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.