Infinitesimal Probabilities

1 Introduction; 2 The Limits of Classical Probability Theory:   2.1 Classical probability functions;   2.2 Limitations;   2.3 Infinitesimals to the rescue? 3 NAP Theory:   3.1 First four axioms of NAP;   3.2 Continuity and conditional probability;   3.3 The final axiom of NAP;   3.4 Infinite sums;  ...

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Detalles Bibliográficos
Autores principales: Benci, Vieri, Horsten, Leon, Wenmackers, Sylvia
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Oxford University Press 2018
Materias:
Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6012604/
https://www.ncbi.nlm.nih.gov/pubmed/29977092
http://dx.doi.org/10.1093/bjps/axw013
Descripción
Sumario:1 Introduction; 2 The Limits of Classical Probability Theory:   2.1 Classical probability functions;   2.2 Limitations;   2.3 Infinitesimals to the rescue? 3 NAP Theory:   3.1 First four axioms of NAP;   3.2 Continuity and conditional probability;   3.3 The final axiom of NAP;   3.4 Infinite sums;   3.5 Definition of NAP functions via infinite sums;   3.6 Relation to numerosity theory; 4 Objections and Replies:   4.1 Cantor and the Archimedean property;   4.2 Ticket missing from an infinite lottery;   4.3 Williamson’s infinite sequence of coin tosses;   4.4 Point sets on a circle;   4.5 Easwaran and Pruss; 5 Dividends:   5.1 Measure and utility;   5.2 Regularity and uniformity;   5.3 Credence and chance;   5.4 Conditional probability; 6 General Considerations:   6.1 Non-uniqueness;   6.2 Invariance. Appendix .

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