Weaving Self-Evidence: A Sociology of Logic

Overview

"This is a beautifully crafted book. In it, Claude Rosental proceeds to demonstrate that, as for all scientific and intellectual pursuits, the production and evaluation of theorems depend on conventions and networks that are eminently social. Rosental is widely regarded as one of the most promising social scientists working in France today. He is clearly a rising star in the field of science studies."—Michle Lamont, Harvard University

"This is a fine piece of scholarship and an important book. Rosental shows that...

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Overview

"This is a beautifully crafted book. In it, Claude Rosental proceeds to demonstrate that, as for all scientific and intellectual pursuits, the production and evaluation of theorems depend on conventions and networks that are eminently social. Rosental is widely regarded as one of the most promising social scientists working in France today. He is clearly a rising star in the field of science studies."—Michle Lamont, Harvard University

"This is a fine piece of scholarship and an important book. Rosental shows that in spite of our assumption that new ideas in logic are thought up individually and evaluated in the minds of others, they are presented, read, and judged in a more social and ritual manner—proofs cannot simply be thought into existence. Weaving Self-Evidence is an important contribution to the sociology of knowledge."—Chandra Mukerji, University of California, San Diego

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Editorial Reviews

American Journal of Sociology
Rosentals's Weaving Self-Evidence . . . is timely and much needed.
— Stephan Fuchs
Choice - J.L. Croissant
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.
Canadian Journal of Sociology - Sergio Sismondo
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.
American Journal of Sociology - Stephan Fuchs
Rosentals's Weaving Self-Evidence . . . is timely and much needed.
From the Publisher
"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

Choice
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
Canadian Journal of Sociology
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
Read More Show Less

Product Details

Meet the Author

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.

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Read an Excerpt

Weaving Self-Evidence A Sociology of Logic
By Claude Rosental Princeton University Press
Copyright © 2008
Princeton University Press
All right reserved.

ISBN: 978-0-691-13940-1


Introduction IN A TEXT FROM the mid-1970s, a mathematician estimated that approximately one million theorems were produced in the world every five years. If this affirmation still applies today, a whole set of questions arises at once. If we are indeed dealing with the authentic production of a massive number of statements, what "recognition" can a given theorem acquire, and to what reality does such recognition correspond? Through what pathways can a mathematical result-and its author, or even its challengers-obtain some form of accreditation? In other words, how does the collective validation of a theorem come about in practice? In particular, in fields that involve highly specialized skills, can the decisive role of "experts" be observed, and, if so, in what ways do the latter intervene in the process of certifying (or rejecting) a given theorem?

These questions will be addressed here on the basis of an actual case study documenting the way a theorem in mathematical logic was developed and accredited in the first half of the 1990s. On the basis of my own observations, textual analyses, and interviews, an empirical study carried out simultaneously with the logical research in question, I shall focus on the various tests to which this statement has been subjected and try to specify the factors on which the recognitionit has achieved depends.

In so doing, I shall be exploring an avenue of research that has been largely neglected up to now by the social sciences. Indeed, while Émile Durkheim took "science" and especially "logic" as objects of sociological investigation par excellence, the observations he set forth in 1912 concerning the unfortunate lack of pertinent empirical studies devoted to "logic"-studies destined to establish sociological analysis properly speaking-still apply today. Without celebrating Durkheim's representations of the objects of logic and sociology, the present study aims to help make up for the lack of studies and analyses by seeking to account for certain observable modes of production of certified knowledge in logic in the early 1990s. My aim here is thus as much to take a step forward by offering for sociological reflection a "new" object of empirical investigation-logic being generally understood in the social sciences as an object essentially having to do with method-as to develop tools to describe this object.

But what is meant by certified knowledge in logic? One of the goals of this study is precisely to identify as specifically as possible the reality to which such a proposition may correspond. Thus I shall be able to attribute a precise meaning to this notion only at the conclusion of my work. However, I shall use the term provisionally here to refer to any statement that is relatively stabilized, more or less broadly accepted, advanced and validated by groups of actors in logic, whether they present themselves as philosophers, mathematicians, researchers in artificial intelligence, or in some other guise. I shall relate anything that these researchers may advance as "theorems" in mathematical logic, as philosophical statements in logic, or as statements attributing the working of a given system (especially in computer science) to logical formalisms.

