Translation Invariance and Miller's Weather Example

Jeffrey Paris, Alena Vencovska

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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 awed 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.
    Original languageEnglish
    JournalJournal of Logic, Language and Information
    DOIs
    Publication statusPublished - 13 May 2019

    Keywords

    • Miller'sWeather Example
    • Verisimilitude for relations
    • Translation Invariance
    • Renaming Invariance
    • Pure Inductive Logic
    • Uncertain Reasoning.

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