Meillet's work is often mentioned in support of the precedence of grammatical evidence (over lexical evidence) in determining genetic relationship; however, his championing of grammatical evidence comes with a major, often overlooked caveat.
Meillet considered correspondences involving grammatical elements to be especially important for proving genetic relationship, because they tend to be less prone to borrowing:
"Grammatical correspondences, and those alone, provide rigourous proof [of genetic relatedness], but on condition that one appeals to material detail of the [linguistic] forms and that one establishes that certain specific grammatical forms found in the languages under consideration have a common origin. Lexical correspondence never provides absolute proof because one can never be certain that such correspondences cannot be explained as borrowings." (Meillet 1965:91, apud Harrison 2007)
"Pronunciation and grammar form closed systems; all the parts of each of those systems are linked one to the other. The phonetic system and the morphological system thus lend themselves little to admit borrowings." (Meillet 1965:84, apud Harrison 2007)
However, grammatical morphemes may, on the other hand, display striking similarities across unrelated languages. Meillet discusses particularly the case of pronouns:
"It goes without saying that in order to establish genetic relatedness of languages one must disregard everything that can be explained by general conditions common to all languages. For instance, pronouns must be short words, clearly composed of easily pronounced sounds, generally without consonant clusters. The consequence is that pronouns are similar in almost all languages, though this does not imply a common origin. On the other hand, pronouns often show little resemblance in languages that are otherwise quite similar… Even forms that descend from the same protoform, like French <nous> and English <us>, may no longer have a single element in common (the French <s> is purely graphic). Therefore, pronouns must be used with caution in establishing relatedness of languages." (Meillet 1958[1965]:89-90, apud Campbell 2007)
Although Meillet mentions only pronouns, the issues he raises are also common with other grammatical morphemes. As Campbell (1997:243) explains, "[T]hese limitations [those pointed out by Meillet] mean that consonants from the same small set recur frequently in grammatical affixes of the world's languages, and therefore the probability of an accidental agreement in compared grammatical morphemes is very high and is frequently attested."
It's paradoxical that (1) morphemes that tend to be less prone to borrowing (thus being more reliable evidence for genetic relationship) have a tendency to (2) be independently similarly-shaped across unrelated languages, because of factors having to do with frequency, ease of pronunciation, etc. (thus requiring extra caution when used as evidence of genetic relationship). Such paradox — "Meillet's Paradox" — should be born in mind especially when one is dealing with long-range genetic relationships.
References
Campbell, Lyle. 1997. American Indian Languages: The Historical Linguistics of Native America. Oxford University Press.
Harrison, Shelly. 2007. Antoine Meillet and the Comparative Method: On Shared Aberrancies as Evidence of Genetic Relatedness. http://www.general.uwa.edu.au/~shelly/Publications/Abstracts/MeilletAbs.html
Meillet, Antoine. 1965. Linguistique historique et linguistique générale. Paris: Champion.
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