The Great Proto-Indo-European Thread

[KathTheDragon]

There is absolutely no other reason for reconstructing, say, the laryngeal in "h1es-" except Møller's theory of genetic relationship between IE and Semitic, the hypothesis implying that the PIE roots had an identical structure as the (Proto-)Semitic ones, i.e. C1C2·C3.

... There is no way to derive this regularly from any preform without a laryngeal, and I don't think analogy can account for it in any satisfactory way. ...

Why can't an analogical leveling account for it, given that the conditions that caused the apophony are obscured and no longer productive?

Analogy requires a model, which is almost certainly non-existent in this case. Unless you know of a well-established athematic root present indicative possessing amphikinetic ablaut in the present, but static ablaut in the imperfect, that is not itself a form under consideration?

[Sumelic]

If in several thousand examples no case has come to light, then nothing is added to your theory by separating the features of this segment out into two 'independent' phonemes. Unless perhaps you can show some difference between the results of /ha/ and /ah/. Otherwise you are just adding a complication with no explanatory power. Simply making a complex matter more complex than is necessary. Yes, evidence could come to light. But evidence of any number of things we've failed to imagine, *could* arise. Previously unknown texts in an early IE offshoot *could* be discovered justifying H5-H9 and three different varieties of r-phoneme. Or who knows what? Just because they are *possible* doesn't mean they are probable, and there is no justification in including them in a theoretical model *unless* some other part of the system is simplified as a consequence.

Forgive my naïvety but isn't this just the result of ablaut? I.e. in the zero grade /ɦgu-/ an epenthetic vowel develops which is identified with the /a/ phoneme, so /ɦagu/, whereas elsewhere there is an existing vowel which simply remains? That is I'm saying the 'a' in your 'ah~ha' is not an original phoneme, in so far as it existed it was simply a property/feature of the /ɦ/ which might add a-colouring to an adjacent vowel, e.g. to an epenthetic /ə/ ?

There is a difference; the main one is /ḫa/ only colors directly following vowels and /aḫ/ only colors directly preceding vowels in this system. Jouna assumes the order of *a and *ḫ is consistent in all forms of a root. If you wanted to reduce them to one phoneme each, it would be equivalent to "a laryngeal that only colors preceding vowels" and " a laryngeal that only colors following vowels." Neither the diphonemic nor the mono-phonemic formulations seem very typologically probable to me, but this distinction is required in System PIE.

[JounaPyysalo]

If in several thousand examples no case has come to light, then nothing is added to your theory by separating the features of this segment out into two 'independent' phonemes. Unless perhaps you can show some difference between the results of /ha/ and /ah/. Otherwise you are just adding a complication with no explanatory power. Simply making a complex matter more complex than is necessary. Yes, evidence could come to light. But evidence of any number of things we've failed to imagine, *could* arise. Previously unknown texts in an early IE offshoot *could* be discovered justifying H5-H9 and three different varieties of r-phoneme. Or who knows what? Just because they are *possible* doesn't mean they are probable, and there is no justification in including them in a theoretical model *unless* some other part of the system is simplified as a consequence.

Forgive my naïvety but isn't this just the result of ablaut? I.e. in the zero grade /ɦgu-/ an epenthetic vowel develops which is identified with the /a/ phoneme, so /ɦagu/, whereas elsewhere there is an existing vowel which simply remains? That is I'm saying the 'a' in your 'ah~ha' is not an original phoneme, in so far as it existed it was simply a property/feature of the /ɦ/ which might add a-colouring to an adjacent vowel, e.g. to an epenthetic /ə/ ?

There is a difference; the main one is /ḫa/ only colors directly following vowels and /aḫ/ only colors directly preceding vowels in this system. Jouna assumes the order of *a and *ḫ is consistent in all forms of a root. If you wanted to reduce them to one phoneme each, it would be equivalent to "a laryngeal that only colors preceding vowels" and " a laryngeal that only colors following vowels." Neither the diphonemic nor the mono-phonemic formulations seem very typologically probable to me, but this distinction is required in System PIE.

Sumelic is quite right. This distinction is necessary not only to explain the "a-colouring" but its absence in the forms of one and the same root.

Also note that the Schwa vowel is embedded in the reconstruction in the sense that the vowel /a/ of System PIE is essentially what the Neogrammarians wrote /ə/. Thus the reconstruction is a hybdid of the Neogrammarians and the laryngeal theory.

[marconatrix]

Every syllable that contains a Th, D or Dh calls for a laryngeal of some variety, as presumably do most or all long vowels. That's an awful lot of extra hypothetical segments, even if the unit in question is a single entity. Twice the number if it's double as you claim. If there is just a single /h/ with two allophones, that's a very high frequency for a single phoneme. Maybe possible for a vowel in a language with only two or three vowel phonemes, but unlikely for a consonant, I think.

