Mathematics, Science, and Postclassical Theory (Science and Cultural Theory) - Softcover

Softcover

ISBN 10: 0822318636 ISBN 13: 9780822318637

Verlag: Duke University Press, 1997

Inhaltsangabe

Mathematics, Science, and Postclassical Theory is a unique collection of essays dealing with the intersections between science and mathematics and the radical reconceptions of knowledge, language, proof, truth, and reality currently emerging from poststructuralist literary theory, constructivist history and sociology of science, and related work in contemporary philosophy. Featuring a distinguished group of international contributors, this volume engages themes and issues central to current theoretical debates in virtually all disciplines: agency, causality, determinacy, representation, and the social dynamics of knowledge.

In a substantive introductory essay, the editors explain the notion of "postclassical theory" and discuss the significance of ideas such as emergence and undecidability in current work in and on science and mathematics. Other essays include a witty examination of the relations among mathematical thinking, writing, and the technologies of virtual reality; an essay that reconstructs the conceptual practices that led to a crucial mathematical discovery—or construction—in the 19th century; a discussion of the implications of Bohr’s complementarity principle for classical ideas of reality; an examination of scientific laboratories as "hybrid" communities of humans and nonhumans; an analysis of metaphors of control, purpose, and necessity in contemporary biology; an exploration of truth and lies, and the play of words and numbers in Shakespeare, Frege, Wittgenstein, and Beckett; and a final chapter on recent engagements, or nonengagements, between rationalist/realist philosophy of science and contemporary science studies.

Contributors. Malcolm Ashmore, Michel Callon, Owen Flanagan, John Law, Susan Oyama, Andrew Pickering, Arkady Plotnitsky, Brian Rotman, Barbara Herrnstein Smith, John Vignaux Smyth, E. Roy Weintraub

Über diesen Titel

Über die Autorin bzw. den Autor

Barbara Herrnstein Smith is Professor of Comparative Literature and English and Director of the Center for Interdisciplinary Studies in Science and Cultural Theory at Duke University. Arkady Plotnitsky is Visiting Scholar at Duke University’s Center for Interdisciplinary Studies in Science and Cultural Theory.

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'Mathematics, Science, and Postclassical Theory' is a unique collection of essays dealing with the intersections between science and mathematics and the radical reconceptions of knowledge, language, proof, truth, and reality currently emerging from poststructuralist literary theory, constructive history and sociology of science, and related work in contemporary philosophy.

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Mathematics, Science, and Postclassical Theory

By Barbara Herrnstein Smith, Arkady Plotnitsky

Duke University Press

Copyright © 1997 Duke University Press
All rights reserved.

ISBN: 978-0-8223-1863-7

Contents

Introduction: Networks and Symmetries, Decidable and Undecidable, 
Thinking Dia-Grams: Mathematics, Writing, and Virtual Reality, 
Concepts and the Mangle of Practice: Constructing Quaternions, 
The Moment of Truth on Dublin Bridge: A Response to Andrew Pickering, 
Explanation, Agency, and Metaphysics: A Reply to Owen Flanagan, 
Agency and the Hybrid, 
The Accidental Chordate: Contingency in Developmental Systems, 
Complementarity, Idealization, and the Limits of Classical Conceptions of Reality, 
Is "Is a Precursor of" a Transitive Relation?, 
Fraud by Numbers: Quantitative Rhetoric in the Piltdown Forgery Discovery, 
A Glance at SunSet: Numerical Fundaments in Frege, Wittgenstein, Shakespeare, Beckett, 
Microdynamics of Incommensurability: Philosophy of Science Meets Science Studies, 
Notes on Contributors, 

CHAPTER 1

Thinking Dia-Grams: Mathematics, Writing, and Virtual Reality

Brian Rotman

IN the epilogue to his essay on the development of writing systems, Roy Harris declares:

It says a great deal about Western culture that the question of the origin of writing could be posed clearly for the first time only after the traditional dogmas about the relationship between speech and writing had been subjected both to the brash counterpropaganda of a McLuhan and to the inquisitorial scepticism of a Derrida. But it says even more that the question could not be posed clearly until writing itself had dwindled to microchip dimensions. Only with this ... did it become obvious that the origin of writing must be linked to the future of writing in ways which bypass speech altogether.

Harris's intent is programmatic. The passage continues with the injunction not to "re-plough McLuhan's field, or Derrida's either," but sow them, so as to produce eventually a "history of writing as writing."

