论文标题
在对称下的非古典概率不变[校正]
Non-Classical Probabilities Invariant Under Symmetries [corrected]
论文作者
论文摘要
经典的添加性实用值的概率是以哲学成本的：在许多无限情况下，它们为不可能的情况以及可能的情况分配了相同的概率价值（即零）。有三种非古典方法可以避免这种缺点：完整的条件概率，定性概率和超现实概率。这些方法因未能保留很容易通过经典概率框架来保存的直觉对称性而受到批评，但没有系统地研究这些对称性可以而且不能保留这些对称性的条件。本文通过给出完整的特征来填补这一空白，根据这些特征，这些非古典概率可以保留以某种“强”方式理解的对称性，以及通过提供一些结果以使这里的对称性强大的概念可能是正确的一种。简要讨论了哲学的含义，但本文的主要目的是提供技术结果，以告知更复杂的进一步哲学讨论。
Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value -- namely, zero -- to cases that are impossible as well as to cases that are possible. There are three non-classical approaches to probability that can avoid this drawback: full conditional probabilities, qualitative probabilities and hyperreal probabilities. These approaches have been criticized for failing to preserve intuitive symmetries that can easily be preserved by the classical probability framework, but there has not been a systematic study of the conditions under which these symmetries can and cannot be preserved. This paper fills that gap by giving complete characterizations under which symmetries understood in a certain "strong" way can be preserved by these non-classical probabilities, as well as by offering some results to make it plausible that the strong notion of symmetry here may be the right one. Philosophical implications are briefly discussed, but the main purpose of the paper is to offer technical results to inform more sophisticated further philosophical discussion.
