"The Mathematics of Sentence Structure", in American Mathematical Monthly

Joachim Lambek, "The Mathematics of Sentence Structure", in American Mathematical Monthly, March 1958, vol 65 no. 3, with the Lambek paper on pp 154-169 in the issue of pp 143-228. Original blue wrappers (faded around the edges as always). GOOD solid copy. Also in this issue: Jack Levine, "Varable Matrix Substitution in Algebraic Cryptography", pp 170-178. "The aim of this paper is to obtain an effective rule (or algorithm) for distinguishing sentences from nonsentences, which works not only for the formal languages of interest to the mathematical logician, but also for natural languages such as English, or a t least for fragments of such languages. An attempt to formulate such an algorithm is implicit in the work of Ajdukiewicz.t His method, later elaborated by Bar-Hillel [2], depends on a kind of arithmetization of the so-called parts of speech, here called syntactic types.f The present paper begins with a new exposition of the theory of syntactic types. It is addressed to mathematicians with a t most an amateur interest in linguistics. The choice of sample languages is therefore restricted to English and mathematical logic. For the same reason, technical terms have been borrowed from the field of high school grammar."--from the Lambek paper. Cited 2200+ times.…