Preeminent among dogmas that block such a history is alphabeticism: the insistence that we interpret all writing — understood for the moment as any systematized graphic activity that creates sites of interpretation and facilitates communication and sense making — along the lines of alphabetic writing, as if it were the inscription of prior speech ("prior" in an ontogenetic sense as well as the more immediate sense of speech first uttered and then written down and recorded). Harris's own writings in linguistics as well as Derrida's program of deconstruction, McLuhan's efforts to dramatize the cultural imprisonments of typography, and Walter Ong's long-standing theorization of the orality/ writing disjunction in relation to consciousness, among others, have all demonstrated the distorting and reductive effects of the subordination of graphics to phonetics and have made it their business to move beyond this dogma. Whether, as Harris intimates, writing will one day find a speechless characterization of itself is impossible to know, but these displacements of the alphabet's hegemony have already resulted in an open-ended and more complex articulation of the writing/speech couple, especially in relation to human consciousness, than was thinkable before the microchip.

A written symbol long recognized as operating nonalphabetically — even by those deeply and quite unconsciously committed to alphabeticism — is that of number, the familiar and simple other half, as it were, of the alphanumeric keyboard. But, despite this recognition, there has been no sustained attention to mathematical writing even remotely matching the enormous outpouring of analysis, philosophizing, and deconstructive opening up of what those in the humanities have come simply to call "texts."

Why, one might ask, should this be so? Why should the sign system long acknowledged as the paradigm of abstract rational thought and the without-which-nothing of Western technoscience have been so unexamined, let alone analyzed, theorized, or deconstructed, as a mode of writing? One answer might be a second-order or reflexive version of Harris's point about the microchip dwindling of writing, since the very emergence of the microchip is inseparable from the action and character of mathematical writing. Not only would the entire computer revolution have been impossible without mathematics as the enabling conceptual technology (the same could be said in one way or another of all technoscience), but, more crucially, the computer's mathematical lineage and intended application as a calculating/reasoning machine hinges on its autological relation to mathematical practice. Given this autology, mathematics would presumably be the last to reveal itself and declare its origins in writing. (I shall return to this later.)

A quite different and more immediate answer stems from the difficulties put in the way of any proper examination of mathematical writing by the traditional characterizations of mathematics — Platonic realism or various intuitionisms — and by the moves they have legitimated within the mathematical community. Platonism is the contemporary orthodoxy. In its standard version it holds that mathematical objects are mentally apprehensible and yet owe nothing to human culture; they exist, are real, objective, and "out there," yet are without material, empirical, embodied, or sensory dimension. Besides making an enigma out of mathematics' usefulness, this has the consequence of denying or marginalizing to the point of travesty the ways in which mathematical signs are the means by which communication, significance, and semiosis are brought about. In other words, the constitutive nature of mathematical writing is invisibilized, mathematical language in general being seen as a neutral and inert medium for describing a given prior reality — such as that of number — to which it is essentially and irremediably posterior.

With intuitionist viewpoints such as those of Brouwer and Husserl, the source of the difficulty is not understood in terms of some external metaphysical reality, but rather as the nature of our supposed internal intuition of mathematical objects. In Brouwer's case this is settled at the outset: numbers are nothing other than ideal objects formed within the inner Kantian intuition of time that is the condition for the possibility of our cognition, which leads Brouwer into the quasi-solipsistic position that mathematics is an essentially "languageless activity." With Husserl, whose account of intuition, language, and ideality is a great deal more elaborated than Brouwer's, the end result is nonetheless a complete blindness to the creative and generative role played by mathematical writing. Thus, in "The Origin of Geometry," the central puzzle on which Husserl meditates is "How does geometrical ideality ... proceed from its primary intrapersonal origin, where it is a structure within the conscious space of the first inventor's soul, to its ideal objectivity?" It must be said that Husserl doesn't, in this essay or anywhere else, settle his question. And one suspects that it is incapable of solution. Rather, it is the premise itself that has to be denied: that is, it is the coherence of the idea of primal (semiotically unmediated) intuition lodged originally in any individual consciousness that has to be rejected. On the contrary, does not all mathematical intuition — geometrical or otherwise — come into being in relation to...

Details zur Ausgabe

• Verlag: Duke University Press
• Erscheinungsdatum: 1997
• Sprache: Englisch
• ISBN 10: 0822318636
• ISBN 13: 9780822318637
• Einband: Taschenbuch
• Anzahl der Seiten: 288
• Herausgeber: Smith Barbara Herrnstein, Plotnitsky Arkady
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: preigu; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; 49078; Deutschland