赋予不可测量集合不精确概率的后果

IF 1.8 1区哲学 0 PHILOSOPHY

MIND Pub Date : 2024-05-21 DOI:10.1093/mind/fzae023

Joshua Thong

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引用次数: 0

摘要

本文是关于 Isaacs、Hájek 和 Hawthorne (2022) 的讨论注释，该注释声称基于非可测性的数学现象，为不精确概率提供了一个新的动机。在本说明中，我将澄清该提议的一些后果。我特别指出，如果把该提议应用于有界三维空间，那么我们至少要拒绝以下其中之一：让 A∩C=B∩C=∅.当且仅当(A∪C)与(B∪C)的可能性最大时，A与B的可能性最大。但拒绝其中任何一种说法似乎都没有吸引力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Consequences of Assigning Non-Measurable Sets Imprecise Probabilities

This paper is a discussion note on Isaacs, Hájek and Hawthorne (2022), which claims to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of that proposal. In particular, I show that if the proposal is applied to a bounded 3-dimensional space, then one has to reject at least one of the following: If A is at most as probable as B and B is at most as probable as C, then A is at most as probable as C. • Let A∩C=B∩C=∅. A is at most as probable as B if and only if (A∪C) is at most as probable as (B∪C). But rejecting either statement seems unattractive.

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来源期刊

MIND PHILOSOPHY-

CiteScore

3.10

自引率

5.60%

发文量

期刊介绍： Mind has long been a leading journal in philosophy. For well over 100 years it has presented the best of cutting edge thought from epistemology, metaphysics, philosophy of language, philosophy of logic, and philosophy of mind. Mind continues its tradition of excellence today. Mind has always enjoyed a strong reputation for the high standards established by its editors and receives around 350 submissions each year. The editor seeks advice from a large number of expert referees, including members of the network of Associate Editors and his international advisers. Mind is published quarterly.