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Translation Invariance and Miller’s Weather Example
Journal of Logic, Language and Information ( IF 0.8 ) Pub Date : 2019-05-13 , DOI: 10.1007/s10849-019-09291-6
J. B. Paris , A. Vencovská

In his 1974 paper “Popper’s qualitative theory of verisimilitude” published in the British Journal for the Philosophy of Science David Miller gave his so called ‘Weather Example’ to argue that the Hamming distance between constituents is flawed as a measure of proximity to truth since the former is not, unlike the latter, translation invariant. In this present paper we generalise David Miller’s Weather Example in both the unary and polyadic cases, characterising precisely which permutations of constituents/atoms can be effected by translations. In turn this suggests a meta-principle of the rational assignment of subjective probabilities, that rational principles should be preserved under translations, which we formalise and give a particular characterisation of in the context of Unary Pure Inductive Logic.

中文翻译:

平移不变性和米勒天气示例

在他 1974 年发表在英国科学哲学杂志上的论文“波普尔的真实性定性理论”中,大卫米勒给出了他所谓的“天气例子”,以论证成分之间的汉明距离作为接近真相的衡量标准是有缺陷的,因为与后者不同,前者不是平移不变的。在本文中,我们将大卫米勒的天气例子推广到一元和多元情况下,准确描述了哪些成分/原子的排列可以受到翻译影响。反过来,这表明主观概率的理性分配的元原则,即理性原则应保留在翻译中,我们将其形式化并在一元纯归纳逻辑的上下文中给出特定特征。
更新日期:2019-05-13
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