The Science of Conjecture: Evidence and Probability before Pascal

520 Pages·4.647 MB·English

by  James Franklin

The Science
of Conjecture
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The Science
of Conjecture
Evidence and Probability
before Pascal
With a New Preface
James Franklin
Johns Hopkins University Press
Baltimore
© 2001, 2012, 2015The Johns Hopkins University Press
All rights reserved. Published 2001
Johns Hopkins Paperbacks edition, 2002, 2015
Printed in the United States of America on acid-free paper
2 4 6 8 9 7 5 3 1
Johns Hopkins University Press
2715North Charles Street
Baltimore, Maryland 21218-4363
www.press.jhu.edu
The Library of Congress has cataloged the hardcover
edition of this book as follows:
Franklin, James, 1953–
The science of conjecture : evidence and probability before Pascal /
James Franklin.
p. cm.
Includes bibliographical references and index.
ISBN 0-8018-6569-7(alk. paper)
1. Probabilities—History. 2. Evidence—History. I. Title.
QA273.A4F73 2001
519.¢09—dc21 00-042429
ISBN 978-1-4214-1880-3
A catalog record for this book is available
from the British Library.
Errata
P. 130The discovery of the black swan dates to after Burgersdijck’s Logic.
P. 177The procedure involving random sampling was a quality-control
method in the Mint, but not the one called the trial of the pyx.
Contents
Preface to the 2015 Edition ix
Preface xvii
1. The Ancient Law of Proof 1
Egypt and Mesopotamia 1; The Talmud 3; Roman Law: Proof and
Presumptions 7; Indian Law 10
2. The Medieval Law of Evidence: Suspicion, Half-proof,
and Inquisition 12
Dark Age Ordeals 12; The Gregorian Revolution 14; The Glossators
Invent Half-proof 15; Presumptions in Canon Law 20; Grades of
Evidence and Torture 24; The Postglossators Bartolus and Baldus:
The Completed Theory 28; The Inquisition 33; Law in the East 37
3. Renaissance Law 40
Henry VIII Presumed Wed 40; Tudor Treason Trials 41; Continental
Law: The Treatises on Presumptions 43; The Witch Inquisitors 47;
English Legal Theory and the Reasonable Man 58
4. The Doubting Conscience and Moral Certainty 64
Penance and Doubts 65; The Doctrine of Probabilism 69; Suarez:
Negative and Positive Doubt 76; Grotius, Silhon, and the Morality of
the State 79; Hobbes and the Risk of Attack 81; The Scandal of Lax-
ism 83; English Casuists Pursue the Middle Way 84; Juan Caramuel
Lobkowitz, Prince of Laxists 88; Pascal’s Provincial Letters 94
5. Rhetoric, Logic, Theory 102
The Greek Vocabulary of Probability 103; The Sophists Sell the Art
of Persuasion 104; Aristotle’s Rhetoricand Logic 109; The Rhetoric to
Alexander 114; Roman Rhetoric: Cicero and Quintilian 116; Islamic
Logic 120; The Scholastic Dialectical Syllogism 121; Probability in
Ordinary Language 126; Humanist Rhetoric 127; Late Scholastic
Logics 129
vi Contents
6. Hard Science 131
Observation and Theory 132;Aristotle’s Not-by-Chance Argument
133; Averaging of Observations in Greek Astronomy 134; The Sim-
plicity of Theories 138; Nicole Oresme on Relative Frequency 140;
Copernicus 145; Kepler Harmonizes Observations 147; Galileo on the
Probability of the Copernican Hypothesis 154
7. Soft Science and History 162
The Physiognomics 162; Divination and Astrology 164; The Empiric
School of Medicine on Drug Testing 165; The Talmud and Mai-
monides on Majorities 172; Vernacular Averaging and Quality Control
175; Experimentation in Biology 177; The Authority of Histories 180;
The Authenticity of Documents 184; Valla and the Donation of Constan-
tine 187; Cano on the Signs of True Histories 192
8. Philosophy: Action and Induction 195
Carneades’s Mitigated Skepticism 196; The Epicureans on Inference
from Signs 200; Inductive Skepticism and Avicenna’s Reply 202;
Aquinas on Tendencies 203; Scotus and Ockham on Induction 206;
