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Ad Infinitum: The Ghost in Turing's Machine

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Ad Infinitum: The Ghost in Turing's Machine Cover

 

Synopses & Reviews

Publisher Comments:

This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical, interpretation of whole numbers held by mathematicians and scientists, and replaces it with an original and radical alternative—what the author calls non-Euclidean arithmetic.

The author's entry point is an attack on the notion of the mathematical infinite in both its potential and actual forms, an attack organized around his claim that any interpretation of "endless" or "unlimited" iteration is ineradicably theological. Going further than critique of the overt metaphysics enshrined in the prevailing Platonist description of mathematics, he uncovers a covert theism, an appeal to a disembodied ghost, deep inside the mathematical community's understanding of counting.

Synopsis:

This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical interpretation of whole numbers held by mathematicians, and replaces it with a radical alternative. The author bases his analysis on the development of a semiotic model that characterizes mathematics as a form of discourse organized around certain kinds of waking dreams or thought experiments. The model allows him to articulate the role of the sign-using mathematical subject and of that subject's imagined self which plays a crucial part in achieving mathematical persuasion. Ad Infinitum is a significant contribution to postmodern epistemology and the philosophy of science.

Synopsis:

“Rotman uses semiotics to focus on the infinite and the meaning of the mathematicians ellipsis. . . . He argues persuasively that a constructive model of the infinite is inherent in the literary acts of mathematicians.”—Choice

Description:

Includes bibliographical references (p. [195]-200) and index.

About the Author

Brian Rotman is an independent scholar and the author of, most recently, Signifying Nothing: The Semiotics of Zero.

Product Details

ISBN:
9780804721288
Author:
Rotman, Brian
Author:
Rotman, B.
Publisher:
Stanford University Press
Location:
Stanford, Calif. :
Subject:
General
Subject:
Philosophy
Subject:
Mathematics
Subject:
Modern
Subject:
Metaphysics
Subject:
Infinity
Subject:
Infinite
Subject:
Mathematics -- Philosophy.
Subject:
History & Surveys - Modern
Subject:
General Philosophy
Subject:
Philosophy : General
Edition Number:
1
Edition Description:
1
Series Volume:
9436
Publication Date:
19930931
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
224
Dimensions:
9 x 5.5 in

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Ad Infinitum: The Ghost in Turing's Machine New Trade Paper
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Product details 224 pages Stanford University Press - English 9780804721288 Reviews:
"Synopsis" by , This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical interpretation of whole numbers held by mathematicians, and replaces it with a radical alternative. The author bases his analysis on the development of a semiotic model that characterizes mathematics as a form of discourse organized around certain kinds of waking dreams or thought experiments. The model allows him to articulate the role of the sign-using mathematical subject and of that subject's imagined self which plays a crucial part in achieving mathematical persuasion. Ad Infinitum is a significant contribution to postmodern epistemology and the philosophy of science.
"Synopsis" by ,
“Rotman uses semiotics to focus on the infinite and the meaning of the mathematicians ellipsis. . . . He argues persuasively that a constructive model of the infinite is inherent in the literary acts of mathematicians.”—Choice
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