Translation Invariance and Miller's Weather Example

Paris, Jeff and Vencovska, Alena (2017) Translation Invariance and Miller's Weather Example. [MIMS Preprint]

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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 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.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Miller's Weather Example; Verisimilitude for relations; Translation Invariance; Renaming Invariance; Pure Inductive Logic; Uncertain Reasoning.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 03 Mathematical logic and foundations MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User:	Dr Alena Vencovska
Date Deposited:	18 May 2017
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2553

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