Varieties of Mathematical Abstraction

01.08.2018 - 03.08.2018

Neues Institutsgebäude (NIG), 3rd Floor, Room 3D | Universitätsstraße 7, 1010 Vienna

International Conference "Varieties of Mathematical Abstraction"

Department of Philosophy (NIG, 3rd floor at seminar room 3D)

University of Vienna, August 1-3, 2018



About the conference:

Mathematical abstraction is a general phenomenon, one that comes in several different varieties.  Different forms of abstraction contribute to the characterization of mathematical structures and the development of mathematical theories. Mathematical abstraction also plays an important role in shaping how we think about and understand empirical phenomena.  It is a process by which we generalize from the properties and relations of particular objects to the abstract, mathematical structure that those objects exhibit.  It is a process that can be iterated to achieve higher levels of abstraction. The main objective of this conference is to explore the philosophical significance of mathematical abstraction from different perspectives: metaphysically, epistemologically, historically, and practically.  Particular attention will be devoted to the role of abstraction in mathematical practice.  Specifically, the following research topics will be addressed:

- Abstraction in mathematical practice

- Abstraction in the sciences

- Definition by abstraction

- Fregean abstraction principles 

- Historical discussion of any of the above




The conference location is seminar room 3D (3rd floor) in the Neues Institutsgebäude (NIG) of the University of Vienna, Universitätsstraße 7, 1010 Vienna.



Participation Cost:

Free admission. Everybody is welcome.


Day 1  Wednesday | August 1, 2018

9:00 (s.t.) – 9:15         Opening

9:15 – 10:15   Øystein Linnebo (Universitetet i Oslo, NOR) "Abstraction and Grounding“

10:15 – 10:30 Tea/Coffee                 

10:30 – 12:30 Francesca Boccuni (Università Vita-Salute San Raffaele, ITA) and Marco Panza (Université Paris 1 - Panthéon-Sorbonne, FRA / Chapman University, USA) "Abstraction for Real(s)! Frege’s Theory of Real Numbers“

12:30 – 14:30 Lunch

14:30 – 15:30 Paolo Mancosu (UC Berkeley, USA) "Neologicist Foundations: Inconsistent Abstraction Principles  and Part-Whole“

15:30 – 15:45 Tea/Coffee                 

15:45 – 16:45 Maria Paola Sforza Fogliani (IUSS Pavia, ITA) and Luca Zanetti (IUSS Pavia, ITA) "For Better and for Worse: Abstractionism, Good Company, and Pluralism“


Day 2  Thursday | August 2, 2018

9:00 – 10:00   Elaine Landry (UC Davis, USA) "Mathematics Is Not Metaphysics“

10:00 – 10:15 Tea/Coffee                 

10:15 – 11:15 Sam Roberts (Universitetet i Oslo, NOR) "Property Abstraction, Potentialism, and Truth“

11:15 – 12:15 John Wigglesworth (University of Vienna, AUT) "Modal Semantics for Structural Abstraction“

12:15 – 14:15 Lunch

14:15 – 15:15 Robert Knowles (University of Leeds, GB) "’Explanatory' Mathematical Abstraction in Science“

15:15 – 15:30 Tea/Coffee                 

15:30 – 16:30 Bahram Assadian (University of Amsterdam, NL) "Structure Abstraction and Pure Structures“


Day 3  Friday | August 3, 2018

9:00 – 10:00   Hourya Benis Sinaceur (Université Paris 1 - Panthéon-Sorbonne, FRA) "Facets and Levels of Mathematical Abstraction"

10:00 – 10:15 Tea/Coffee                 

10:15 – 11:15 Erich Reck (UC Riverside, USA) "Abstraction and Abstractionism in the Nineteenth Century“

11:15 – 12:15 Henning Heller (University of Vienna, AUT) "Groups without Elements“

12:15 – 14:15 Lunch

14:15 – 15:15 Ansten Klev (Filosofický ústav Akademie ved Ceské republiky, CZ) "Definition by Abstraction from the Point of View of Martin-Löf Type Theory"

15:15 – 15:30 Tea/Coffee                 

15:30 – 16:30 Jean-Pierre Marquis (Université de Montréal, CAN) "A Concrete Take on the Abstract Method in Mathematics“


More Information:

For more information about the conference, please visit our website:



To register, please send an e-mail to our project administrator:

Deadline for registration: July 20, 2018



Georg Schiemer, Francesca Biagioli and John Wigglesworth

University of Vienna, Department of Philosophy

ERC Starting Grant Project “The Roots of Mathematical Structuralism”, Project Nr. 715222.


This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 715222).

The conference is thematically connected to the event “Workshop on Frege’s logic”, which will be held in Prague July 30th, 2018, Institute of Philosophy, Czech Academy of Sciences, AKC - Husova 4a 110 00, Prague, Czech Republic.