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STRUCTURALISM SIGNED

The Roots of Mathematical Structuralism

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Project "STRUCTURALISM" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITAT WIEN 

Organization address
address: UNIVERSITATSRING 1
city: WIEN
postcode: 1010
website: www.univie.ac.at

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Austria [AT]
 Project website https://structuralism.phl.univie.ac.at/
 Total cost 1˙364˙097 €
 EC max contribution 1˙364˙097 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-03-01   to  2022-02-28

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAT WIEN AT (WIEN) coordinator 1˙364˙097.00

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 Project objective

Mathematical structuralism is a central position in contemporary philosophy of mathematics. It is the view that mathematical theories describe only abstract structures or structural properties of their subject fields. This project will investigate the mathematical and philosophical roots of structuralism in a ground-breaking way. The focus will be set on two historical developments in nineteenth century mathematics and early twentieth century philosophy of science: 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 analyzed 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 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 the first comparative investigation of these early contributions to structuralism and their immediate mathematical background. The integrative study of the history and the philosophy of modern mathematics will not only change our conception of the evolution of the philosophy of mathematics in the twentieth century. It will also transform the ways in which we presently think about mathematics. Specifically, the project will provide new systematic insights relevant to contemporary structuralism, in particular a new understanding of notions such as mathematical structure, structure abstraction, and structural property, as well as of their significance for the philosophy of mathematical practice.

 Publications

year authors and title journal last update
List of publications.
2020 Georg Schiemer (University of Vienna) and Erich Reck (University of California, Riverside)
Structuralism in the Philosophy of Mathematics
published pages: , ISSN: 1095-5054, DOI:
The Stanford Encyclopedia of Philosophy online: First published Mon Nov 2020-04-15
2020 Francesca Biagioli
Ernst Cassirer\'s transcendental account of mathematical reasoning
published pages: 30-40, ISSN: 0039-3681, DOI: 10.1016/j.shpsa.2019.10.001
Studies in History and Philosophy of Science Part A Volume 79, February 2020 2020-04-15
2019 John Wigglesworth
Individuating Logics: A Category‐Theoretic Approach
published pages: 200-208, ISSN: 2161-2234, DOI: 10.1002/tht3.425
Thought: A Journal of Philosophy 8/3 2019-10-31
2018 Francesca Biagioli
Articulating Space in Terms of Transformation Groups: Helmholtz and Cassirer
published pages: , ISSN: 2159-0303, DOI: 10.15173/jhap.v6i3.3436
Journal for the History of Analytical Philosophy 6/3 2019-06-13
2018 Georg Schiemer, John Wigglesworth
The Structuralist Thesis Reconsidered
published pages: , ISSN: 0007-0882, DOI: 10.1093/bjps/axy004
The British Journal for the Philosophy of Science 2019-06-13
2018 Georg Schiemer
Cassirer and the Structural Turn in Modern Geometry
published pages: , ISSN: 2159-0303, DOI: 10.15173/jhap.v6i3.3439
Journal for the History of Analytical Philosophy 6/3 2019-06-13
2017 Johannes Korbmacher, Georg Schiemer
What Are Structural Properties?†
published pages: 1-29, ISSN: 0031-8019, DOI: 10.1093/philmat/nkx011
Philosophia Mathematica 27. June 2017 2019-06-13
2018 John Wigglesworth
Mathematical Philosophy
published pages: 22-23, ISSN: 1757-0522, DOI:
The Reasoner Volume 12, Number 4 – April 2018 2019-06-13
2018 John Wigglesworth
Bi-Modal Naive Set Theory
published pages: 139, ISSN: 1448-5052, DOI: 10.26686/ajl.v15i2.4859
The Australasian Journal of Logic 15/2 2019-05-14
2018 John Wigglesworth
Non-eliminative Structuralism, Fregean Abstraction, and Non-rigid Structures
published pages: 1-15, ISSN: 0165-0106, DOI: 10.1007/s10670-018-0096-3
Erkenntnis 2019-05-14

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