Reconstructions as Proof of Relationship
The notion of reconstruction easily derives from that of sound correspondence. Suppose that among five related languages there is correspondence such that three have p and two have f. If we take the further step of assuming that the original sound was *p we are making an additional assertion, namely that the original p became f in two of the five languages. Suppose that four of the languages had f and only one had p? Should we go with the majority and reconstruct *f?. Clearly new and basically typological factors arise here. One has to do with the diachrony typology. Is the change *p > f more likely than *f > p? Most linguists would agree, I believe, and reconstruct *p. Suppose there were another correspondence in which all of the five languages had f. Since the reconstruction of *f here would be overwhelmingly favored, the reconstruction of *p for the first correspondence would be strongly preferred even if only one of the languages had p. This would be for a different and synchronic typological reason. The proto-language would otherwise have two *f phonemes. We would also require unconditional split, the sin against the Holy Ghost in comparative linguistics.
There are a fair number of instances e.g. Blackfoot in Algonkian, Cherokee in Iroquoian and Kamchadal in Chukotian, in which reconstructions have not been possible for the languages indicated yet everyone admits that they belong to these respective families. Given this and the possibility of reconstructing a perfectly good proto-system in some instances for loan words, reconstruction becomes neither a necessary nor a sufficient condition for the languages to be related.
Strictly speaking, I believe that reconstruction in cases such as Blackfoot and Cherokee is possible by positing a very large and typologically implausible number of phonemes for the proto-language.
In one well-known instance, the vowel system of Uralic, actually that of the initial syllable where a full set occurs, there have been two major theories: that of Steinitz and that of Itkonen. The former makes the system like that of Proto Ostyak as he reconstructs it and the latter quite like that of Finnish. Steinitz posits a whole series of Ablaut variations in the proto-language which saves the regularity by assuming inherited vowel variations, while Itkonen is more tolerant of irregularities but in either case a large number of instances are irregular. At one point, Décsy said that in Finno-Ugric the second part of Voltaire’s famous bon mot concerning etymology holds, namely that the vowels count for nothing.
Since, as we have seen, Finno-Ugric was discovered even earlier than Indo European and no one doubts its validity, the question arises as to whether lack of regular sound correspondences could ever disprove a relationship based on numerous and obvious similarities. The answer seems to be that it could not. In principle, there should not be any difference between consonants and vowels in this regard. If there was ever a case for rejecting a hypothesis on the basis of irregular correspondences it would be Finno-Ugric, but it is universally accepted. A theory not disprovable by any data is not an empirical theory.