We must ask :
(1) Is this plausible, given we want our model of PIE to resemble a real language, not simply to be a mathematical formula;
(2) Is this really useful or does it simply 'multiply entities ...' ?

-----------------

You have /h/ affecting stops in all positions, labial, dental and all varieties of K. But /i~j/ and /u~w/ only 'infect' a single series /k kh g gh/. In early Irish the quality of the vowels affected adjacent consonants giving rise (some believe) to initially a threefold division into neutral (a-coloured), palatalised (i-coloured) and labialised (u-coloured) consonants. Later this simplified into a twofold division of palatal vs neutral (although in some modern dialects some 'neutral' consonants are clearly labialised). The system is not unlike the 'soft' vs 'hard' consonants of Slavonic languages. In both cases however most or all consonants are affected.

Now you want your /h/ to colour stops at all points of articulation, yet your /i u/ only modify the K series? Why should that be? You would at least expect the dentals to palatalise and the labials to gain a /w/ off-glide. So you would need to account for this (unnatural?) restriction.

[Btw I'd be interested to hear of any cases of threefold consonant affection other than early Irish].

[WeepingElf]

To be fair, I think that velars are more prone to palatalization and labialization by adjacent vowels than alveolar, dental or labial consonants, simply because they, like vowels, are primarily articulated by the back of the tongue. Indeed, I fancy that the three velar series of PIE arose from a single Proto-Indo-Uralic velar series by palatalizations and labializations induced by front and rounded vowels, respectively, which later merged into */a/ (at a time well before ablaut evolved, and very well before the breakup of PIE).

Voicing and aspiration, in contrast, are processes that have nothing to do with the place of articulation, and should affect stops of all POAs equally.

[JounaPyysalo]

Every syllable that contains a Th, D or Dh calls for a laryngeal of some variety, as presumably do most or all long vowels. That's an awful lot of extra hypothetical segments, even if the unit in question is a single entity. Twice the number if it's double as you claim. If there is just a single /h/ with two allophones, that's a very high frequency for a single phoneme. Maybe possible for a vowel in a language with only two or three vowel phonemes, but unlikely for a consonant, I think.

We must ask :
(1) Is this plausible, given we want our model of PIE to resemble a real language, not simply to be a mathematical formula;
(2) Is this really useful or does it simply 'multiply entities ...' ?

-----------------

You have /h/ affecting stops in all positions, labial, dental and all varieties of K. But /i~j/ and /u~w/ only 'infect' a single series /k kh g gh/. In early Irish the quality of the vowels affected adjacent consonants giving rise (some believe) to initially a threefold division into neutral (a-coloured), palatalised (i-coloured) and labialised (u-coloured) consonants. Later this simplified into a twofold division of palatal vs neutral (although in some modern dialects some 'neutral' consonants are clearly labialised). The system is not unlike the 'soft' vs 'hard' consonants of Slavonic languages. In both cases however most or all consonants are affected.

Now you want your /h/ to colour stops at all points of articulation, yet your /i u/ only modify the K series? Why should that be? You would at least expect the dentals to palatalise and the labials to gain a /w/ off-glide. So you would need to account for this (unnatural?) restriction.

[Btw I'd be interested to hear of any cases of threefold consonant affection other than early Irish].

"Every syllable that contains a Th, D or Dh calls for a laryngeal of some variety"
- Yes. The rationale for that is that this is provable. The traditional roots with *th *dɦ alternate with roots *t(e/o)h- and d(e/o)ɦ-. When this happens not only the alternation Th : T and Dɦ : D emerges, but also the ‘a-colouring’ becomes visible. For an example of this please open the PIE Lexicon full data page in
http://pielexicon.hum.helsinki.fi/?alpha=ALL
Then Ctrl+F PIE √giɦɑn-, √gieɦɑn-, √gioɦɑn- √giɦɑen-, √giɦɑon- ‘(an)erkennen, wahrnehmen’
There two roots appear, one beginning with √gieɦɑn-, √gioɦɑn- and another with √giɦɑen-, √giɦɑon- displaying Dɦ and 'a-colouring".

"as presumably do most or all long vowels."
- No. The compensatory lengthening rule for eh/eɦ is overstated. There is never a lengthening caused by PIE *h/ɦ except in the open syllable of Indo-Iranian (= Brugmann’s Law II), i.e. only *oh/ɦCV results in long /a:/ in Iranian and Old Indo-Aryan. All this detailed in the Chapter 2 of my dissertation, but in a nutshell quantity does not imply a laryngeal.

