CfP special issue of Topoi on "Mathematical Practice & Social Ontology", Deadline: Dec 2021

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CfP special issue of Topoi on "Mathematical Practice & Social Ontology", Deadline: Dec 2021

Call for Papers - Mathematical Practice and Social Ontology
TOPOI.<https://www.springer.com/journal/11245/> An International Review of Philosophy

Guest Editors : Paola Cantù (CNRS and Université Aix-Marseille); Italo
Testa (Università di Parma)

Deadline for Submission: December 2021

Overview: The relationship between mathematics and social ontology is
often guided by the question of the possibility of applying mathematics to
social sciences, especially economy. As interesting as these questions may
be, they neglect the inverse possibility of applying a conceptual analysis
derived from social ontology to mathematics. The issue will be devoted to
the question whether the distinction between social object and social
fact, on the one hand, and between different theoretical approaches to the
notion of social fact, can be successfully applied to mathematical
practice.

There is a well-established tendency in recent philosophy of mathematics
to emphasize the importance of scientific practice in answering certain
epistemological questions such as visualization, the use of diagrams,
reasoning, explanation, purity of evidence, concept formation, the
analysis of definitions, and so on. While some of the approaches to
mathematical practice are based on Lakatos? interpretation of mathematics
as a quasi-empirical science, this project takes this statement a step
further, as it relies on the idea that the objectivity of mathematical
concepts might be the result of a social constitution.

What theory of social facts and social objects could explain the
characteristics of mathematical objects and concepts? Are there new
ontological or epistemological perspectives that can be developed in this
social philosophy of mathematics?

This project is not a renewal of David Bloor's research, aiming at a
sociological study of mathematics. It is rather a study of the possibility
of applying philosophical theories of social objectivity to mathematical
objects. This is a new topic that requires the search for adequate
mathematical examples that could satisfy the objectivity constraints
proposed by the philosophy of social ontology.

Tendencies in this direction can be traced, but no general survey has been
offered. For example, Salomon Feferman (2011) characterizes mathematical
objectivity as a special case of intersubjective social objectivity. José
Ferreiros (2016) defines mathematical practice as an activity supported by
individual and social agents and characterized by stability, reliability,
and intersubjectivity. Julian C. Cole (2013, 2015) sees mathematical
objects as institutional rather than mental objects, referring to Searle's
theory of collective intentionality.

The purpose of the issue is not to determine which social philosophical
ontology is best applied to the construction of a mathematical social
ontology, but rather to verify whether new epistemological and ontological
issues might emerge from the comparison of different theories of social
ontology in an interdisciplinary perspective.

This special issue will focus on the relationship between social and
mathematical objectivity, and more generally on the role of
intersubjectivity in the constitution of mathematical objects. The
contributions might discuss the role of individual, planned or shared
intentionality as well as of rules or habits in the constitution and
development of intersubjective practices. Essays might refer primarily to
social sciences or to mathematics, but the objective is to build a
framework that might allow detecting new cross-relations.

Cross-relations might emerge from the discussion of several of the
following questions.

? Does intersubjective mathematical objectivity come in different
degrees, depending on the properties of the theories that describe them?
Does objectivity depend on the degree of certainty or simplicity of the
relevant axiomatic theories?

? Is intersubjective mathematical objectivity necessarily
connected to a structuralist position, or can it be compatible with
platonism, logicism, intuitionism ? And what is its relation to naturalism
?

? Is it possible for mathematical objects to have the same
intersubjective objectivity of social facts, or is there a fundamental
difference between social facts, that are present in all cultures but
usually differ in form, as e.g. marriage, and the natural number system,
which seems to be more or less the same in any culture? Differently said,
is the distinction between type and token applicable both to social and
mathematical objects?

? If mathematics is the result of practices that depend on agents,
having individual goals and values, how can one avoid relativism and
explain the convergence towards some kind of objective truth? Are
mathematical practices governed by their historicity, or by some rational
constraints imposed by their intersubjective nature?

? In order to have a unified vision of science, is it necessary to
have the same kind of objectivity in mathematics and in social sciences?
Does the distinction between constitutive and regulative rules apply to
mathematical practices?

? If social ontology theories have some paradigmatic examples as
test cases: marriage, private property and money, does the same hold for
mathematical ontology? What would the paradigmatic examples be?

? Does the distinction between grounding and anchoring apply to
mathematical objects ? Is the question about the instantiations and
identity conditions of a mathematical property or kind significantly
different from the questions why these are the conditions a given
mathematical object needs to satisfy in order to have that property or
belong to that kind?

? What differences would it make to ground intersubjective
mathematical objectivity on intentions (phenomenological, planned or
shared intentions), on rules or on habits? How would the role of language
and symbolism change?

Possible topics include but are not limited to:

? The distinction between constitutive and regulative rules

? Different degrees of intersubjective objectivity and of
generality

? The relation between different definitions of intersubjective
objectivity (based on intentions or not) and scientific naturalism

? The distinction between grounding and anchoring and possible
applications to mathematical examples

? Definitions of the notion of mathematical practice

? Strategies to account for the historicity of mathematical
practices

? The role of the type-token distinction in mathematical and
social objects

? Paradigmatic examples of institutions in social sciences and in
mathematical sciences

Invited Contributors: Julian Cole (Suny Buffalo), José Ferreiros
(Universidad de Valencia), Valeria Giardino (Institut Jean Nicod, Paris),
Yacin Hamami (Vrije Universiteit Brussel), Mirja Hartimo (Helsinki and
Tampere University), Pierre Livet (Université Aix-Marseille), Sebastien
Gandon (Université Clermont Auvergne), Jessica Carter (University of
Southern Denmark)

Instructions for Submission: All papers will be double-blind
peer-reviewed. Submission is organized through TOPOI?s online editorial
manager: https://www.editorialmanager.com/topo/default.aspx

Please upload: 1) a manuscript prepared for double-blind peer-review and
2) a title page containing the title of the paper, name, affiliation and
contact details of the author, word-count, abstract and key-words.

Papers should not exceed 8000 words (excluding notes).

If you have questions, please do not hesitate to contact: Paola Cantù
paola.cantu@univ-amu.fr<mailto:paola.cantu@univ-amu.fr> or Italo Testa
italo.testa@unipr.it<mailto:italo.testa@unipr.it> For further information,
please visit Topoi?s website:
https://www.springer.com/journal/11245/updates/18364346
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