The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference Cambridge Series on Statistical & Probabilistic Mathematics

223 Pages·2009·1.47 MB·English

THE EMERGENCE OF PROBABILITY
Second Edition
Historical records show that there was no real concept of probability in Europe
before the mid-seventeenth century, although the use of dice and other
randomizing objects was commonplace. Ian Hacking here presents a
philosophical critique of early ideas about probability, induction, and statistical
inference and the growth of this new family of ideas in the fifteenth, sixteenth,
and seventeenth centuries. The contemporary debates center around figures such
as Pascal, Leibniz, and Jacques Bernoulli.
What brought about the change in ideas? Hacking invokes a wider intellectual
framework involving the growth of science, economics, and the theology of the
period. He argues that the transformations that made it possible for probability
concepts to emerge have constrained all subsequent development of probability
theory and determine the space within which philosophical debate on the subject
is still conducted.
This book was first published in 1975, when it opened up a whole new field of
historical and philosophical studies of the very idea of probability. This edition
includes a new introduction in which Hacking explains how Michel Foucault’s
‘archaeology’ enabled him to do this. It concludes with reflections on the
immense body of work done by others after the first publication of this book.
Ian Hacking is Professor Emeritus at the Collège de France (Chair of philosophy
and history of scientific concepts) and University Professor Emeritus at the
University of Toronto. His many books include Representing and Intervening,
Probability and Inductive Logic, Rewriting the Soul, Mad Travelers, Historical
Ontology, and The Social Construction of What? The Modern Library included
Hacking’s The Taming of Chance – a sequel to Emergence – in its list of 100
best non-fiction works published in the twentieth century.
THE EMERGENCE OF PROBABILITY
A PHILOSOPHICAL STUDY OF
EARLY IDEAS ABOUT PROBABILITY, INDUCTION AND STATISTICAL
INFERENCE
Second Edition
IAN HACKING
CAMBRIDGE UNIVERSITY PRESS
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Mexico City Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York www.cambridge.org
Information on this title: www.cambridge.org/9780521866552
© Ian Hacking 1975, 2006
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective
licensing agreements, no reproduction of any part may take place without the written permission of
Cambridge University Press.
First published 1975
Second edition first published 2006
Reprinted 2007
A catalogue record for this publication is available from the British Library Library of Congress
Cataloging in Publication Data Hacking, Ian.
The emergence of probability: a philosophical study of early ideas about probability, induction, and
statistical inference / Ian Hacking. - 2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-52186655-2
ISBN-10: 0-521-86655-3
ISBN-13: 978-0-521-68557-3 (pbk.) ISBN-10: 0-521-68557-5 (pbk.) 1. Probabilities - History. 2. Induction
(Mathematics) - History. 3. Mathematical statistics - History. I. Title.
QA273.H22 2006
519.209 - dc22 2006040643
ISBN 978-0-52186655-2 Hardback ISBN 978-0-521-68557-3 Paperback Cambridge University Press has
no responsibility for the persistence or accuracy of URLs for external or third-party internet websites
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FOR DANIEL
CONTENTS
Introduction 2006
1 An absent family of ideas
Although dicing is one of the oldest of human pastimes, there is no known mathematics of randomness
until the Renaissance. None of the explanations of this fact is compelling.
2 Duality
Probability, as we now conceive it, came into being about 1660. It was essentially dual, on the one
hand having to do with degrees of belief, on the other, with devices tending to produce stable long-run
frequencies.
3 Opinion
In the Renaissance, what was then called ‘probability’ was an attribute of opinion, in contrast to
knowledge, which could only be obtained by demonstration. A probable opinion was not one
supported by evidence, but one which was approved by some authority, or by the testimony of
respected judges.
