Computable and Uncomputable Elements of Syntax

Publisher Summary Syntax of a language tries to find the general rules of paraphrasing, the general rules of consequence, and the general rules of constant semantic changes in the language. These general rules will use some general concepts, grammatical categories, and their combinations. The attempts to formulate the syntax of a natural language indicate a far greater degree of complexity. The syntax of a language of mathematics seems computable. There is a decision procedure for the well-formedness of a string of symbols. And there is a decision procedure that assigns the proper structure to any well-formed string—i.e., to any formula so that the set of all formulas for that language is recursive and the set of the structures assigned to the formulas is recursive. No syntax can be expected to enumerate recursively all commonly known sentences, which are implicitly used in referentials. Syntax, however, can to some extent find out what sentences were implicitly used for the referentials of given texts. Syntax and semantics merge. The use of a language presupposes the facts that are too trivial or too well known to be stated, though they are used for more involved locutions. The facts must be supplied independently of the syntactic theory, and they constitute the recurrent anchorage of the theory in empirical linguistic data.