CfP TC Synthese - Linguistically Informed Philosophy of Mathematics - March 15, 2022

[Deniz Sarikaya]

Call for Papers: Topical Collection of Synthese

Title: Linguistically Informed Philosophy of Mathematics: How the  
study of mathematical texts contributes to the investigation of  
philosophical problems

Guest Editors: Bernhard Fisseni (University of Duisburg-Essen),  
Deborah Kant (University of Konstanz), Deniz Sarikaya (University of  
Hamburg) and Bernhard Schröder (University of Duisburg-Essen)

See also: https://www.springer.com/journal/11229/updates/19385258


Text is a crucial medium for transferring mathematical ideas, agendas,  
and results within the scientific community and in educational  
contexts. This makes the focus on mathematical texts a natural and  
important part of the philosophical study of mathematics. Moreover,  
research on mathematical texts can take advantage of the huge body of  
knowledge and toolbox of methods from other disciplines such as  
linguistics and computer science to investigate problems in the  
philosophy of mathematics. Linguistically informed research addresses  
general questions of the philosophy of mathematics. Among those  
philosophical questions are the following, including methodological  
reflections on this approach.

- What are mathematical proofs, and which role does their textual  
representation play for mathematical communication and theorizing?
- What is mathematical explanation of mathematical facts and how is it  
valued by mathematicians?
- How have mathematical concepts developed historically? For instance,  
how does the concept of a plane in Euclid differ from a modern  
geometric approach?
- What is the role of metaphor in mathematical practice?
- How do argumentative foundations change historically?
- How are mathematical objects conceptualized: is there a difference  
between formal and textual approaches?
- (How) Do tools like LaTeX, blogs, and forums influence mathematical  
practice? For instance, have LaTeX environments strengthened the  
tendency to typeset proof structure more explicitly?

This topical collection aims to bring together and build bridges  
between researchers from different methodological backgrounds to  
tackle questions concerning the philosophy of mathematics. This  
includes approaches from philosophical analysis, linguistics (e.g.,  
corpus studies) and literature studies, but also methods from computer  
science and artificial intelligence (e.g., big data approaches and  
natural language processing), cognitive sciences, and mathematics  
education (relevant studies include Mancosu et al. 2005; Giaquinto  
2007; Schlimm 2008; Pease et al. 2013; Fisseni et al. 2019, Cramer et  
al. 2021).

Note that this remains a philosophical issue. So while methods are  
interdisciplinary, we aim for a philosophical upshot.

The impressive progress in natural language processing on the one side  
and automated theorem proving on the other side make it attractive to  
develop good models of mathematical texts to make use of state of the  
art techniques for better tooling in documenting and developing  
mathematics. The language of mathematics as a technical jargon or as a  
special natural language with a rich structure is an important  
test-case for practical and theoretical study of language, and also  
has consequences for the philosophy of language and the philosophy of  
mathematical practice. In this collection, we target mathematical text  
in a broad sense, including written interaction such as blogs, forums,  
reviews as well as textbooks and research articles.

Bibliography:
M. Carl, M. Cramer, B. Fisseni, D. Sarikaya and B. Schröder. “How to  
Frame Understanding in Mathematics: A Case Study Using Extremal  
Proofs”. Axiomathes (2021).

B. Fisseni, B. Schröder, D. Sarikaya and M. Schmitt. “How to frame a  
mathematician. Modelling the cognitive background of proofs.” In: S.  
Centrone, D. Kant and D. Sarikaya (Eds.): Reflections on the  
Foundations of Mathematics: Univalent Foundations, Set Theory and  
General Thoughts. Berlin: Synthese Library, Springer (2019), pp.  
417-436.

M. Giaquinto: Visual thinking in mathematics. An epistemological  
study. Oxford: Oxford University Press (2007).

P. Mancosu, K.F. Jørgensen and S.A. Pedersen (Eds.): Visualization,  
explanation and reasoning styles in mathematics. Dordrecht, Norwell,  
MA: Synthese Library 327, Springer (2005).

A. Pease, M. Guhe and A. Smaill: “Developments in research on  
mathematical practice and cognition”, Topics in cognitive science 5(2)  
(2013), pp. 224–230.

D. Schlimm: “Two Ways of Analogy. Extending the Study of Analogies to  
Mathematical Domains”, Philosophy of Science 75(2) (2008), pp. 178–200.

For further information, or if you are unsure whether your paper idea  
fits the theme, please contact ideally all of us:  
bernhard.fisseni at uni-due.de, kantdebo at gmail.com,  
Deniz.Sarikaya at uni-hamburg.de, and bernhard.schroeder at uni-due.de

The deadline for submissions is March 15, 2022

Papers should be submitted via the Synthese’s editorial manager at  
https://www.editorialmanager.com/synt/default.aspx . When the system  
asks you to “Choose Article Type”, please scroll down in the pull-down  
menu to choose this topical collection: "T.C. : Linguistically  
Informed Philosophy of Mathematics" When preparing your paper, please  
read the journal’s ‘Instructions for authors’ at  
https://www.springer.com/journal/11229/submission-guidelines