4 Evidence
Until the end of the Renaissance, one of our concepts of evidence was lacking: that by which one thing
can indicate, contingently, the state of something else. Demonstration, versimilitude and testimony
were all familiar concepts, but not this further idea of the inductive evidence of things,
5 Signs
Probability is a child of the low sciences, such as alchemy or medicine, which had to deal in opinion,
whereas the high sciences, such as astronomy or mechanics, aimed at demonstrable knowledge. A
chief concept of the low sciences was, that of the sign, here described in some detail. Observation of
signs was conceived of as reading testimony. Signs were more or less reliable. Thus on the one hand a
sign made an opinion probable (in the old sense of Chapter 3) because it was furnished by the best
testimony of all. On the other hand, signs could be assessed by the frequency with which they spoke
truly. At the end of the Renaissance, the sign was transformed into the concept of evidence described
in Chapter 4. This new kind of evidence conferred probability on propositions, namely made them
worthy of approval. But it did so in virtue of the frequency with which it made correct predictions.
This transformation from sign into evidence is the key to the emergence of a concept of probability
that is dual in the sense of Chapter 2.
6 The first calculations
Some isolated calculations on chances, made before 1660, are briefly described.
7 The Roannez circle (1654)
Some problems solved by Pascal set probability rolling. From here until Chapter 17 Leibniz is used as
a witness to the early days of probability theory.
8 The great decision (1658?)
‘Pascal’s wager’ for acting as if one believed in God is the first well-understood contribution to
decision theory.
9 The art of thinking (1662)
Something actually called ‘probability’ is first measured in the Port Royal Logic, which is also one of
the first works to distinguish evidence, in the sense of Chapter 4, from testimony. The new awareness
of probability, evidence and conventional (as opposed to natural) sign, is illustrated by work of
Wilkins, first in 1640, before the emergence of probability, and then in 1668, after the emergence.
10 Probability and the law (1665)
While young and ignorant of the Paris developments Leibniz proposed to measure degrees of proof
and right in law on a scale between 0 and 1, subject to a crude calculation of what he called
‘probability’.
11 Expectation (1657)
Huygens wrote the first printed textbook of probability using expectation as the central concept. His
justification of this concept is still of interest.
12 Political arithmetic (1662)
Graunt drew the first detailed statistical inferences from the bills of mortality for the city of London,
and Petty urged the need for a central statistical office.
13 Annuities (1671)
Hudde and de Witt used Dutch annuity records to infer a mortality curve on which to work out the fair
price for an annuity.
14 Equipossibility (1678)
The definition of probability as a ratio among ‘equally possible cases’ originates with Leibniz. The
definition, unintelligible to us, was natural at the time, for possibility was either de re (about things) or
de dicto (about propositions). Probability was likewise either about things, in the frequency sense, or
about propositions, in the epistemic sense. Thus the duality of probability was preserved by the duality
of possibility.
15 Inductive logic
Leibniz anticipated Carnap’s notion of inductive logic. He could do so because of the central place
occupied by the concept of possibility in his scheme of metaphysics. Within that scheme, a global
system of inductive logic makes more sense than Carnap’s does in our modern metaphysics.
16 The art of conjecturing (1692[?] published 1713)
The emergence of probability is completed with Jacques Bernoulli’s book, which both undertakes a
self-conscious analysis of the concept of probability, and proves the first limit theorem.
17 The first limit theorem
The possible interpretations of Bernoulli’s theorem are described.
18 Design
The English conception of probability in the early eighteenth century, guided by the Newtonian
philosophy espoused by members of the Royal Society, interprets the stability of stochastic processes
proven by the limit theorems as evidence of divine design.
19 Induction (1737)
Hume’s sceptical problem of induction could not have arisen much before 1660, for there was no
concept of inductive evidence in terms of which to raise it. Why did it have to wait until 1737? So long
as it was still believed that demonstrative knowledge was possible, a knowledge in which causes were
proved from first principles, then Hume’s argument could always be stopped. It was necessary that the
distinction between opinion and knowledge should become a matter of degree. That means that high
distinction between opinion and knowledge should become a matter of degree. That means that high
and low science had to collapse into one another. This had been an ongoing process throughout the
seventeenth century. It was formalized by Berkeley who said that all causes were merely signs. Causes
had been the prerogative of high science, and signs the tool of the low. Berkeley identified them and
Hume thereby became possible.
