Main phonological schools

Let us consider the phrase [на лугу кос нет] and words [вАлы ], [сАма]. Logically, there can only be three answers to the question: which phonemes are represented by the consonant sound [c] in [кос] and by the vowel sound [А] in [вАлы]:
M (1) If [кос] and [вАлы] are grammatical forms of the words коза and вол respectively, then the consonant [c] represents phoneme /з/, while the vowel [А] is an allophone of the phoneme /o/. If [кос] and [вАлы] are grammatical forms of the words коса and вал respectively, then the consonant [c] belongs to the phoneme /с/, while the vowel [А] should be assigned to the phoneme /а/.
СП (2) The consonant [c] in [кос] belongs to the phoneme Id no matter whether it is a form of коза or that of коса, while the vowel [А] in [вАлы] represents the phoneme /a/ no matter whether it is a form of вол or that of вал.
П (3) The consonant [c] represents neither phoneme /з/, nor phoneme Id, while the vowel [А] in [вАлы] does not belong either to the phoneme /a/ or to the phoneme /о/.
Since there are three possible answers to the above questions, there are three schools of thought on the problem of identifying phonemes.
Those linguists who give the first answer belong to the so-called morphological (Moscow phonological) school (R.I. Avanesov, V.N. Sidorov, P.S. Kuznetsov, A.A. Reformatsky, and N.F. Yakovlev). The exponents of this school maintain that two different phonemes in different allomorphs of the same morpheme may be represented on the synchronic level by one and the same sound, which is their common variant and, consequently, one and the same sound may belong to one phoneme in one word and to another phoneme in another word.
In order to decide to which phoneme the sounds in a phonologically weak (neutral) position belong, it is necessary to find another allomorph of the same morpheme in which the phoneme occurs in the strong position, i.e. one in which it retains all its distinctive features. The strong position of a Russian consonant phoneme is that before a vowel sound of the same word, whereas the strong position of a vowel phoneme is that under stress. The consonant [c] in кос belongs to the phoneme Id because in the strong position in such allomorphs of the same morpheme as in коса, косы the phoneme is definitely /с/. In коз the same sound [c] is a variant of the phoneme /з/ because in the strong position, as in коза, козы, the phoneme is definitely /з/. The vowel [А] in валы is an allophone of the phoneme /a/ because the phoneme occurs in the strong position in вал while the same vowel [А] in волы is a variant of the phoneme /o/ because this phoneme is found in the strong position in вол.
According to this school of thought, the neutral vowel sound in original should be assigned to the English phoneme /σ/ because this phoneme occurs in the strong position in such word as origin.
The second school of thought, originated by L.V. Shcherba, advocates the autonomy of the phoneme and its independence from the morpheme. Different allomorphs of a morpheme may differ from each other on the synchronic level not only in their allophonic, but also in their phonemic composition. According to the Leningrad (Petersburg) phonological school (L.V. Shcherba, L.R. Zinder, M.I. Matusevich), speech sounds in a phonologically neutral position belong to that phoneme with whose principal variant they completely or nearly coincide. Thus, the sound [c] in [кос] should be assigned to the phoneme /с/ because it fully coincides with the latter's principal variant, which is free from the influence of neighboring speech sounds. The vowel [А] in [вАлы] should be assigned to the phoneme /a/ because it nearly coincides with the latter's principal variant [a]. The vowel [ъ] in [въдАвос] does not even resemble either [o] or [a] or [А] but it is still assigned to the /a/ phoneme because both /o/ and /a/ are reduced to [ъ].
According to the third school of thought, there exist types of phonemes higher than the unit phoneme. Different linguists call them differently. One of the terms for them introduced by Prague Linguistic Circle, namely by N.S. Trubetzkoy and R. Jacobson, is archiphoneme. According to them, the archiphoneme is a combination of distinctive features common to two phonemes. Thus each of the speech sounds [c], [з] represents the phonemes /c/, /з/. These two phonemes differ from each other only in matter of voice, while both of them possess the other two distinctive features: (1) forelingual (2) fricative articulation. These two features together constitute the archiphoneme to which both [c] and [з] belong. This archiphoneme is, therefore, neither voiceless nor voiced. It designated by Russian capital letter C. The sound [c] in [кос] in both На лугу кос нет and На лугу коз нет belongs to this archiphoneme andnot to the phoneme /c/ or /з/.
The phoneme /а/ and /о/ belong to archiphoneme which is realized in the sound [A], as in [вАлы] meaning both валы and волы.