[Automatic Translation of Languages: NATO Summer School...July 1962] FOUR LECTURES ON ALGEBRAIC LINGUISTICS AND MACHINE TRANSLATION†

LINGUISTICS, as every other empirical science, is a complex mixture of theory and observation. The precise nature of this mixture is still not too well understood, and in this respect the difference between linguistics and, say, physics is probably at most one of degree. This lack of methodological insight has often led to futile disputes between linguists and other scientists dealing with language, such as psychologists, logicians, or communication theoreticians, as well as among linguists themselves. Recently, however, considerable progress has been made in the understanding of the function of theory in linguistics, as a result of which theoretical linguistics has come into full-fledged existence. Interestingly enough, the present customary name for this new subdiscipline is rather mathematical linguistics. This is slightly unfortunate: though the adjective ‘mathematical’ is quite all right if ‘mathematics’ is understood in the sense of ‘theory of formal systems’, which is indeed one of its many legitimate senses, it is misleading inasmuch as it is still associated, at least among the non-specialists, including the bulk of the linguists themselves, with numbers and quantitative treatment. That subdiscipline of linguistics, however, which deals with numbers and statistics should better be called statistical linguistics and rather carefully be kept apart from mathematical linguistics qua theoretical linguistics. Should one prefer to regard ‘mathematical linguistics’ as a term for a genus of which statistical linguistics is a species, then the other species should perhaps be named algebraic linguistics. After this terminological aside which, I think, was not superfluous, let us briefly sketch the background and development of algebraic linguistics. In the hands of such authors as Harris [1] and Hockett [2] in the United States, Hjelmslev [3] and Uldall [4] in Europe, structural linguistics became more and more conscious of the chasm between theory and observation, and linguistic theory deliberately got an algebraic look. At the same time, Carnap [5] and the Polish logicians, especially Ajdukiewicz [6], developed the logical syntax of language which was, however, too much preoccupied with rules of deduction, and too little with rules of formation, to exert a great influence on current linguistics. Finally, Post [7] succeeded in formally assimilating rules of formation to rules of deduction, thereby paving the way for the application of the recently developed powerful theory of recursive functions, a branch of mathematical logic, to all ordinary languages viewed as combinatorial systems