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Full Idea
Because the definition of satisfaction must have a separate clause for each predicate, Tarski's method only works for languages with a finite number of predicates, ...but natural languages have an infinite number of predicates.
Gist of Idea
If we define truth by listing the satisfactions, the supply of predicates must be finite
Source
Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.5)
Book Ref
Kirkham,Richard L.: 'Theories of Truth: a Critical Introduction' [MIT 1995], p.159
A Reaction
He suggest predicates containing natural numbers, as examples of infinite predicates. Davidson tried to extend the theory to natural languages, by (I think) applying it to adverbs, which could generate the infinite predicates. Maths has finite predicates.
| 18369 | There are at least fourteen candidates for truth-bearers [Kirkham] |
| 19318 | A 'sequence' of objects is an order set of them [Kirkham] |
| 19319 | If one sequence satisfies a sentence, they all do [Kirkham] |
| 19315 | In quantified language the components of complex sentences may not be sentences [Kirkham] |
| 19317 | An open sentence is satisfied if the object possess that property [Kirkham] |
| 19320 | If we define truth by listing the satisfactions, the supply of predicates must be finite [Kirkham] |
| 19322 | Why can there not be disjunctive, conditional and negative facts? [Kirkham] |