"History of Logic" Seminar Series - Talk: G. Schiemer, "Hilbert’s program and the status of ideal elements in nineteenth-century geometry" (06.03.2025)

[antpic...@gmail.com]

Dear all,

I am happy to announce the fifth session of our History of Logic seminar series. The session will be held on Thursday, March 6, from 3 pm to 5 pm (CET).

The session will be held in hybrid form. We will meet at the Battaglia Library Hall of the Department of Humanities of the University of Naples Federico II (Stairs B, Third Floor - Maps). It will be broadcast via Zoom. To have the Zoom link, please subscribe to the mailing list of the Seminar, by writing at the addresses indicated here.

On this occasion, we will host a talk by Georg Schiemer, Professor at the Department of Philosophy and Head of the Department of the Institute Vienna Circle, University of Vienna.  He is also an external fellow at the Munich Center for Mathematical Philosophy at LMU Munich. His research focuses on the history and philosophy of mathematics and early analytic philosophy. He is also interested in the history and philosophy of logic and formal philosophy of science. Among his many research works on these topics, I would like to mention here the volume The Prehistory of Mathematical Structuralism (co-edited with Erich Reck, Oxford University Press 2020), the SEP entry Structuralism in the philosophy of mathematics (with Erich Reck), and the paper on Non-standard logicism (in Uebel, T. (Ed.), The Handbook of Logical Empiricism, Routledge 2021) - all essential inspirations for elaborating the conceptual framework of our seminar series.

His talk is titled Hilbert’s program and the status of ideal elements in nineteenth-century geometry. Here is a short 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.

More information can be found on our website.

Do not hesitate to contact historyofl...@gmail.com for any questions you might have. Please feel free to share the news and invite other scholars to subscribe to this mailing list.

Kind regards,

Antonio Piccolomini d'Aragona