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Single Idea 15593

[filed under theme 5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic ]

Full Idea

The alternative Tarskian way of indicating how a variable is to be interpreted is that a variable x will be a special case of the semantic value of the term; it will be a function which takes each assignment into the individual which it assigns to x.

Gist of Idea

Variables can be viewed as special terms - functions taking assignments into individuals

Source

Kit Fine (Semantic Relationism [2007], 1.B)

Book Ref

Fine,Kit: 'Semantic Relationism' [OUP 2007], p.11

Related Ideas

Idea 15592 The usual Tarskian interpretation of variables is to specify their range of values [Fine,K]

Idea 18887 The perfect case of direct reference is a variable which has been assigned a value [Salmon,N]

The 18 ideas from 'Semantic Relationism'

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]