Nicholas of Autrecourt 210; The Decline of the West 216; Bacon and
Descartes: Certainty? or Moral Certainty? 217; The Jesuits and Hobbes
on Induction 222; Pascal’s Deductivist Philosophy of Science 224
9. Religion: Laws of God, Laws of Nature 228
The Argument from Design 228; The Church Fathers 230; Inductive
Skepticism by Revelation 232; John of Salisbury 233; Maimonides on
Creation 235; Are Laws of Nature Necessary? 237; The Reasonable-
ness of Christianity 242; Pascal’s Wager 249
10. Aleatory Contracts: Insurance, Annuities, and Bets 258
The Price of Peril 259; Doubtful Claims in Jewish Law 261; Olivi on
Usury and Future Profits 262; Pricing Life Annuities 269; Speculation
in Public Debt 272; Insurance Rates 273; Renaissance Bets and Specu-
lation 278; Lots and Lotteries 283; Commerce and the Casuists 285
11. Dice 289
Games of Chance in Antiquity 289; The Medieval Manuscript on the
Interrupted Game 291; Cardano 296; Gamblers and Casuists 300;
Galileo’s Fragment 302; De Méré and Roberval 302; The Fermat-
Contents vii
Pascal Correspondence 306; Huygens’ Reckoning in Games of Chance
313; Caramuel 316
12. Conclusion 321
Subsymbolic Probability and the Transition to Symbols 324; Kinds of
Probability and the Stages in Discovering Them 326; Why Not Ear-
lier? 330; Two Parallel Histories 340; The Genius of the Scholastics
and the Orbit of Aristotle 343; The Place of Law in the History of Ideas
348; Conclusion and Moral 360
Epilogue: The Survival of Unquantified Probability 362
The Port-RoyalLogic 362; Leibniz’s Logic of Probability 363; To the
Present 365
Appendix: Review of Work on Probability before 1660
373
Notes 385
Index 487
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Preface to the 2015 Edition
The first edition of The Science of Conjecturereconfigured the field of the
history of probability in two ways. The first concerned a wider than
usual conception of the nature of probability. The second involved a
Renaissance-free view of the history of Western ideas. In the decade
since the book’s publication, the first of these has gained traction, the
second has not.
The book’s conception of the subject matter stemmed from an ob-
jective Bayesian(or logical probabilist) theory of probability. According
to that theory, as developed by Keynes in his Treatise on Probabilityand
by later authors,1the main notion of probability is of an objective logi-
cal relation holding between a body of evidence and a conclusion. The
body of evidence available in court does or does not make the defen-
dant’s guilt highly probable; the known facts do or do not support the
theory of global warming, irrespective of any contingent facts about the
world or what anyone’s opinion is. Logical probability may or may not
be numerical; even if it is, qualitative or approximate judgments are
often of most importance.
That perspective opened up all kinds of evaluation of uncertain evi-
dence as the natural subject matter of a history of probability. Thus, The
Science of Conjecture focused on the law of evidence, which, over many
centuries of thought, especially in medieval Roman law, had developed
evidential concepts like the modern proof beyond reasonable doubt.
Moral theory and business were also familiar with concepts of proba-
bilities and risks, mostly quantified only loosely.
During the late twentieth century, debate on “interpretations of
probability” largely took the form of pitched battles between frequen-
tists and related schools (who held that probability dealt with relative
frequencies or objective propensities) and subjective Bayesians (who
took probability to be about degrees of belief, subject to some con-
1. The classic works are J. M. Keynes, A Treatise on Probability (London,
1921) and E. T. Jaynes, Probability Theory: The Logic of Science (Cambridge,
2003).
ix