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STRUCTURALISM SIGNED

The Roots of Mathematical Structuralism

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

STRUCTURALISM project word cloud

Explore the words cloud of the STRUCTURALISM project. It provides you a very rough idea of what is the project "STRUCTURALISM" about.

gradual attempts 1860 1940 century theories property abstract carnap notions structure historical cassirer thinkers science 1900 view investigation evolution describe geometry techniques philosophy formal systematic mathematical history edmund central 1910 significance ways theoretic conceptual consolidation model structures modern first breaking philosophical mathematics abstraction subject contemporary twentieth structuralism reflection integrative position ground think led nineteenth principal group transform contributions turn ernst axiomatics background rudolf structuralist presently roots successive conception geometrical implications insights structural spell husserl reasoning beginnings

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 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.	AT (WIEN)	coordinator	1˙364˙097.00

Map

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

List of publications.
year	authors and title	journal	last update
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 Categoryâ€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?â€ 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 â€“ 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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