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Wittgenstein on Mathematics, Minds and Mental Machines

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Taking into account the real historical development of Wittgenstein's writings, the author studies the development of his thought and investigates his view concerning the possible existence of a genuine machine intelligence. Topics include the logicist research program, Wittgenstein on inference, the limit of mathematical language, intuitionism and philosophy, Brouwer's impact on Wittgenstein, calculation and experiment, and the foundations of mathematics. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9781840143089
  • Publisher: Ashgate Publishing, Limited
  • Publication date: 2/1/1998
  • Series: Avebury Series in Philosophy
  • Pages: 370
  • Product dimensions: 6.22 (w) x 8.94 (h) x 0.98 (d)

Table of Contents

Acknowledgements
List of Abbreviations
Introduction 1
Pt. I The Universal 'Game' of Mathematics
I.1 The Early Years
From Schopenhauer to Boltzmann 27
The Logicist Research Programme 36
An Alternative Account 46
The 'Theory of Symbolism' 56
Logic is Transcendental 70
The Metaphysical Subject 78
I.2 The Early Calculus Conception
Operations in Mathematics 94
The Structure of Mathematics 102
Wittgenstein on Inference 113
Mathematical Calculations 118
The Limit of Mathematical Language 126
Tautologies: A Misunderstanding 131
I.3 The Idealistic Intuitionism
Intuitionism and Philosophy 146
Constructive Mathematics 152
Brouwer's Vienna Lecture 159
Brouwer and Wittgenstein: Similarities 165
Wittgenstein: The Impact of Brouwer 175
Pt. II Conceptual Problems in Calculations
II.1 The Later Calculus Conception
Mathematics as Calculations 201
Surveyability of Calculations 210
The Law of the Excluded Middle 219
Calculation and Experiment 223
Calculation and Conventionalism 230
Calculation and Prose 236
II.2 The 'Foundations' of Mathematics
The Meta-Mathematical Illusion 255
Consistency and Mathematics 262
The Decision Problem 269
Godel's Incompleteness Theorem 273
II.3 Wittgenstein on 'Machine Intelligence'
On Church's Thesis 299
Turing's Operationalist Thesis 304
Turing's 'Imitation Game' 308
Wittgenstein: Can Machines Think? 312
Machine Intelligence as 'Prose' 316
The Transcendental Dimension 320
Conclusion 337
Index 345
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