Weaving Self-Evidence

The development of theorems in logic is generally thought to be a solitary and purely cerebral activity, and therefore unobservable by sociologists. InWeaving Self-Evidence, French sociologist Claude Rosental challenges this notion by tracing the history of one well-known recent example in the field of artificial intelligence--a theorem on the foundations of fuzzy logic. Rosental's analyses disclose the inherently social nature of the process by which propositions in logic are produced, disseminated, and established as truths.Rosental describes the different phases of the emergence of the theorem on fuzzy logic, from its earliest drafts through its publication and diffusion, discussion and reformulation, and eventual acceptance by the scientific community. Through observations made at major universities and scholarly conferences, and in electronic forums, he looks at the ways students are trained in symbolic manipulations and formal languages and examines how researchers work, interact, and debate emerging new ideas. By carefully analyzing the concrete mechanisms that lead to the collective development and corroboration of proofs, Rosental shows how a logical discovery and its recognition within the scholarly community are by no means the product of any one individual working in isolation, but rather a social process that can be observed and studied.Weaving Self-Evidencewill interest students and researchers in sociology and the history and philosophy of science and technology, and anyone curious about how scientists work.

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

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