In "Truth and Meaning," Donald Davidson argued that any learnable language must be statable in a finite form, even if it is capable of a theoretically infinite number of expressions—as we may assume that natural human languages are, at least in principle.
If it could not be stated in a finite way then it could not be learned through a finite, empirical method such as the way humans learn their languages. It follows that it must be possible to give a theoretical semantics for any natural language which could give the meanings of an infinite number of sentences on the basis of a finite system of axioms. "Giving the meaning of a sentence", he further argued, was equivalent to stating its truth conditions, so originating the modern work on truth-conditional semantics.
In sum, he proposed that it must be possible to distinguish a finite number of distinct grammatical features of a language, and for each of them explain its workings in such a way as to generate trivial (obviously correct) statements of the truth conditions of all the (infinitely many) sentences making use of that feature.
If it could not be stated in a finite way then it could not be learned through a finite, empirical method such as the way humans learn their languages. It follows that it must be possible to give a theoretical semantics for any natural language which could give the meanings of an infinite number of sentences on the basis of a finite system of axioms. "Giving the meaning of a sentence", he further argued, was equivalent to stating its truth conditions, so originating the modern work on truth-conditional semantics.
In sum, he proposed that it must be possible to distinguish a finite number of distinct grammatical features of a language, and for each of them explain its workings in such a way as to generate trivial (obviously correct) statements of the truth conditions of all the (infinitely many) sentences making use of that feature.
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See that post with different algorithms in metabole
See the journal French Metablog with today different posts
