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