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116-118. 2 Chomsky and Halle in The Sound Pattern of English (New York, 1968), in essentially rejecting the phonetic/phonemic distinction, see it as useful chiefly or solely in describing environmental allophones. Environmental allophones come up under the name "positional transformations" in S. K. Saumjan, Problems of Theoretical Phonology (The Hague, 1968). See particularly p. 21, p. 32, and pp. 53ff. Saumjan makes very profitable use of Reichenbach, Tarski, Quine, and other mathematical logicians; his book begins, in fact, with a quotation from Frege and recognition of his greatness.

MORPHEMIC PROGRESSIONS Purely complex words are so close in their development to the artificial progressions described in (VII) above that they scarcely seem to belong to a natural language: 0. 1. 2. 3. (4) west northwest north northwest north northwest ¿north a F A F2 (Fx a) (F, (F1 a)) F3 is an example of such a development, and even here the refractory or incalcitrant character of a natural language shows itself in the third stage of the progression, where F3 is not a third successive prefix but a first suffix.

Ignoring for the moment diphthongs which may be of the form [ g ^ ] . and treating [iu] as an allophone of the \j[qi\ diph- 44 THE SOUNDS OF ENGLISH (IL) thong I jíi¡, there are only two more important phonemic diphthongs, as in the following matrices for t h e sounds of ( o w ) and : /au/ = [au au seo œu ou eu 9ττ] and /oi/ = [oi Ol 01 oi Ol OI 91 ΘΙ 91] I n most dialects of B E a n d some dialects of AE, diphthongs are produced when /q2l = /Θ/. Giving ¡ q j t h e successive values of t h e left-hand item in t h e phonemic equations involving vowels, we have a total of twelve theoretical possibilities: (1) (2) (5) (8) /oe/ /»e/ /oe/ M (9) (10) (14) (15) (16) (24) (32) (33) /ΘΘ/ /ee/ /io/ /io/ /»/ /oe/ /U9/ M Of these twelve, (9) is eliminated as not being a diphthong, a n d ( 16) is eliminated as n o t sufficiently distinct f r o m (15).

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A Mathematical Grammar of English by George Hemphill

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