An objective theory of probability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Methuen
1973
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 250 S. |
| ISBN: | 0416773508 |
Internformat
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| 245 | 1 | 0 | |a An objective theory of probability |c D. A. Gillies |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface page ix
Introduction 1
Von Mises theory of probability, p. 1; Keynes theory of
probability, p. 7; Comparison between von Mises and
Keynes, p. 14; Development of the logical tradition after
Keynes, p. 15; Characterization of the scientific approach,
p. 25; The two concept view, p. 27; General outline of the
book, p. 31.
PART i: THE SPECIAL SCIENCES
IN GENERAL
1 Von Mises Philosophy of Science: Its Machian Origins 37
Mach s development of mechanics, p. 38; Operationalism,
p. 42; Some objections to operationalism, p. 44.
2 Force and Mass 48
The concepts of force and mass before Newton, p. 48; How
Newton introduced the concepts of force and mass, p. 50;
The moon test of the law of gravity, p. 54; How force and
mass came to be measurable, p. 57.
3 Conceptual Innovation in the Exact Sciences 59
Another illustration of conceptual innovation: the concept
of temperature, p. 59; General theory of conceptual innova¬
tion, p. 63; How our theory of conceptual innovation avoids
the difficulties in operationalism, p. 63; A digression on
testing and accepting scientific theories, p. 65; The
problem of depth, p. 69; The generalized principle of
correspondence and related questions, p. 71; How the
ideas of Part I will be applied to the theory of probability,
p. 73.
vi Contents
PART n: THE AXIOMATIC SUPERSTRUCTURE
4 Probability and Frequency 77
Three views on the relations between probability and
frequency, p. 77; Randomness in von Mises theory, p. 82;
Comparison between von Mises and Kolmogorov, p. 87;
Two criticisms of Kolmogorov by von Mises, p. 89.
5 Repeatability and Independence 94
Analysis of repeatability, p. 94; Repeatable conditions with
dependent outcomes, p. 97; Arguments against the axiom
of independent repetitions, p. 99; Main argument for the
axiom of independent repetitions, p. 101; Derivation of the
law of stability of statistical frequencies, p. 103; Comparison
with Newtonian mechanics, p. 107; Criticism of the views of
von Mises and Kolmogorov on the relations between proba¬
bility and frequency, p. 108; An answer to some arguments
of Doob s, p. 110; Criticism of the laws of large numbers
view, p. 112; The significance of the laws of large numbers,
p. 116.
6 Deduction of the Law of Excluded Gambling Systems:
The Role of Randomness in Probability Theory 119
Deduction of the law of excluded gambling systems, p. 119;
Independence and gambling systems, p. 120; A practical
example, p. 124; Definition of random sequences and their
generation in practice, p. 127; Relation to randomness as
denned in the frequency theory, p. 130; Answer to an objec¬
tion of Braithwaite s, p. 132; Probability theory and de¬
terminism, p. 133; Discussion of some arguments of
Khintchine s, p. 134; Possible modifications of the axioms
of probability in the light of experience, p. 137.
7 Probabilities of Single Events .Popper s Propensity Theory 140
Singular probabilities, p. 140; Popper s propensity theory,
p. 143; Similarities between Popper s propensity theory and
von Mises frequency theory, p. 147; A criticism of the
propensity theory, p. 149; Another argument for the axiom
of independent repetitions, p. 150; Discussion of a possible
simplification, p. 153; An answer to some objections of
Ayer s, p. 156.
Contents vii
PAET III: A FALSIFYING KTTLE FOE PKOBABILITY
STATEMENTS
8 The Falsification Problem for Probability Statements 161
Statement of the problem, p. 161; Popper s proposed solu¬
tion, p. 162; The problem of producing an F.R.P.S., p. 163;
Some notes on the history of the problem, p. 164.
9 Formulation of a Falsifying Rule 167
First version of the rule, p. 167; Second version of the rule,
p. 168; Third version of the rule, p. 169; Final version of the
rule, p. 171; Application of the rule to an important special
case, p. 173; Relation of the present approach to the
Neyman Pearson theory, p. 176.
10 Evaluation of the Falsifying Rule 180
Braithwaite s theory of probability: statement, p. 180;
Braithwaite s theory of probability: criticism, p. 182;
Possible ways of justifying the F.R.P.S., p. 186; The
practical success but inconsistency of the F.R.P.S., p. 187;
The F.R.P.S. in relation to the theory of errors, p. 191;
Resolution of a problem connected with the F.R.P.S., p. 193.
11 The Neyman Pearson Theory 195
Outline of the Neyman Pearson theory, p. 195; The
Neyman Pearson theory without an F.R.P.S., p. 199; The
Neyman Pearson theory with a falsifying rule, p. 202; Two
counter examples from statistical practice, p. 206; Quanti¬
tative versus qualitative considerations, p. 216; A reply to
some objections of Neyman s, p. 219.
Appendix: Explanation of Technical Terminology 227
References 239
Index to Appendix 245
General Index 247
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:46Z |
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| isbn | 0416773508 |
| language | English |
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| spelling | Gillies, Dee A. Verfasser aut An objective theory of probability D. A. Gillies 1. publ. London Methuen 1973 X, 250 S. txt rdacontent n rdamedia nc rdacarrier Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001271673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gillies, Dee A. An objective theory of probability Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | An objective theory of probability |
| title_auth | An objective theory of probability |
| title_exact_search | An objective theory of probability |
| title_full | An objective theory of probability D. A. Gillies |
| title_fullStr | An objective theory of probability D. A. Gillies |
| title_full_unstemmed | An objective theory of probability D. A. Gillies |
| title_short | An objective theory of probability |
| title_sort | an objective theory of probability |
| topic | Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Probabilities Wahrscheinlichkeitstheorie |
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