Weaving self-evidence: a sociology of logic

Acknowledgments

Introduction

A Sociologist among Logicians

Observing Demonstrations

A Necessarily Detailed Analytic Account

Grasping the Emergence of a Logical Theorem

Accessing the Specialized Skills of Workers in Logic

Part 1. Accessing the World of Producers of Logical Statements

Chapter 1. How Can We Grasp What Logic-Makers Do? Questions Raised in the Human Sciences and Philosophy about Logic and Mathematics

Do Researchers in Logic Invoke Ideal Principles?

How Do Multiple Social Actors Put Forward Various Definitions and Practices of Logic?

Questions Raised by Certain Works in the Social History of Mathematics

Can Institutional Sociology Account for the Ways in Which Research in Mathematics Is Carried Out?

Can One Grasp the Role of Networks of Actors and Practices in the Production of a Theorem?

What Role Does the Scale of Adoption of Specific Practices of Demonstration Play in the Dynamics of Recognition of a Result?

Can the Analysis of Demonstrative Practices Be Inscribed Solely within the Framework of the History of a Scientific Discipline?

What Demonstrative Resources Are Used for What Recognition?

Questions Raised by Some Studies That Focus on, or Formulate a Research Program to Address, Practices in Logic

Conclusion

Chapter 2. Spaces and Tools for Exchange

Preliminary Information about the Way an Electronic Forum Works

Shared Skills in Logic

Part 2. Practices of De-Monstration: Debating a Theorem in an Electronic Forum

Chapter 3. Bringing to Light: Demonstration Put to the Test of Antagonistic Logical Practices

The Formal Presentation of a Demonstration Does Not Lead Automatically to Consensus

The Absence of Universally Recognized Central Logical Principles

The Heterogeneity of Ways of Doing Logic

The Use Values of Demonstrations

De-monstrating and Appearing

The Practice of Substituting Proofs

Making Logical Principles Appear and Disappear in Demonstrations

Making Certain De-monstrations Maximally Visible

Chapter 4. Evaluating the Correctness of a Theorem and the Properties of a Logic at the Intersection between Several De-monstrative Modes

Bringing to the Fore the Properties of a Logical System in Technological Devices in Order to Cast Doubt on the Correctness of a Proof

Personalizing the Debates in Order to Evaluate the Correctness of a Theorem

Trying to Neutralize a Proof by Invoking General Antagonisms

Contesting a Proof and Defending Logical Properties by Evoking a Cultural Specificity

Part 3. Mediations Used to Advance a Logical Theorem

Chapter 5. Accompanying De-monstrations: The Publication of a De-monstration at the Heart of the Action of Groups of Actors

How One and the Same De-monstration Can Be Rejected and Then Accepted for Publication

From De-monstration to Publication: The Importance of Interactions

Elkan's Proof and the Conference Paper Selection Process

Chapter 6. Federating a Counter-De-monstration or Producing Hand-Tailored Responses

Producing More Stable and Visible Responses, in Limited Number

The Formation and Use of Sedimented Repertories of De-monstration

Advancing Adaptive, Polysemic, and Differentiated De-monstrations

Chapter 7. The Emergence of a Quasi-Object and a Collective Statement

Recourse to Tacit Manipulations: De-monstration as a Quasi-Object

Defending a Proof by Reformulating It

Nuances and Precautions

A Polysemic Textual Device to Stabilize Debates

The Successive Versions of a Proof: Records of Negotiations

De-monstrations Serving to Stabilize a Controversy

Federating and Stabilizing Positions and Thereby Helping to Marginalize the Adversary

Devices of Reiteration and Reference Contributing to a Stabilization of the Debates

Conclusion: A Sociology of the Practices of De-monstration

Destylizing the Unfolding of Debates in Logic

Following the Production of Certified Knowledge in Logic

Observing the Work of De-monstration

Logic and Sociology

Toward a Social and Material History of Forms of De-monstration

Works Cited

Index