Some observations on truth hierarchies

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We show how in the hierarchies FÆ of Fieldian truth sets, and Herzberger’s HÆ revision sequence starting from any hypothesis for F0 (or H0) that essentially each HÆ (or FÆ) carries within it a history of the whole prior revision process.
As applications (1) we provide a precise representation for, and a calculation of the length of, possible path independent determinateness hierarchies of Field’s construction in [4] with a binary conditional operator. (2) We demonstrate the existence of generalised liar sentences, that can be considered as diagonalising past the determinateness hierarchies definable in Field’s recent models. The ‘defectiveness’ of such diagonal
sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of [4] that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’
Original languageEnglish
Pages (from-to)1-40
Number of pages40
JournalReview of Symbolic Logic
Issue number1
Early online date2 Jan 2014
Publication statusPublished - 1 Mar 2014

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