2015/5/7【GIS Linguistic Mapping Workshop】SMATTI 語言中之基數詞與分類詞：一個類型學上的三明治

SMATTI是世界中最多數目分類詞語言地區的六個主要語族，包括漢語系、苗瑤語系、南亞語系、壯侗語系、藏緬語系和雅利安語系．這些語言當中，名詞(N)會透過分類詞(C)或是量詞(M)與數字(Num)結合，邏輯上有六個可能的組合但是SMATTI中、甚至世界的語言當中只有四種出現，而從此我們得以發現兩個現象(Greenberg 1990[1972]:185, Aikhenvald 2000:104-105)：

1) 數詞，分類/量詞和名詞的順序
a. 只要名詞不出現在數詞和分類/量詞間，任何排列皆可行
b. 分類/量詞前置的順序遠比分類/量詞後置的狀況常見

我們透過數理的角度提出解釋並認為數詞和分類/量詞間存在乘法的關係，我們把數詞當作乘數而把分類/量詞當作被乘數，同樣的架構在有乘法的數字系統中相當普遍，比方說：[n × base]，將分類/量詞當作被乘數得以推演出兩個語言通則：首先語言當中分類/量詞勢必和乘法同行出現，其二數詞和分類/量詞的詞序應當和乘法系統中的被乘數同步．我們透過分析SMATTI當中的153個分類詞語言得以驗證這個理論。

SMATTI is an acronym referring to six language groups in the world’s foremost hot spot of numeral classifier languages: Sinitic, Miao-Yao, Austro-Asiatic, Tai-Kadai, Tibeto-Burman, and Indo-Aryan. In classifier languages, a classifier (C) or measure word (M) is used when a noun (N) is quantified by a numeral (Num). Mathematically, there are 6 possible word orders; yet, only 4 are attested in SMATTI, and elsewhere, from which two revealing generalizations obtain, as in (1) (Greenberg 1990[1972]:185, Aikhenvald 2000:104-105).

1) Generalizations of Word Orders among Num, C/M, and N
a. Any order is possible as long as N does not intervene between Num and C/M.
b. C/M-final [Num-C/M] orders are far more common than C/M-initial [C/M-Num] orders.

We offer an account for (1) based on an insight form a mathematical perspective. In essence, the function between Num and C/M is multiplication, regardless of word order, where Num is a multiplier, and C/M, a multiplicand. The same function exists in a multiplicative numeral as [n×base]. The identical role of C/M and base as multiplicands entails two implicational universals: Co-presence of base and C/M in a language and word order synchronization between base and C/M in a language. Our survey of 153 classifier languages in SMATTI shows highly significant evidence supporting this hypothesis.