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The sonants in PIE have consonantal and vocalic allophones, so the consonantal sonant and the vocalic sonant are regarded as one consonant phoneme. But many daughter languages of PIE (at least at some stage) have independent consonant phonemes /j/, /v/, /r/, /l/, /m/, /n/ and vowel phonemes /i/, /ī/, /u/, /ū/ respectively. Some of them even have /r̥/, /l̥/, /m̥/, /n̥/, /r̥̄/, /l̥̄/, /m̥̄/, /n̥̄/. So when did the vocalic allophones of consonant phonemes in PIE become independent vowel phonemes? Is the disappearance of laryngeals a watershed?

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    You could easily argue that several of the daughter languages also have single continuant archiphonemes, just like PIE. The same sort of alternations often apply in the daughter languages too, though a reduction in the productivity of many types of derivation and inflection means that they’re often less transparent than in reconstructed PIE itself. – Janus Bahs Jacquet Apr 29 at 18:09
  • @JanusBahsJacquet Which languages are you thinking of? The only one where I think that might be arguable is Sanskrit, but even there it would be much harder to make it work than in PIE (and the nasals would be excluded). – TKR Apr 30 at 0:26
  • @TKR Sanskrit, Greek and Latin, primarily. As you say in your answer, it only really applies to the glides in the daughter languages, but especially in Sanskrit and Latin, it does apply. It’s a different system from PIE, not primarily ablaut-based, but the automatic change between interconsonantal vowel and intervocalic glide is still found, with some exceptions (like Latin allowing /CiV/ and /CuV/). – Janus Bahs Jacquet Apr 30 at 6:44
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Phonemes are a theoretical construct, so the answer will depend to some extent on one's theoretical preferences; note that even for PIE many scholars posit independent vowel phonemes /i u/. But basically, after PIE the analysis you describe becomes much less attractive.

The grounds for the allophonic analysis in PIE are that practically all cases of vocalic liquids and nasals appear in alternation with consonantal ones, and to a lesser extent something similar holds for the vowels [i u] and the glides [j w]; and that the alternation is patterned, so that morphophonology -- specifically, ablaut grade -- largely predicts which alternant appears where. This isn't really true for any of the daughter languages.

For the liquids and nasals, only Sanskrit preserves PIE *r̥ (and possibly marginally *l̥) as such. Otherwise the syllabic liquids and nasals changed to something else in all the attested daughter languages. So the question really boils down to the vowels/glides, and in Sanskrit also the rhotic. (Most of the daughter languages do preserve the PIE glides, but not all: Greek lost *y and in Attic also *w, so Greek is definitely out.)

So what would make an allophony analysis attractive in the daughter languages? Ideally you'd want patterned alternations of the PIE kind. The problem is that sound changes and other changes have messed up these alternations in all the languages. Their remnants are often still visible (e.g. Latin solvō - solūtus), but they're no longer predictable, because the PIE ablaut system which produced them has been eroded: synchronically you can't really talk in terms of zero grades and full grades anymore (at least not without a ton of exceptions), so the conditions for the allophony have been lost.

Sanskrit comes closest to preserving the PIE ablaut system, and Sanskrit grammarians did describe the language basically in terms of what we now call ablaut and saw a relationship between vowels and glides and between syllabic and consonantal liquids. So to some extent an allophony analysis is still arguably possible for Sanskrit (though again excluding nasals), but even there it's a lot less neat than in PIE.

To your last question, the disappearance of laryngeals comes into it indirectly in that it was one of the factors (though not the only one) in the demise of the ablaut system; and note that the long syllabic resonants, and many or maybe all instances of long *ī *ū, are now usually thought to represent a resonant/vowel+laryngeal sequence.

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