Translation Invariance and Miller's Weather Example

Alena Vencovska (Manchester)

Frank Adams 1,

In his 1974 paper ``Popper's Qualitative Theory of Verisimilitude"  David Miller gave an example to argue that the Hamming distance between constituents is flawed as a measure of  proximity to truth since it is not translation-invariant. His example is in propositional logic but it can serve equally for full descriptions of one individual in monadic predicate logic. I shall explain the example and the theory behind it and proceed to show what happens when we consider languages with relations of higher arities. I shall also outline the relevance of this research to the problem of rational assignment of subjective probabilities.

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