Bibliography
Index
INTRODUCTION 2006: THE ARCHAEOLOGY OF
PROBABLE REASONING
After 1975: histories of probability and statistics
This book happened to be the first in a wave of new studies of probability and its
past. Such work was soon to be cultivated by a research group at the Zentrum für
interdisziplinäre Forshchung in Bielefeld, 1982–3. Lorenz Krüger gathered
together twenty-odd scholars, many of them young and working on their first
major project. Such groups seldom gel. Krüger’s did – thanks to his planning
and leadership, and his own exceptional character. The subject was changed
permanently, and not only by the in-house publications emanating from
Bielefeld.1 New benchmarks were established, starting with books by members
of the group: Ted Porter’s The Rise of Statistical Thinking 1820–1900 (Princeton
1986), Steve Stigler’s The History of Statistics: The Measurement of Uncertainty
before 1900 (Chicago 1986), Raine Daston’s Classical Probability in the
Enlightenment (Princeton 1988). Add in my own Taming of Chance (Cambridge
1990) and you have the start of an amazing little library.
Doubtless the take-off in history would have occurred without this collective
activity. Much of the work published directly after 1983 was already in
preparation before Lorenz brought us together in Bielefeld. Donald Mackenzie
had already written Statistics in Britain 1865–1930: The Social Construction of
Scientific Knowledge (Edinburgh 1981). And I should mention an amusing
reminder that many more minds were out there. English-speakers at Bielefeld
met regularly to try to improve our German. We mostly read lesser works of
Robert Musil, under the guidance of Christa Krüger. We never thought about
how probability and The Man without Qualities might be connected. It was left
to Jacques Bouveresse’s amazing book to show us what had been before our
faces.2
Bielefeld was an extraordinary catalyst, and I am enormously grateful for
having had the opportunity to work with such colleagues. Since then, histories of
probability have become part of the history of science, and of science studies
more generally. Cultural studies have become aware. This is hardly surprising,
for probability is part of how we think about our chancy world. Literary critics
are beginning to acknowledge that fact. The writing has been on the wall for
some time. The last chapter of Taming ended by invoking Mallarmé’s poem of
1897, A throw of the die, which begins by swearing that we ‘NEVER will annul
chance’.
When The Emergence of Probability was published, there was little recent
history of probability besides the excellent mathematical histories by Oscar
Sheynin. Now there is plenty. But Emergence was not written as history.
Archaeology
Emergence is about the past, yes, but it is subtitled A Philosophical Study. I
never called it history. It was the first long piece of writing, in any language, that
captured, adapted and applied the new kind of analysis that Michel Foucault
called archaeology. At the time, few readers who came across the book were
familiar with his work. Today his achievements are almost too well known,
beloved by some, loathed by others. I continue to be a fan, but I have no
intention of writing about Foucault. I continue to use him in my own way, with
no thought about whether I am faithful to the traditions he began. I shall say just
enough about them to frame The Emergence of Probability.
Les Mots et les choses came out in 1966. Its translation, The Order of Things,
was published in 1970. Foucault began by thinking of this project as ‘his book
about signs’.3 That was how I read the first part of his book, as is pretty obvious
in my first few chapters. I hardly ever acknowledged debts to Foucault, because
I wrongly thought they were obvious and did not need stating. Moreover I did
not want to appear merely trendy. His name appears only twice in the index.
Soon after the book was published, I happened to read this sentence in some
notes on the book written by Anne Fagot-Largeault: ‘An investigation in the
style of Michel Foucault, though a great deal more clear.’ I mentioned this
pleasing remark in a 1978 report on work in progress, called ‘From the
emergence of probability to the erosion of determinism’ which also gives a brief
summary of my debt to Foucault as I saw it then.4 ‘The erosion of determinism’
– I was obviously already at work on Taming. The summary of that book begins,
‘Determinism was eroded during the 19th century and a space was cleared for
autonomous laws of chance.’5
In May 1974, the year that Emergence went to press, I gave a talk to the Moral
Sciences Club in Cambridge called ‘One way to do philosophy’. It was an
account of how an analytic philosopher trained at Cambridge University in the
shadows of G. E. Moore and the rest could learn a new approach to conceptual
analysis of problematic concepts – such as probability.6 The version of