A Note on Nathanial’s Invariance Principle in Polyadic Inductive Logic

Paris, Jeffrey; Vencovská, Alena

doi:10.1007/978-3-642-18026-2_12

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The Polyadic Case1

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2019

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“…In this case too, equivalent forms of the Invariance Under Translation Principle already exist in the literature, see (Paris and Vencovská 2015, Chapters 39, 40;Paris and Vencovská 2011;Ronel and Vencovská 2014). Most directly, the principle is equivalent to the the Permutation Invariance Principle, PIP.…”

Section: The Polyadic Casementioning

confidence: 94%

Translation Invariance and Miller’s Weather Example

Paris

Vencovská

2019

J of Log Lang and Inf

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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.

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Section: The Polyadic Casementioning

confidence: 94%