CfP: Mathematical Practice and Social Ontology. TOPOI Special Issue

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

Deadline for Submission: December 31, 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:

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).
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