Disquotationalism and expressiveness (Q2572386)

Kemp argues against the view that a truth predicate axiomatised be the disquotation scheme can serve the purpose of expressing generalisations that are not already expressible without the disquotation scheme. In particular, he argues against the claim that \textit{V. Halbach}'s [Mind 108, 1--22 (1999)] account of expressing generalization is of any help to the disquotationalism. Halbach showed that the sentence \(\forall x (\phi (x)\rightarrow T x)\) and all sentences \(T [\psi ]\leftrightarrow \psi\) (where \(\psi\) does not contain \(T\)) have the same \(T\)-free consequences as the sentences \(\phi (\psi )\rightarrow (\psi )\) where \(\psi\) is again any sentence not containing \(T\). Both theories do have the same \(T\)-free consequences. But the theory with a \(T\)-predicate does not have any advantages, according to Kemp. In particular, both theories cannot be finitely axiomatised. Moreover, the disquotationalist will never come to assert a sentence of the form \(\forall x (\phi (x)\rightarrow T x)\), because the disquotation scheme will never allow him to derive such a sentence with the exception of the trivial cases where \(\phi (x)\) applies provably to finitely many sentences only. It could be argued against that the truth predicate allows one to express a certain generalisation on the background of an (infinitely axiomatised) theory of truth by a single sentence. So once the theory of \(T\)-sentences is taken for granted, certain things can be fintiely expressed that were not expressible by a single sentence before. Still another defect of Halbach's account is discussed by \textit{R. G. Heck} [Synthese 142, No. 3, 317--352 (2004; Zbl 1072.03008)].