Could you please explain the meaning of this sentence (the bold sentence) in the following paragraph? "Thus a classification valid in one is no more likely than any other arbitrary classification to be valid in either of the other two."
"Linguistic typology , genetic classification, and areal classification are in principle distinct enterprises. Thus a classification valid in one is no more likely than any other arbitrary classification to be valid in either of the other two. While linguists generally recognize this today, the three enterprises have been confused in the past. Armenian was wrongly classified as an Iranian language because the overwhelming similarities in vocabulary between Armenian and the Iranian languages were not recognized as the result of Armenian borrowing from various Iranian languages. The Uralic languages were assigned to the same genetic family as the Turkic languages on the sole basis of shared typological features, such as word order patterns. The problem is complicated by the fact that the study of areal similarities among languages is often referred to as areal typology. For completeness, I include a brief discussion of areal typology here. It is an undertaking distinct from linguistic typology."
Bernard Comrie. "Linguistic Typology". in Annual Review of Anthropology. 1988: vol. 17. pp 145-159.
First, for me the sentence in bold doesn't add much interest or meaning to the paragraph. You could leave it out and still understand the message of the paragraph.
Then, if I had to rewrite the sentence, I might say something like. "A classificationof languages by any one of these three methods might not produce the same result."
I don't know why the writers says "no more likely than any other arbitrary classification to be valid", since I'm not aware of examples of arbitrary classification systems for languages (that is, ones not based on anything in particular, other than personal opinions. Maybe something earlier in the article explains that reference. The use of the word "other" implies to me that the writer considers each of the classification methods mentioned to be arbitrary ones.