The problem raised in this book has parallels, needless to say, in various projects undertaken in the humanities and in philosophy, and especially in a set of analyses produced by sociologists of the so-called experimental sciences, analyses based on the study of the research process, the elaboration of facts, and the administration of proofs. In the first chapter, I embark on a discussion with the authors of a certain number of these texts, in a dialogue that will continue throughout the book. For now, it seems important to clarify certain aspects of my approach to the project and of the empirical investigations I undertook in order to "observe" modes of production of certified knowledge in logic.

A SOCIOLOGIST AMONG LOGICIANS

I carried out my first observations during the academic year 1991-92 at the University of California, San Diego (UCSD). I first sought to identify as exhaustively as possible the various forms of logical activity that were being undertaken on that campus. Because I had been unable to find any sociological studies devoted to work in logic or to the profession of logician, the establishment of a cartography of logical activity seemed to be a necessary first step in order to arrive at an empirical understanding of the various exercises to which this term was applied, and in order to make initial contact with the actors involved, with an eye to later, more focused studies. Since there was no consensus among the faculty members I encountered as to how to define the field of logic-indeed, the matter often remained an object of debate-I studied the distribution of often mutually exclusive definitions, without making any a priori exclusions of my own. A phase of preliminary investigation, carried out through a series of interviews, analyses of written accounts of activities, and observations made during seminars, led me to a number of departments specializing in mathematics, philosophy, cognitive science, and computer science.

Prior to taking on this project, I had acquired a general background in science while I was taking more specialized courses in sociology, logic, history, and the philosophy of science. This itinerary turned out to be an asset that made it easy for me to engage researchers in dialogue and read their texts rapidly, without needing to begin by identifying and acquiring a mass of highly sedimented skills and knowledge. But training in mathematics and logic alone would have been insufficient for this project. It would have been difficult for me to construct a problematics from a sociological perspective, to formulate an empirical research project on such an object and not deviate from it, had I not had the opportunity to become familiar with an already vast literature in the sociology of the experimental sciences, and had I not already been interested in the notion of self-evidence in logic and in the possibility of developing a sociological approach to the issue. Since this specific form of "openness" compensated for the "difficulties" deriving from my own form of competence in logic and in science, my background was ultimately beneficial in that it enabled me to circulate freely within the framework of these preliminary investigations.

After I had grasped certain phases of the formation of statements in mathematical logic during research seminars by observing the participants' discussions, their interventions at the blackboard, and the written traces they produced, I was finally led by the relatively limited scope of logical activity practiced at UCSD to look for more appropriate sites in which to pursue my problematic. On the basis of bibliographical research and the testimony of various informants, I decided to continue my investigations at the Massachusetts Institute of Technology and Harvard University in a first phase, and at Stanford University and the University of California, Berkeley, in a second phase. Stanford had been represented to me on numerous occasions as one of the foremost centers of logical activity in the world.

Despite difficulties in setting up meetings at these sites with the faculty members involved and in obtaining authorization to observe certain of their activities, I was able to carry out a large number of interviews, take notes on interactions as they occurred, and observe and analyze a substantial production of texts (on paper, blackboards, or computer screens), especially during research seminars and lectures given by philosophers, researchers in artificial intelligence, and specialists in mathematical logic. In all these spaces, the production of logical knowledge was the work of scholars associated with a variety of disciplines: mathematics, philosophy, computer science, cognitive science, or linguistics.

During my study, I followed the day-by-day progress of several projects involving the simultaneous development of software and logical formalisms, projects carried out by teams in laboratories where I stationed myself as an observer. I used methods that had already been developed and tested in the sociology of the experimental sciences, bringing to bear ethnographic or ethnomethodological approaches. Among the various forms of logic developed by the actors in question, I chose to follow systematically, in the various sites, the steps involved in developing and setting forth a specific logical formalism known as fuzzy logic. This decision was based primarily on a convergence of oral and written accounts that stressed the "tremendous flowering" of fuzzy logic at the time.

What were the material results of this course of action? All in all, between 1991 and 1996 I devoted about a year and a half to on-site observations. Supplemented by retranscriptions of interviews, these observations filled several notebooks. Some of the interviews, seminars, and project meetings were recorded on audio cassettes. I was also given permission to copy video recordings of certain project presentations and seminars, whether I had been in attendance or not. In addition, my research led me to collect a very large set of documents both on paper and in electronic form.

The process of reviewing and partially analyzing these data was spread over some three years. But since I have been talking about "observations," it is perhaps time to specify what sorts of things I was able to see.

OBSERVING DEMONSTRATIONS

In the course of my investigations, the actors I met characterized the objects of logic in contrary ways, sometimes arguing about them among themselves. Their own efforts were in fact invested in quite a wide range of activities. For my part, not wanting to prejudge what might be characteristic of their practices, I continually asked myself what it was important to observe. I sought to remain attentive to aspects that might have escaped me earlier, and I had many doubts about the object and the appropriate sites for my inquiry. Nevertheless, I was particularly struck early on by the considerable resources in time and energy deployed by the researchers in the activity of demonstrating. This work corresponded to the implementation of variable practices, as the following examples will make clear.

Let us consider first of all a project I followed in a laboratory at MIT involving the simultaneous development of a logical formalism and of software. Both were designed to be used to archive and annotate multimedia documents. This project brought together five researchers who spent most of their time preparing or carrying out, on the one hand, presentations at the blackboard among themselves or in front of others to explain the "principles" behind the software and the formalism to be implemented and, on the other hand, computer-based "demos" in front of small groups of invited guests, sometimes including the project's sponsors, to show them how the software worked. These activities were constitutive of the emergence of the formalism and the software, as much from the standpoint of pursuing and obtaining financing as from that of its content: indeed, the critiques formulated during these meetings largely determined the project's evolution, down to its smallest details. The moments of demonstration were essential to the advancement of this process, and in fact they structured the overall activity of the group.

In the same way, the time devoted to demonstration (including all the requisite preparatory steps) by academics affiliated with the departments of philosophy or mathematics at Stanford was also quite considerable. The preparation and presentation of articles or exposés at the blackboard, implying a large number of interactions and a material work of writing, played a central role in the formation and reformulation of statements or proofs. Moreover, the written or oral demonstrations gave rise to stagings that were as theatrical, as routine and stabilized, relatively speaking, as were the "demos."

The activity of logical production thus bore little resemblance to the image of actors working in near-total isolation, and it was not exclusively circumscribed by the minds of individuals. As a sociologist, then, I was not condemned to abandon my investigation for lack of competence to account for the activity in question. The work of logic unfolded through a great number of interactions, and these played an essential role in the production and transformation of statements. The activity involved also mobilized a huge gamut of material resources (written documents and arrangements for writing: blackboards, computers, laboratories, and so on), and its stakes varied according to the actors. In other words, logical activity looked like an authentic object for sociology, for it was eminently "social," if only because it involved groups of actors whose ties were in part forged or dissolved in the course of frequent and intense interactions.

Moreover, this activity did not appear "abstract" in itself: the process of abstraction could be grasped in its materiality. While the activity had to be characterized as "theoretical," it seemed to me that that term should not be used in opposition to the term "practical," insofar as it implied a material work of writing that was carried out at various work sites and that called on a set of particular manual and visual skills. The expression "theoretical practice" thus seemed well suited to account for the specificity of the practices at work.

In other words, I found myself confronted with a large number of mediations of logic. I borrow the term mediation from studies in the sociology of music dealing with the way music is presented through the media. The history of music seems in fact to have encountered the same difficulties with so-called immaterial objects as the history of logic and mathematics. I use the term "mediation," as opposed to "intermediary," in order to characterize all the resources that can be considered as "go-betweens" or conveyors (texts conveying ideas to readers or instruments conveying music to listeners, for example), and in order to make them visible as beings in their own right and as beings constituting the objects they are said to convey. During my investigation, texts and devices such as computers were often presented by researchers as putting the "principles" of a certain logic to work, while for me, as an analyst, they constituted mediations of that very logic.

Finally, I must stress the fact that the exercise of demonstration always struck me as the activity that best characterized the actors' work, structuring rather than punctuating it. The word "demonstration" implied variable practices-"demos," written proofs, and so on-that could be distinguished through observation, even if these practices were conflated under a single umbrella term. The examination of modes of demonstration focused primarily on the intersection between the analysis of technologies of proof and the analysis of forms of ostentation. The observation of a wide range of demonstrative practices, with significant corresponding divergences of principle, allowed me in any event to grasp, without having to pass judgment as to the legitimacy of any particular point of view, a remarkably "chaotic" situation: statements that certain specialists took to be "rock solid" were contested just as vigorously by others, so that there was, on the whole, a pronounced splintering of the logical certainties advanced.

(Continues...)



Excerpted from Weaving Self-Evidence by Claude Rosental
Copyright © 2008 by Princeton University Press. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
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Table of Contents

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

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