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Single Idea 15595

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

Full Idea

In the 'algebraic' approach to variables, we move from a quantified sentence to the term specifying a property (the λ-term), and then reducing to the algebraic operations for atomic formulas.

Gist of Idea

The 'algebraic' account of variables reduces quantification to the algebra of its component parts

Source

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

Book Ref

Fine,Kit: 'Semantic Relationism' [OUP 2007], p.13

A Reaction

[Bealer is a source for this view] Fine describes it as an 'algebra of operations'. I presume this is a thoroughly formalist approach to the matter, which doesn't seem to get to the heart of the semantic question.

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]