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The phonological system of proto-Indo-European (and of any other proto-language without written records) is reconstructed via the comparative method, which inevitably leaves some questions open.

One such open question is the stops' manner of articulation problem. There are currently the two competing viewpoints concerning this problem - the traditional theory (which claims that stops were pronounced as voiced, voiceless, or murmorred) and the glottalic theory (which proposes that stops were pronounced in an ejective, plain, or (breathy) voiced manner). It should be mentioned, though, that in all other aspects the two theories agree i.e. given the available data, pIE had exactly 3 distinct rows of stops; there were 5 places of articulation - labial, dental, palatal, velar, labio-velar; roots couldn't contain a sequence of traditional "plain voiced" stops or a combination of a traditional "voiceless" and a "breathy voiced" stop...

I am fully aware that as of today nobody can give an unambiguous answer to the manner-of-articulation dilemma, however, I was wondering how confident we can be regarding the remaining assumptions? In particular, what is the proof the pIE didn't have retroflex stops? Or that it lacked affricates? In general, can we be sure that there are no major gaps in the pIE phonological system?

Remark: One particular peculiarity of pIE that incited me to ask the above question is that it had 3 varieties of velar stops (palatal, plain, and labio-velar), while the coronal and the labial stops had just one. If, for example, there were retroflex coronal stops, then the picture would have been more "balanced".

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    I see no reason to close this one: It is about linguistics, and it has provoked good answers. – jk - Reinstate Monica Jul 7 '16 at 15:09
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In particular, what is the proof the pIE didn't have retroflex stops? Or that it lacked affricates? In general, can we be sure that there are no major gaps in the pIE phonological system?

It turns out, there is none! And no, we can't be sure. We know nothing at all about PIE phonetics except for a few informed guesses.

The reconstructions you're talking about are phonological models, not phonetic ones. And the trick with phonology is, it doesn't study anything we can actually measure in the real world. Instead, phonology is a field of models—and any given model is "good" only insofar as it explains the data in a clear and insightful way.

This is why the "standard model" of PIE currently includes laryngeals like *h₁. Saussure realized that he could explain the existing data more clearly and succinctly if he added a few special phonemes, which had no direct reflexes in any language known at the time. Since then, no theory without laryngeals has ever given us as clear or as complete of an explanation. So the laryngeals have stayed.

Could PIE have had retroflex stops? Absolutely! Could you come up with a theory that incorporates them, perhaps saying that they merged into the dental/alveolar stops in all environments? Sure!

The real question is—does this addition actually add anything to the model? Does it make anything clearer, or explain the data in a better way, or make better predictions? Because if not, Occam's razor suggests that we should stick with the simpler model—and the simpler model here is the one with fewer phonemes.

As TKR put it in his answer:

the PIE sound system as currently reconstructed works pretty well -- i.e., in combination with posited rules of sound change, it predicts the attested reflexes with high accuracy

That is, the existing model makes very good predictions. So unless there's some clear and visible improvement that can be made by adding a new stop series, it's unlikely to catch on.

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There's any number of possible sounds in human languages that have not been reconstructed for PIE, because no one's seen any reason to reconstruct them. There's no specific argument for reconstructing retroflex stops, so no one has reconstructed retroflex stops. The fact that a language has more than one dorsal series doesn't imply that it should also have multiple series in other place-of-articulation categories.

Of course we can never be 100% sure we're not missing something, but the PIE sound system as currently reconstructed works pretty well -- i.e., in combination with posited rules of sound change, it predicts the attested reflexes with high accuracy. It doesn't look like something major is missing, and most Indo-Europeanists would be very surprised if it turned out there was a whole additional series of stops, or anything of that order.

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I think the question is misconceived, albeit not an embarrassing error (it unfortunately reflects a widespread view). The question really reduces to asking "How certain should we be that a claim lacking any evidence is false?". Actually we should simply never entertain any hypotheses for which no evidence has been advanced. This is the fundamental distinction between the imaginable (which science fiction deals with) and the possible (which science deals with). The possible is something for which there is some evidence; the imaginable is, as the word suggests, something that you can imagine – which depends on what limits you have on your imagination. Until some evidence is set forth suggesting that there were retroflex consonants, there is no reason to say that there were.

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