## Janus-Faced ProbabilityThe 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. |

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### Contents

1 | |

2 | |

3 | |

9 | |

3 Probability Validation | 23 |

4 About the Compatibility of the Diverging Interpretations | 39 |

5 Criticism on the Philosophical Pollution | 45 |

Part II Considerations Around the Probability Axiomatization
| 58 |

7 Classical Modeling of the Probability Argument | 69 |

8 Structural Modeling of the Probability Argument | 77 |

9 Some Topics on Probability and Structural Models | 91 |

10 Exploring into the Essence of Events | 103 |

Appendix A Interpretations of ProbabilityAn Outline
| 113 |

Pluralist WorksA Partial Bibliography
| 135 |

Law of Large NumbersA Proof | 139 |

144 | |

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### Common terms and phrases

abstract analysis applications approach argument of probability assumptions axioms Bayesian networks Bayesian statistics belief Bernoulli Bernoulli trials Bruno de Finetti Carnap classical conclusion conditional probability ð Þ decision theory definition of probability equation example experiment Finetti frequentist function graph hypothesis indeterminate inference International Publishing Switzerland interpretations of probability Janus-Faced Probability Keynes Kolmogorov Laplace large numbers law of large mathematical mathematicians means measure methods Mises notion number of trials Ó Springer International objective occurs outcome P(An PAðÞ parameters Pascal philosophical physical pluralist Popper principle Probabilités probability calculus probability theory problem propensity Publishing Switzerland 2014 quantum quantum mechanics Ramsey random event random variables relationship relative frequency result Richard von Mises Rocchi sample scientific sequence significant single event single number Springer International Publishing statisticians structural model subjective probability subjectivist theorem of large theorists theory of probability thinkers University Press