Weaving Self-Evidence

Claude Rosental is a sociologist and researcher at the Centre National de la Recherche Scientifique and a member of the Institut Marcel Mauss at the Ecole des Hautes Etudes en Sciences Sociales in France.

• ACKNOWLEDGMENTS ix INTRODUCTION 1 A Sociologist among Logicians 2 Observing Demonstrations 4 A Necessarily Detailed Analytic Account 7 Grasping the Emergence of a Logical Theorem 8 Accessing the Specialized Skills of Workers in Logic 12 PART ONE: ACCESSING THE WORLD OF PRODUCERS OF LOGICAL STATEMENTS 15 CHAPTER 1: How Can We Grasp What Logic-Makers Do? Questions Raised in the Human Sciences and Philosophy about Logic and Mathematics 17 Do Researchers in Logic Invoke Ideal Principles? 18 How Do Multiple Social Actors Put Forward Various Definitions and Practices of Logic? 20 Questions Raised by Certain Works in the Social History of Mathematics 24 Can Institutional Sociology Account for the Ways in Which Research in Mathematics Is Carried Out? 24 Can One Grasp the Role of Networks of Actors and Practices in the Production of a Theorem? 31 What Role Does the Scale of Adoption of Specific Practices of Demonstration Play in the Dynamics of Recognition of a Result? 33 Can the Analysis of Demonstrative Practices Be Inscribed Solely within the Framework of the History of a Scientific Discipline? 36 What Demonstrative Resources Are Used for What Recognition? 40 Questions Raised by Some Studies That Focus on, or Formulate a Research Program to Address, Practices in Logic 44 Conclusion 53 CHAPTER 2: Spaces and Tools for Exchange 55 Preliminary Information about the Way an Electronic Forum Works 55 Shared Skills in Logic 59 PART TWO: PRACTICES OF DE-MONSTRATION: DEBATING A THEOREM IN AN ELECTRONIC FORUM 75 CHAPTER 3: Bringing to Light: Demonstration Put to the Test of Antagonistic Logical Practices 77 The Formal Presentation of a Demonstration Does Not Lead Automatically to Consensus 77 The Absence of Universally Recognized Central Logical Principles 77 The Heterogeneity of Ways of Doing Logic 83 The Use Values of Demonstrations 93 De-monstrating and Appearing 96 The Practice of Substituting Proofs 96 Making Logical Principles Appear and Disappear in Demonstrations 98 Making Certain De-monstrations Maximally Visible 109 CHAPTER 4: Evaluating the Correctness of a Theorem and the Properties of a Logic at the Intersection between Several De-monstrative Modes 116 Bringing to the Fore the Properties of a Logical System in Technological Devices in Order to Cast Doubt on the Correctness of a Proof 116 Personalizing the Debates in Order to Evaluate the Correctness of a Theorem 125 Trying to Neutralize a Proof by Invoking General Antagonisms 127 Contesting a Proof and Defending Logical Properties by Evoking a Cultural Specificity 136 PART THREE: MEDIATIONS USED TO ADVANCE A LOGICAL THEOREM 149 CHAPTER 5: Accompanying De-monstrations: The Publication of a De-monstration at the Heart of the Action of Groups of Actors 151 How One and the Same De-monstration Can Be Rejected and Then Accepted for Publication 151 From De-monstration to Publication: The Importance of Interactions 161 Elkan's Proof and the Conference Paper Selection Process 171 CHAPTER 6: Federating a Counter-De-monstration or Producing Hand-Tailored Responses 187 Producing More Stable and Visible Responses, in Limited Number 187 The Formation and Use of Sedimented Repertories of De-monstration 198 Advancing Adaptive, Polysemic, and Differentiated De-monstrations 204 CHAPTER 7: The Emergence of a Quasi-Object and a Collective Statement 211 Recourse to Tacit Manipulations: De-monstration as a Quasi-Object 211 Defending a Proof by Reformulating It 217 Nuances and Precautions 218 A Polysemic Textual Device to Stabilize Debates 221 The Successive Versions of a Proof: Records of Negotiations 233 De-monstrations Serving to Stabilize a Controversy 237 Federating and Stabilizing Positions and Thereby Helping to Marginalize the Adversary 238 Devices of Reiteration and Reference Contributing to a Stabilization of the Debates 244 CONCLUSION A Sociology of the Practices of De-monstration 250 Destylizing the Unfolding of Debates in Logic 250 Following the Production of Certified Knowledge in Logic 253 Observing the Work of De-monstration 256 Logic and Sociology 259 Toward a Social and Material History of Forms of De-monstration 266 WORKS CITED 271 INDEX 287

"Sociologist Rosental meticulously argues for the materiality of logic as a field of inquiry. He rigorously grounds his work in science studies, extending the reach of social analysis into a domain superficially thought to be purely mental: that of logical formalism and proof."--J.L. Croissant, Choice "In the history of STS, hard cases, from mathematics to laboratory manipulations, have played key roles. This book should enter the field as an exemplary treatment of a hard case."--Sergio Sismondo, Canadian Journal of Sociology "Rosentals's Weaving Self-Evidence ... is timely and much needed."--Stephan Fuchs, American Journal of Sociology