27.11.2024

Institutskolloquium: "Hilbert's Program and the Status of Ideal Elements"

Dozent: Prof. Dr. Georg Schiemer (Wien); Zeit und Ort: Mittwoch, 27.11.24, 18 Uhr, Raum X, Alte Burse

Abstract: 
The focus in this talk will be on the mathematical roots of Hilbert’s conservativity program, i.e., the attempt of showing the conservativity of ideal over real mathematics. It is well-known that Hilbert's foundational work from the 1920s and 1930s was strongly influenced by preceding developments in nineteenth-century mathematics. Specifically, his program was clearly inspired by the "method of ideal methods“ in mathematics (cf. Hilbert 1926, 1928). In the present talk, I will argue that Hilbert’s discussion of the usefulness and eliminability of “ideal constructs” in his proof-theoretic work was directly motivated by a particular understanding of ideal elements in nineteenth-century projective geometry. Moreover, I will show that a closer comparison with different accounts of ideal elements, as discussed by different synthetic geometers at the period in question, will allow us to reassess Hilbert’s reductive instrumentalism underling his proof-theoretic program.