That's an awful lot of extra hypothetical segments, even if the unit in question is a single entity. Twice the number if it's double as you claim. If there is just a single /h/ with two allophones, that's a very high frequency for a single phoneme. Maybe possible for a vowel in a language with only two or three vowel phonemes, but unlikely for a consonant, I think.
- The vowel /a/ attached to PIE *h/ɦ is usually provable (see the example above).

"But /i~j/ and /u~w/ only 'infect' a single series /k kh g gh/. (...) Now you want your /h/ to colour stops at all points of articulation, yet your /i u/ only modify the K series? Why should that be? You would at least expect the dentals to palatalise and the labials to gain a /w/ off-glide. So you would need to account for this (unnatural?) restriction."
- The "unnatural" restriction is simply what inductively exists in the (late) PIE, viz. the palatovelar and labiovelar series. Other similar sets are not postulated because there has been no need for, say, "dento-labial" series (or anything alike).

J.

[marconatrix]

If you want to bring in Indo-Uralic, might a system of consonant gradation account for some of the complexity of the PIE consonants?

[marconatrix]

Jouna :
Saying "it's like that because that's how it is" is simply restating the data, it is not an explanation of anything.

[JounaPyysalo]

If you want to bring in Indo-Uralic, might a system of consonant gradation account for some of the complexity of the PIE consonants?

Already mastering and working with 100+ ancient IE languages is a suitable challenge for myself at the moment. Bringing Uralic in would enforce me to learn some 30 more languages, a process that could easily take five years or even more, so this is currently not in the menu.

J.

[JounaPyysalo]

Jouna :
Saying "it's like that because that's how it is" is simply restating the data, it is not an explanation of anything.

I am a natural scientist. Therefore everything reconstructed is simply inductively restated data for me.

[JounaPyysalo]

WeepingElf is quite correct in his assessment. I fully agree.

[WeepingElf]

"Every syllable that contains a Th, D or Dh calls for a laryngeal of some variety"
- Yes. The rationale for that is that this is provable. The traditional roots with *th *dɦ alternate with roots *t(e/o)h- and d(e/o)ɦ-.

WHAT? It is generally accepted that voiceless aspirates in Sanskrit, and some instances of aspirated stops in Greek, come from voiceless stops followed by a laryngeal, but with the breathy-voiced ("voiced aspirated") stops, your claim is not borne out by the facts. There are no alternations between *dh and *d(e/o)H anywhere in PIE. It seems like you are just misinterpreting Grassmann's Law, which is a parallel development in Old Indic and Greek.

It is clear, however, that, if Indo-Uralic is real (we don't know yet), one of the two language families must have innovated regarding manners of articulation of the stops. Either Uralic has lost voicing and aspiration distinctions, or IE has innovated them. As long as we cannot reconstruct conditions which determine which stop ends up in which grade in PIE, we must assume the former. If such a change happened in Tocharian (where it certainly did), why couldn't it have happened in Proto-Uralic as well?

[marconatrix]

If you want to bring in Indo-Uralic, might a system of consonant gradation account for some of the complexity of the PIE consonants?

Already mastering and working with 100+ ancient IE languages is a suitable challenge for myself at the moment. Bringing Uralic in would enforce me to learn some 30 more languages, a process that could easily take five years or even more, so this is currently not in the menu.

Well clearly nobody can be an expert in every detail of everything, that's why science is a collaborative venture. I assume there are experts in Uralic, not least in your part of the world. It's interesting that you feel you would need to "reinvent the wheel" from scratch, rather than simply check out any points that looked doubtful in the existing reconstructions of Proto-Uralic. For example, few of the people who have worked on PIE would claim to have "mastered 100+ languages" and I really wonder exactly what you mean by that. Making such apparently outrageous claims does nothing for you general credibility.

Btw. my original remark was mainly directed at WeepingElf, not an attempt to wind you up.

[marconatrix]

Jouna :
Saying "it's like that because that's how it is" is simply restating the data, it is not an explanation of anything.

I am a natural scientist. Therefore everything reconstructed is simply inductively restated data for me.

Yes, but if the explanation is more complex and confusing than the data it's supposed to 'explain', what is the point? Any given data set could in principle be accounted for by an infinity of hypotheses. Most however would be neither plausible nor helpful.

If I leave a piece of fish unattended in my kitchen, and return to find it gone, a likely hypothesis is that my cat has eaten it. A very unlikely hypothesis is that it's been beamed up to an alien spacecraft. And there are any number of possibilities in between, some may be testable, others not. But the cat hypothesis will be favoured because it is well known that cats eat fish, this has frequently been observed, whereas alien intervention has not been reliably recorded. In the same way if we propose a model of PIE and its development that uses processes and structures commonly observed in real languages, that is more likely to be correct than a theory involving rare or entirely hypothetical constructs. They are not of course impossible in an absolute sense, but should only be given serious consideration after more probable models have been eliminated.

