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3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth

['satisfaction' as a means of defining truth]

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