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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 Ref
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]
| 15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
| 15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
| 15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
| 15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
| 15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
| 15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
| 15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
| 15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
| 15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
| 15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
| 15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
| 15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
| 15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
| 15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
| 15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
| 15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
| 15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
| 15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |