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Single Idea 13634
[filed under theme 3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
]
Full Idea
In a sense, satisfaction is the notion of 'truth in a model', and (as Hodes 1984 elegantly puts it) 'truth in a model' is a model of 'truth'.
Gist of Idea
Satisfaction is 'truth in a model', which is a model of 'truth'
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 1.1)
Book Ref
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.6
A Reaction
So we can say that Tarski doesn't offer a definition of truth itself, but replaces it with a 'model' of truth.
Related Ideas
Idea 10017
Truth in a model is more tractable than the general notion of truth [Hodes]
Idea 10170
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
The
18 ideas
with the same theme
['satisfaction' as a means of defining truth]:
14454
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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]
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15410
|
Truth only applies to closed formulas, but we need satisfaction of open formulas to define it
[Burgess on Tarski]
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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]
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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]
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19146
|
Satisfaction is a sort of reference, so maybe we can define truth in terms of reference?
[Davidson]
|
19145
|
We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth
[Davidson]
|
19174
|
Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths
[Davidson]
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10817
|
Tarski just reduced truth to some other undefined semantic notions
[Field,H]
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19319
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If one sequence satisfies a sentence, they all do
[Kirkham]
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19318
|
A 'sequence' of objects is an order set of them
[Kirkham]
|
13504
|
Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do
[Hart,WD]
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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]
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