Abstract
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”.’
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 language | English |
|---|---|
| Pages (from-to) | 1-40 |
| Number of pages | 40 |
| Journal | Review of Symbolic Logic |
| Volume | 7 |
| Issue number | 1 |
| Early online date | 2 Jan 2014 |
| DOIs | |
| Publication status | Published - 1 Mar 2014 |
Research Groups and Themes
- FSB