Moritz Bodner Ph.D.
September 1, 2023 until February 29, 2024
Affiliation:
Research for a study about:
Felix Kaufmann's Philosophy of Mathematics and its Aftermath
My time as research fellow at the IVC shall be devoted to Felix Kaufmann. In particular, I will study two phases in Kaufmann's exceptionally varied career: first, the period leading up to the publication of Kaufmann's 1930 book The Infinite in Mathematics and its Elimination, which, although conceived and written while Kaufmann was a regular and active participant in meetings of the Vienna Circle, differs in key respects from what its key protagonists would probably have said -- and did indeed say, albeit only later -- about mathematics; a principal point of difference is Kaufmann's rejection of empiricism in favour of Husserl's phenomenological framework. Second, I will study Kaufmann's transition during his final years (spent in exile in the USA) to becoming a follower of Dewey, seemingly effected mainly by a lengthy correspondence with A. F. Bentley which began as an exchange about their respective views -- and books -- about mathematics. In both connections, I aim to take into account also unpublished manuscripts and letters from Kaufmann's Nachlass as well as that of Carnap, Ernest Nagel and A.F. Bentley.
Lecture
Felix Kaufmann's philosophy of mathematics in the context of the Vienna Circle
Philosophy of Science Colloquium
Date: 02/11/2023
Time: 15h00
Venue: New Institute Building (NIG), Universitätsstraße 7, 1010 Wien, SR 2H
Abstract:
Felix Kaufmann was the first figure within the vicinity of the Vienna Circle to devote a whole monograph to the philosophy of mathematics. The result, Kaufmann's The Infinite in Mathematics and its Elimination (1930), however, is surprisingly out of line with the Vienna Circle: In it Kaufmann articulates a defense of Brouwerian Intuitionism on the basis of Husserl's phenomenology. Unpublished documents and letters further underscore these differences, showing Kaufmann, e.g., explicitly request not to be included in the list of "affiliated authors" in the 1929 brochure on Wissenschaftliche Weltauffassung (in a letter to Carnap) because he did not think of himself as sharing the empiricism championed there. My aim is to reconstruct how Kaufmann came to write his book and why he adopted the position he articulates in it, then compare and contrast Kaufmann's views to those other members of the Vienna Circle expressed either later on in print (such as Waismann or Carnap) or mainly in lectures (such as Schlick). Finally, I will take my survey of these different approaches as an opportunity to reflect on the general question what one could, and should, expect from a philosophy of mathematics.
Lecture
Sociologist dips into the Foundations of Mathematics: The Case of A.F. Bentley
Logik Café Lecture
Date: Janury 22, 2024
Time: 16h45 - 18h15
Meetings are usually held on Mondays from 16:45 to 18:15 in Raum 3F (D0313), 3. floor Department of Philosophy
Abstract:
In 1923 the American sociologist Arthur F. Bentley became interested in the work of LEJ Brouwer, whose methodological principle that "the possibility of [further] interpolation must [always] be assumed" Bentley found greatly congenial. From then on until 1932, when he published his subsequent studies in book-form as The Linguistic Analysis of Mathematics, Bentley corresponded and met with many prominent mathematicians of the day, including Brouwer himself, Hermann Weyl and Karl Menger (among others). The position Bentley eventually articulate amounts to a rejection of the very project of providing foundations for mathematics, which he came to see as an effort to provide definite answers where none were available (or, indeed, called for). My aim in this presentation is twofold: First, to illustrate the breadth of Bentley's engagement with the mathematical community during the 1920s, as documented in unpublished letters I have found and studied at various archives; and, second, to present Bentley's position as a typical example of a pragmatist's approach to (the foundations of) mathematics.
Report
Although Felix Kaufmann wrote Über das Unendliche in der Mathematik und seine Ausschaltung (1930) while being an active member of the Vienna Circle, the philosophy of mathematics he presents in this book turns out – upon closer inspection, which my time as a fellow of the Institute Vienna Circle has mainly been dedicated to –, to be out of line with the philosophical standpoint of the Vienna Circle. (Indeed, Kaufmann saw himself as an outlier, asking (in a letter to Carnap dated June 24 1929) to have his name removed from the list of authors “affiliated” with the “Scientific Worldview” of the Vienna Circle, among whom Kaufmann had originally been included; and did so on account of substantive philosophical disagreements.) What set Kaufmann apart from the other members of the Vienna Circle was his sympathy for the approach and doctrines of Husserl’s phenomenology, on which also Kaufmann’s 1930 book is to a significant extent based. Kaufmann’s appreciation of Husserl’s work was likely imparted on Kaufmann by the other Circle he chiefly belonged to: that surrounding Hans Kelsen, who held Husserl in high regard. (Kaufmann, however, seems to have read and made use of Husserl’s work more keenly and fully than Kelsen did.) Comparing in substance Kaufmann’s book on mathematics to what other members of the Vienna Circle either then or later wrote about mathematics shows that, unlike, for example, Waismann, Kaufmann was happy to not only analyse and clarify mathematical theories, but also to impose philosophically motivated restrictions on them.