11 de marzo de 2017

PhD and Postdoc position in ERC Project “The Roots of Mathematical Structuralism“, University of Vienna

The Department of Philosophy at the University of Vienna is inviting applications for the positions of a PhD candidate (100%, 3 years) and a postdoctoral researcher (100%, 2 years) in the areas of history and philosophy of mathematics within the ERC Starting Grant project “The Roots of Mathematical Structuralism“ (2017-2022). The project is led by Principal Investigator Georg Schiemer, Assistant Professor at the Department of Philosophy. 

(A second postdoctoral position and a second PhD position related to the ERC project will be advertised in 2019 and 2020 respectively.)


Project Description:

The project will investigate the mathematical and philosophical roots of mathematical structuralism. It will focus on several historical developments in nineteenth century mathematics and early twentieth century philosophy: the first one concerns several conceptual changes in geometry between 1860 and 1910 that eventually led to a “structural turn” in the field. This includes the gradual implementation of model-theoretic techniques in geometrical reasoning, the study of geometrical theories by group-theoretic methods as well as the successive consolidation of formal axiomatics. The second development considered here concerns the beginnings of the philosophical reflection on structural mathematics between 1900 and 1940. This includes different attempts by thinkers such as Rudolf Carnap, Edmund Husserl, and Ernst Cassirer (among others) to spell out the philosophical implications of the new structuralist methodologies at work in modern geometry. The principal objective of the project is to provide a first comparative investigation of these early contributions to structuralism and of their immediate mathematical background. The second aim of the project is to connect these early contributions with more recent debates on mathematical structuralism. Specifically, the project will provide new systematic insights relevant to contemporary structuralism, in particular a new understanding of notions such as mathematical structure, structural abstraction, and structural properties, as well as of their significance for the philosophy of mathematical practice. 
The PhD candidate and the postdoctoral candidate will both work within the subprojects “Geometrical Roots“ and “Early Mathematical Structuralism“ and will be expected to carry out research relevant for the general aims of the ERC project. Specifically, the candidates will focus on either one of the following topics: early model theoretic reasoning in nineteenth-century geometry,  the rise of formal axiomatics and of “structural” mathematics, Klein’s Erlangen Program and related group-theoretic methods in geometry, as well as early philosophical contributions by Cassirer, Husserl, and Carnap to mathematical structuralism. 

The PhD candidate will carry out research on one of these topics (or on a related topic) with the aim of publishing a doctoral thesis under the supervision of Prof. Georg Schiemer. Both candidates are expected to present the results of their research in peer-reviewed journals and at international conferences. They are also expected to assist in the organization of workshops and/or conferences. The positions come without teaching obligations. No German language competency is required.

Requirements:
The successful candidates will have a PhD (for the Postdoctoral position) or a Master’s degree (for a PhD-student position) in philosophy and/or mathematics, respectively. If the PhD applicant does not have a Master’s degree, the applicant can submit a letter by the university confirming that the MA thesis has been submitted.

Successful candidates for both positions will have demonstrable competence in the history or philosophy of mathematics. The postdoctoral candidate is expected to have contributions in peer-reviewed journals and to show a strong research profile in one of the areas studied in the project.


Applications:

Applications (including CV, certificates, list of publications), a description of planned research (500-1000 words), as well as a writing sample should be sent by email to


The deadline for applications is April 10, 2017. The starting date for both positions is June 1, 2017 (a later starting date is possible in exceptional cases).

For further questions please contact Georg Schiemer.