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  1.  87
    Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
    Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _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 (...)
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  2. Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
    We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by (...)
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  3.  31
    An Aristotelian Notion of Size.Vieri Benci, Mauro Di Nasso & Marco Forti - 2006 - Annals of Pure and Applied Logic 143 (1-3):43-53.
    The naïve idea of “size” for collections seems to obey both Aristotle’s Principle: “the whole is greater than its parts” and Cantor’s Principle: “1-to-1 correspondences preserve size”. Notoriously, Aristotle’s and Cantor’s principles are incompatible for infinite collections. Cantor’s theory of cardinalities weakens the former principle to “the part is not greater than the whole”, but the outcoming cardinal arithmetic is very unusual. It does not allow for inverse operations, and so there is no direct way of introducing infinitesimal numbers. Here (...)
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  4. An Euclidean Measure of Size for Mathematical Universes.Vieri Benci, Mauro Nasso & Marco Forti - 2007 - Logique Et Analyse 50.
  5. Axioms for Non-Archimedean Probability (NAP).Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2012 - In De Vuyst J. & Demey L. (eds.), Future Directions for Logic; Proceedings of PhDs in Logic III - Vol. 2 of IfColog Proceedings. College Publications.
    In this contribution, we focus on probabilistic problems with a denumerably or non-denumerably infinite number of possible outcomes. Kolmogorov (1933) provided an axiomatic basis for probability theory, presented as a part of measure theory, which is a branch of standard analysis or calculus. Since standard analysis does not allow for non-Archimedean quantities (i.e. infinitesimals), we may call Kolmogorov's approach "Archimedean probability theory". We show that allowing non-Archimedean probability values may have considerable epistemological advantages in the infinite case. The current paper (...)
     
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  6.  72
    A New Variational Principle for the Fundamental Equations of Classical Physics.Vieri Benci & Donato Fortunato - 1998 - Foundations of Physics 28 (2):333-352.
    In this paper we introduce a variational principle from which the fundamental equations of classical physics can be deduced. This principle permits a sort of unification of the gravitational and the electromagnetic fields. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter a which carries some physical information, namely it is related to the rest mass and to the charge. In particular, the (inertial) rest mass will not be a (...)
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  7.  67
    Quantum Phenomena in a Classical Model.Vieri Benci - 1999 - Foundations of Physics 29 (1):1-28.
    This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.
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