Rocchi Janus-Faced Probability

1. Auflage 2014
ISBN: 978-3-319-04861-1
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 147 Seiten

Reihe: Mathematics and Statistics

The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability. Beyond the radical followers of the two schools, a circle of pluralist thinkers tends to reconcile the opposing concepts. The author uses two theorems in order to prove that the various interpretations of probability do come into opposition and can be used in different contexts. The goal here is to clarify the multi fold nature of probability by means of a purely mathematical approach and to show how philosophical arguments can only serve to deepen actual intellectual contrasts. The book can be considered as one of the most important contributions in the analysis of probability interpretation in the last 10-15 years.

Zielgruppe

Research

Autoren/Hrsg.

Rocchi, Paolo

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Introduction;11
4;Part I On the Meaning of Probability
;12
5;1 Interpretations of Probability;13
5.1;1.1…Variety of Theories;14
5.2;1.2…Pluralists;16
5.3;References;18
6;2 A Mathematical Approach to the Interpretation Problem;19
6.1;2.1…Why I am a Pluralist;19
6.2;2.2…Guidelines;20
6.3;2.3…An Analytical Approach;21
6.3.1;2.3.1 Theorem of Large Numbers (Strong);21
6.3.2;2.3.2 Theorem of a Single Number;22
6.4;2.4…Two Remarks on Mathematics and Science;22
6.4.1;2.4.1 Physical Mapping;22
6.4.2;2.4.2 Division of Labor;26
6.5;2.5…Different Arguments, Different Probabilities;27
6.6;References;31
7;3 Probability Validation;33
7.1;3.1…A Parameter that Cannot be Validated Does Not Exist;33
7.2;3.2…Theoretical Proof and Empirical Validation;34
7.3;3.3…From Controllability to Realism;35
7.3.1;3.3.1 Statistics of Long-Term Events;36
7.4;3.4…From Uncontrollability to Unrealism;37
7.4.1;3.4.1 Statistics of Single Events;40
7.5;3.5…Sorry Science;41
7.5.1;3.5.1 Severe Constraint;42
7.5.2;3.5.2 Opponents to Unrealism;43
7.5.3;3.5.3 Things are No Longer the Same;44
7.6;3.6…Closing Remarks;45
7.7;References;46
8;4 About the Compatibility of the Diverging Interpretations;48
8.1;4.1…Not Contradictory Approaches;48
8.2;4.2…Method of Working;49
8.2.1;4.2.1 Lemma of Obligatory Subjectivism;49
8.2.2;4.2.2 Mutually Exclusive Tactics;50
8.3;References;53
9;5 Criticism on the Philosophical Pollution;54
9.1;5.1…Analytical Assumptions;54
9.2;5.2…Separation of Areas;55
9.3;5.3…Inclusiveness;55
9.4;5.4…Terms of Comparison;56
9.5;5.5…Moderated Debates;59
9.5.1;5.5.1 Death of Dogmatism;59
9.5.2;5.5.2 Empirical Problem Solving;61
9.6;5.6…Open Doors;63
9.7;References;64
10;Part II Considerations Around the Probability Axiomatization
;65
11;6 Some Remarks on the Argument of Probability;66
11.1;6.1…Abstract Axioms;66
11.2;6.2…System Modeling;67
11.2.1;6.2.1 DFDs;68
11.2.2;6.2.2 ERD;69
11.3;6.3…A Negligible Topic?;69
11.3.1;6.3.1 Famous Correspondence;70
11.3.2;6.3.2 Pascal’s Conjecture;70
11.4;References;73
12;7 Classical Modeling of the Probability Argument;75
12.1;7.1…Subset;75
12.2;7.2…Sentence;77
12.3;7.3…Precise and Generic Arguments;80
13;8 Structural Modeling of the Probability Argument;83
13.1;8.1…Structural Model;83
13.1.1;8.1.1 Graph Model;84
13.1.2;8.1.2 Algebraic Model;84
13.1.3;8.1.3 Use of the Structural Model;86
13.2;8.2…Compound Structures;87
13.2.1;8.2.1 Meta-Relationships;87
13.2.2;8.2.2 Basic Structural Forms;89
13.3;8.3…Structure of Levels;91
13.3.1;8.3.1 A Case;93
13.4;References;94
14;9 Some Topics on Probability and Structural Models;96
14.1;9.1…Demanding Structural Analysis;96
14.2;9.2…Illustration of Events;97
14.2.1;9.2.1 Complete Structure;98
14.2.2;9.2.2 Incomplete Structure;99
14.2.3;9.2.3 Ignorance, Uncertainty and Perfect Knowledge;100
14.2.4;9.2.4 Structures and Probability;101
14.3;9.3…In Search of a Precise Argument;102
14.3.1;9.3.1 Experiments;102
14.3.2;9.3.2 Classical Definition;103
14.3.3;9.3.3 Definitional Arguments of Probability;105
14.3.4;9.3.4 Useful Arguments of Probability;105
14.4;References;107
15;10 Exploring into the Essence of Events;108
15.1;10.1…The Core;109
15.1.1;10.1.1 Equivocal Description;109
15.1.2;10.1.2 More or Less Steady;111
15.1.3;10.1.3 Multiplication Law;113
15.1.4;10.1.4 Addition Law;114
15.2;10.2…About Event’s Outcome;115
15.3;10.3…Final Remark;116
15.4;References;117
16;Appendix A Interpretations of Probability—An Outline
;118
17;Appendix B: Pluralist Works—A Partial Bibliography
;140
18;Appendix C: Law of Large Numbers—A Proof;143
19;Index;148

Über Autor(innen)

Prof. Rocchi has already produced original proposals in various research fields such as computing, reliability theory, didactics and software programming and this book also suggests a creative solution.