Janus-Faced Probability

1. Front Matter

   Pages i-xiii

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2. On the Meaning of Probability

   1. Front Matter

      Pages 1-1

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   2. Interpretations of Probability

      • Paolo Rocchi

      Pages 3-8

   3. A Mathematical Approach to the Interpretation Problem

      • Paolo Rocchi

      Pages 9-22

   4. Probability Validation

      • Paolo Rocchi

      Pages 23-37

   5. About the Compatibility of the Diverging Interpretations

      • Paolo Rocchi

      Pages 39-44

   6. Criticism on the Philosophical Pollution

      • Paolo Rocchi

      Pages 45-55

3. Considerations Around the Probability Axiomatization

   1. Front Matter

      Pages 57-57

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   2. Some Remarks on the Argument of Probability

      • Paolo Rocchi

      Pages 59-67

   3. Classical Modeling of the Probability Argument

      • Paolo Rocchi

      Pages 69-76

   4. Structural Modeling of the Probability Argument

      • Paolo Rocchi

      Pages 77-89

   5. Some Topics on Probability and Structural Models

      • Paolo Rocchi

      Pages 91-102

   6. Exploring into the Essence of Events

      • Paolo Rocchi

      Pages 103-112

4. Back Matter

   Pages 113-147

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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.

• frequentist theory
• probability interpretation
• subjective theory

“I highly recommend this book for those readers interested in an accessible introduction to the problems related to the foundations of probability theory and statistics, with a very interesting compilation of references on the subject. Beside this, the ideas presented in the book open the door to interesting research inquiries in the field, especially those related to the foundations of quantum probability theory, quantum information theory and quantum statistical techniques.” (Federico Holik, Mathematical Reviews, December, 2015)

“Rocchi (IBM and LUISS Univ., Italy) begins by discussing two of these, the frequentist and the subjectivist approaches. … Each of the book's ten chapters ends with a list of recent papers on the topic, and the book ends with an interesting series of three appendixes. … This specialized work will mainly appeal to philosophers of probability. Summing Up: Recommended. Only comprehensive mathematics collections serving researchers/faculty.” (M. Bona, Choice, Vol. 52 (9), May, 2015)

• CeRSI, LUISS, Guido Carli University, Roma, Italy

  Paolo Rocchi

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.

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