Call for Papers - Mathematical Practice and Social Ontology
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
Log in, click on "submit new manuscript" and select "Math & Social Ontology "
from the menu "article type".
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.ca...@univ-amu.fr<mailto:paola.ca...@univ-amu.fr> or Italo Testa
italo.te...@unipr.it<mailto:italo.te...@unipr.it> For further information,
please visit Topoi's website:
https://www.springer.com/journal/11245/updates/18364346
_________________________
Paola Cantù Chercheur CNRS
Université Aix-Marseille
Maison de la Recherche
29, Avenue Schuman
13621 Aix-en-Provence Cedex 1
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