Full Idea
Once Frege had provided a clear syntactic account of variables and once Tarski had supplemented this with a rigorous semantic account, it would appear that there was nothing more of significance to be said.
Gist of Idea
It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that
Source
Kit Fine (Semantic Relationism [2007], 1)
Book Reference
Fine,Kit: 'Semantic Relationism' [OUP 2007], p.6
A Reaction
He later remarks that there are now three semantic accounts: the Tarskian, the instantial, and the algebraic [see xref ideas]. He offers a fourth account in his Semantic Relationism. This grows from his puzzles about variables.
Related Ideas
Idea 15587 That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K]
Idea 15592 The usual Tarskian interpretation of variables is to specify their range of values [Fine,K]
Idea 15594 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K]
Idea 15595 The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K]