Philosophy of Mathematics Seminar (Monday - Week 2, TT26)

Abstract: The focus in this talk will be on the mathematical roots of Hilbert’s conservativity program, that is, the attempt at 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 what he called the “method of ideal elements” in mathematics.  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 argue that a closer comparison with different accounts of ideal elements, as discussed in synthetic projective geometry in the period in question, will allow us to reassess Hilbert’s instrumentalist leanings underlying his proof-theoretic program.

Registration: If you do not hold a University card which gives access to the upper floors of the Schwarzman Centre, please write to admin@philosophy.ox.ac.uk copied to daniel.isaacson@philosophy.ox.ac.uk at least two working days before a seminar to register your attendance.  

Please note: A notice will be sent out for each talk with the Zoom link.