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Internality, transfer, and infinitesimal modeling of infinite processes†
Philosophia Mathematica ( IF 1.1 ) Pub Date : 2020-09-29 , DOI: 10.1093/philmat/nkaa033
Emanuele Bottazzi 1 , Mikhail G Katz 2
Affiliation  

A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson's transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields (surreals, Levi-Civita field, Laurent series) may have advantages over hyperreals in probabilistic modeling. We show that probabilities developed over such fields are less expressive than hyperreal probabilities.

中文翻译:

无限过程的内部性、传递和无穷小建模†

当没有合理的理由将特定的无穷小值指定为单个事件的概率时,概率模型是不确定的。普鲁斯声称超真实概率是不确定的。该声明基于外部超真实值度量。我们表明,内部超有限度量并不是不确定的。内部性的重要性源于这样一个事实,即罗宾逊转移原则仅适用于内部实体。我们还评估了无转移有序场(超现实、Levi-Civita 场、Laurent 系列)在概率建模中可能比超现实更具优势的说法。我们表明,在这些领域开发的概率不如超真实概率具有表现力。
更新日期:2020-09-29
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