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Single Idea 13504

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

Full Idea

We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not.

Gist of Idea

Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do

Source

William D. Hart (The Evolution of Logic [2010], 4)

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.107

A Reaction

This is the hardest part of Tarski's theory of truth to grasp.

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]