Truth as translation, part B (Convention T, first-order languages)

Authors
Citation
H. Leitgeb, Truth as translation, part B (Convention T, first-order languages), J PHILOS LO, 30(4), 2001, pp. 309-328
Citations number
7
Categorie Soggetti
Philosiphy
Journal title
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN journal
00223611 → ACNP
Volume
30
Issue
4
Year of publication
2001
Pages
309 - 328
Database
ISI
SICI code
0022-3611(200108)30:4<309:TATPB(>2.0.ZU;2-Z
Abstract
This is the second part of a paper dealing with truth and translation. In P art A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a prec ise definition. At the end of Part A it has been shown that interpreted lan guages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate--this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to f irst-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted lan guage with a high degree of expressiveness leads to changes in the ontology of the language.