CALL FOR APPLICATIONS

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

georg.schiemer@univie.ac.at

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.