[2013-07-07-1], [2013-07-08-1]の記事に引き続き，wave_theory と lexical_diffusion の関係について．言語変化が中心地から波状に周辺地域へ伝播してゆくことをモデル化した波状理論と，言語変化が語彙の間を縫うようにして段階的に進んでゆくことを提案した語彙拡散との親和性は高い．背後にはS字曲線という数学モデルも想定されており，理論の名に値しそうな雰囲気が漂っている．
　両者ともに何らかの意味で伝播 (diffusion) を扱っているのだが，具体的な違いは，波状理論が地理的空間を話題としているのに対して，語彙拡散は言語的空間を話題にしていることである．Wardhaugh (222--23) がこの点を指摘しているので，該当箇所を引用しよう．

The theory of lexical diffusion has resemblances to the wave theory of language change: a wave is also a diffusion process. . . .
   The wave theory of change and the theory of lexical diffusion are very much alike. Each attempts to explain how a linguistic change spreads through a language; the wave theory makes claims about how people are affected by change, whereas lexical diffusion makes claims concerning how a particular change spreads through the set of words in which the feature undergoing change actually occurs: diffusion through linguistic space. That the two theories deal with much the same phenomenon is apparent when we look at how individuals deal with such sets of words. What we find is that in individual usage the change is introduced progressively through the set, and once it is made in a particular word it is not 'unmade', i.e., there is no reversion to previous use. What is remarkable is that, with a particular change in a particular set of words, speakers tend to follow the same order of progression through the set; that is, all speakers seem to start with the same sub-set of words, have the same intermediate sub-set, and extend the change to the same final sub-set. For example, in Belfast the change from [ʊ] to [ʌ] in the vowel in words like pull, put, and should shows a 74 percent incidence in the first word, a 39 percent incidence in the second, and only an 8 percent incidence in the third . . . . In East Anglia and the East Midlands of England, a sound change is well established in must and come but the same change is found hardly at all in uncle and hundred . . . . This diffusion is through social space.

　ここでは語彙拡散が "linguistic space" に対応し，波状理論が "social space" に対応している．後者は "geographical space" をも包括する広い概念としてとらえたい．言語変化に進行順序や不可逆性があることにも触れられているが，これは共時的には含意尺度 (implicational scale) があることに対応する．
　social space や geographical space における伝播とは，より具体的には共同体から共同体への伝播のことであり，さらにミクロには話者から話者への伝播のことである．これを S-diffusion と呼び，それに対して語から語への伝播を W-diffusion と呼んで，両者の性質の異同を論じたのは，Ogura and Wang である．拙著 (Hotta 120) で導入したことがあるので，以下に引用する．

Ogura and Wang call these two different levels of diffusion W-diffusion and S-diffusion. W-diffusion proceeds from word to word of a single speaker or at a single site, while S-diffusion proceeds from speaker to speaker, or from site to site of a single word. Students of language change have sometimes spoken of this "double diffusion," which may be compared to diffusion of infectious diseases:

These diffusion processes are comparable to epidemics of infectious diseases, and the standard model of an epidemic produces an S-curve (called logistic) describing the increase of frequency of the trait. There are potentially two epidemics, or more exactly two dimensions in which the epidemic can proceed. One dimension is represented by W-diffusion and the other dimension by S-diffusion. (Ogura and Wang, "Evolution Theory" 322)

　言語変化が2重の意味で伝播してゆくという "double diffusion" の考え方に，大きな可能性を見いだすことができそうである．Hudson (183) であれば，"cumulative diffusion" という表現を使うかもしれない．

How does the theory of lexical diffusion relate to the wave theory . . . . According to the latter, changes spread gradually through the population, just as, according to the former, they diffuse through the lexicon, so we might expect a connection between them. A reasonable hypothesis is that changes spread cumulatively through the lexicon at the same time as they spread through the population, so that the words which were affected first by the change will be the first to be adopted in the new pronunciation by other speakers.

　・ Wardhaugh, Ronald. An Introduction to Sociolinguistics. 6th ed. Malden: Blackwell, 2010.
　・ Hotta, Ryuichi. The Development of the Nominal Plural Forms in Early Middle English. Hituzi Linguistics in English 10. Tokyo: Hituzi Syobo, 2009.
　・ Ogura, Mieko and William S-Y. Wang. "Evolution Theory and Lexical Diffusion." Advances in English Historical Linguistics. Ed. Jacek Fisiak and Marcin Krygier. Berlin: Mouton de Gruyter, 1998. 315--43.
　・ Hudson, R. A. Sociolinguistics. 2nd ed. Cambridge: CUP, 1996.

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