Philosophy of Mathematics before 1900: An Early Manuscript by David Hilbert

Abstract I present and discuss an unknown early manuscript by David Hilbert, which bears witness both to now largely forgotten debates, as well as to the breadth of Hilbert’s knowledge of nineteenth-century philosophy: in it, Hilbert surveys a variety of criticisms of, and ultimately subscribes to (a version of), Kant’s philosophy of mathematics. I present a carefully documented conjecture concerning the time and context of composition, arguing that the manuscript is likely a draft of something like a term-paper written for a course taught by Günther Thiele in the Sommersemester 1885. (It incidentally contains one of the earliest documented engagements with Frege.) I also highlight one instance where Hilbert takes up a position from this manuscript later, thus showing that engagement with the philosophy of his time shaped Hilbert’s views on the nature and methodology of mathematics from the earliest stages of his career.