Church's Thesis, Markov's Principle, and the completeness problem for intuitionistic logic. In the area of history, he has written on Wittgenstein, Carnap, Frege, Hilbert, Brouwer, Dedekind, du Bois-Reymond and on the "Ignorabimus" controversy. In addition to his work in logic and the philosophy of mathematics, McCarty maintains broad interests in and has taught courses on 19th Century German philosophy, cognitive science, philosophy of language, political philosophy, metaethics and aesthetics. To date, he has supervised or is supervising Ph.D. dissertations on such topics as philosophy of language in Wittgenstein's middle period, formal logics that prove their own completeness theorems, Church's Thesis and the philosophy of mind, contemporary metaethics, and the philosophy of mathematics in Wittgenstein's "Tractatus."