The emergence of probability: a philosophical study of early ideas about probability, induction and statistical inference
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 2. ed., repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 187-202) and index |
| Physical Description: | XXXIII, 209 S. 23 cm |
| ISBN: | 9780521866552 9780521685573 0521866553 0521685575 |
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Record in the Search Index
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| adam_text | 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.
Contents
14 Equipossibility (1678) 122
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
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
|
| any_adam_object | 1 |
| author | Hacking, Ian 1936-2023 |
| author_GND | (DE-588)121208354 |
| author_facet | Hacking, Ian 1936-2023 |
| author_role | aut |
| author_sort | Hacking, Ian 1936-2023 |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | PHI 350f MAT 600f WIS 375f MAT 030f |
| ctrlnum | (OCoLC)694977683 (DE-599)BVBBV037411665 |
| dewey-full | 519.209 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.209 |
| dewey-search | 519.209 |
| dewey-sort | 3519.209 |
| dewey-tens | 510 - Mathematics |
| discipline | Psychologie Mathematik Philosophie / Ethik Wirtschaftswissenschaften Wissenschaftskunde |
| edition | 2. ed., repr. |
| era | Geschichte 1660-1740 gnd Ideengeschichte 1600-1740 gnd Geschichte 1600-1740 gnd Geschichte gnd |
| era_facet | Geschichte 1660-1740 Ideengeschichte 1600-1740 Geschichte 1600-1740 Geschichte |
| format | Book |
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| id | DE-604.BV037411665 |
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| spelling | Hacking, Ian 1936-2023 Verfasser (DE-588)121208354 aut The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference Ian Hacking 2. ed., repr. Cambridge [u.a.] Cambridge Univ. Press 2007 XXXIII, 209 S. 23 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 187-202) and index Geschichte 1660-1740 gnd rswk-swf Ideengeschichte 1600-1740 gnd rswk-swf Geschichte 1600-1740 gnd rswk-swf Geschichte gnd rswk-swf Geschichte Induction (Mathematics) History Mathematical statistics History Probabilities History Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Geschichte 1600-1740 z DE-604 Wahrscheinlichkeit (DE-588)4137007-7 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Philosophie (DE-588)4045791-6 s Ideengeschichte 1600-1740 z 1\p DE-604 Geschichte 1660-1740 z 2\p DE-604 Geschichte z 3\p DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022564107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hacking, Ian 1936-2023 The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference Geschichte Induction (Mathematics) History Mathematical statistics History Probabilities History Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4137007-7 (DE-588)4064324-4 (DE-588)4045791-6 |
| title | The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference |
| title_auth | The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference |
| title_exact_search | The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference |
| title_full | The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference Ian Hacking |
| title_fullStr | The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference Ian Hacking |
| title_full_unstemmed | The emergence of probability a philosophical study of early ideas about probability, induction and statistical inference Ian Hacking |
| title_short | The emergence of probability |
| title_sort | the emergence of probability a philosophical study of early ideas about probability induction and statistical inference |
| title_sub | a philosophical study of early ideas about probability, induction and statistical inference |
| topic | Geschichte Induction (Mathematics) History Mathematical statistics History Probabilities History Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Geschichte Induction (Mathematics) History Mathematical statistics History Probabilities History Wahrscheinlichkeitstheorie Wahrscheinlichkeit Wahrscheinlichkeitsrechnung Philosophie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022564107&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hackingian theemergenceofprobabilityaphilosophicalstudyofearlyideasaboutprobabilityinductionandstatisticalinference |