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Single Idea 19316

[filed under theme 3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth ]

Full Idea

Tarski's great insight is find another property, since open sentences are not truth. It must be had by open and genuine sentences. Clauses having it must generate it for the whole sentence. Truth can be defined for sentences by using it.

Gist of Idea

Insight: don't use truth, use a property which can be compositional in complex quantified sentence

Source

report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Richard L. Kirkham - Theories of Truth: a Critical Introduction 5.4

Book Ref

Kirkham,Richard L.: 'Theories of Truth: a Critical Introduction' [MIT 1995], p.152

A Reaction

The proposed property is 'satisfaction', which can (unlike truth) be a feature open sentences (such as 'x is green', which is satisfied by x='grass'),

Related Idea

Idea 19315 In quantified language the components of complex sentences may not be sentences [Kirkham]

The 18 ideas with the same theme ['satisfaction' as a means of defining truth]:

14454 An argument 'satisfies' a function φx if φa is true [Russell]
19184 The best truth definition involves other semantic notions, like satisfaction (relating terms and objects) [Tarski]
19191 Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]
15410 Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski]
18811 Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt]
15365 We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten]
19314 For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham]
19316 Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham]
19175 Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]
19145 We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson]
19146 Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson]
19174 Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson]
10817 Tarski just reduced truth to some other undefined semantic notions [Field,H]
19318 A 'sequence' of objects is an order set of them [Kirkham]
19319 If one sequence satisfies a sentence, they all do [Kirkham]
13504 Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD]
13634 Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro]
19128 If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]