(Cambridge Series on Statistical & Probabilistic Mathematics)
Ian Hacking | 2006 | 246 páginas | DjVu (3 mb)
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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 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. Hacking invokes a wide 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. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009.
CONTENTS
Introduction 2006 page xi
1 An absent family of ideas 1
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 11
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 18
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 31
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 39
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
Contents
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 49
Some isolated calculations on chances, made before 1660, are briefly
described.
7 The Roannez circle (1654) 57
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?) 63
'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) 73
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) 85
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) 92
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) 102
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) 111
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) 122
The definition of probability as a ratio among 'equally possible cases1
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 134
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) 143
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 154
The possible interpretations of Bernoulli's theorem are described.
18 Design 166
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) 176
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 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 186
Index 203
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