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Single Idea 19128
[filed under theme 3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
]
Full Idea
If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate.
Gist of Idea
If a language cannot name all objects, then satisfaction must be used, instead of unary truth
Source
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7
A Reaction
I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction.
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]
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19184
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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]
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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]
|