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Single Idea 14454

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

Full Idea

We say that an argument a 'satisfies' a function φx if φa is true.

Gist of Idea

An argument 'satisfies' a function φx if φa is true

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], XV)

Book Ref

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.164


A Reaction

We end up with Tarski defining truth in terms of satisfaction, so we shouldn't get too excited about what he achieved (any more than he got excited).


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

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]
Truth only applies to closed formulas, but we need satisfaction of open formulas to define it [Burgess on Tarski]
Tarski uses sentential functions; truly assigning the objects to variables is what satisfies them [Tarski, by Rumfitt]
We can define the truth predicate using 'true of' (satisfaction) for variables and some objects [Tarski, by Horsten]
For physicalism, reduce truth to satisfaction, then define satisfaction as physical-plus-logic [Tarski, by Kirkham]
Insight: don't use truth, use a property which can be compositional in complex quantified sentence [Tarski, by Kirkham]
Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]
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]
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]
A 'sequence' of objects is an order set of them [Kirkham]
If one sequence satisfies a sentence, they all do [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]
If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]