[Tropylium]

There are quite a few criticisms I could levy against System PIE, but if I had to pick a couple top problems, I'd go with these basic methodological issues:

1. The overloading of ablaut as a "black box" that is used to explain, almost as a deus ex machina, a number of embarrassing vowel reflexes that are normally explained using regular sound laws within the mainstream laryngeal theory of reconstruction. It should be a clear fact that a theory that allows unlimited alternation between five entities is greatly weaker than theories that seek to set constraints on where, how, and when different ablaut grades could occur.

We are quite unconcerned of that, since the five vowels are those that actually existed. No claim of unlimited alternation is made as such, but we simply allow the vowels of the cognates to be what they are.

"Allowing vowels to be what they are" is, I dare say, a failure to understand the comparative method. It does not consist of just pooling together cognates and saying that they all "existed as variants" in the proto-language.

One reconstruction idea of yours that seems particularly terrible is that for standard CVh₁C roots and stems, long ē-grades should be reconstructed instead of compensatory lengthening thru the loss of the laryngeal. If ē-grade variants of any PIE words could exist, how come it is only certain roots where such "long grades" appear in a wide number of reflexes?

Moreover, are you aware that some cases of *h₁ are even directly attested in loanwords into Finnic? E.g.
*ǵenh₁- 'to beget' → √inhi- in Finnish inhimillinen 'humane', ihminen (< *inhiminen) 'human'
*bʰleh₁-t- 'leaf' → Finnish lehti 'id.'
*gʰroh₁-to- 'plant' → Finnish rohto 'medicine'
*dʰeh₁-to- 'doing' → Finnish tehdas 'workplace' (> modern Fi. 'factory')

Personally I suspect though that also mainstream IE studies has suffered from the same problem to some extent, and that some number of what is even normally explained as "ablaut variants" might be explainable through conditional sound changes. Of course, we'd need significantly better-organized data than what exists currently to be able to look into this. So for that purpose, pooling together different apparent vowel variants and looking for general patterns seems likely to be indeed useful.

There is a vast complementary distribution in the vocabularly which allows the scholars to attach the labiovelar roots to their non-labiovelar counterparts.

This would be interesting to see, but it seems that you've so far only asserted this, not quite demonstrated it.

For a simple example, what would be the 'non-labiovelar counterparts' of *nokʷts 'night' or *gʷōws 'cow'?

In fact unconditional or near-unconditional /a/ : /i/ correspondences are quite easy to attest and quite easy to derive from a single proto-segment, e.g. between Finnish and Northern Sami:
Finnish ilma = Northern Sami albmi 'air'
Finnish liki = Northern Sami lahka 'near'
Finnish nimi = Northern Sami namma 'name'
Finnish silmä = Northern Sami čalbmi 'eye'
(In addition to the regular correspondence F i : NS a that this ought to demonstrate, all other correspondences appearing here are actually regular as well, in particular including even the "inverse" correspondence F a : NS i in stem-final position as in 'air'.)

I can say only little about Finno-Ugrian, (…)

I'm not asking you to. What I am pointing out that one of your arguments for reconstructing *a behind instances of standard *ə — an unelaborated assertion that the former would imply phonetic developments that are "next to impossible" — completely fails to hold water.

Jouna :
Saying "it's like that because that's how it is" is simply restating the data, it is not an explanation of anything.

I am a natural scientist. Therefore everything reconstructed is simply inductively restated data for me.

This is a misinterpretation of "natural science", both of its methodology and of its scope.

The "axiomatizing" of historical phonology is in a sense certainly useful, but it can never output theorems; only theories. Sometimes competing ones. This is for one part because a proto-form for any given data can always be reconstructed in multiple ways, many of them homeomorphic with each other. Which reconstruction we should prefer within any such group (e.g. any of the formulations of the Glottalic Theory, versus standard PIE, which agree on three series of stops and disagree merely on their phonetic values) can never be decided on grounds of regularity, only on grounds of typological naturality of the reconstructed inventory and implied sound changes.

For another part this is because the input of historical phonology is etymological data, which is in itself the result of research and always risks containing mistakes (lookalikes, loanwords, etc.)

The vowel /a/ attached to PIE *h/ɦ is usually provable (see the example above).

No, an attested /a/ cannot "prove" an *a — unless, of course, you circularly assume that your own theory already is true and that *a is the sole source of later /a/.

(There is, of course, no such thing as proof in historical linguistics anyway, though I hope you are already aware of this and are merely in the bad habit of using "prove" for "demonstrate".)

[JounaPyysalo]

"Every syllable that contains a Th, D or Dh calls for a laryngeal of some variety"
- Yes. The rationale for that is that this is provable. The traditional roots with *th *dɦ alternate with roots *t(e/o)h- and d(e/o)ɦ-.

WHAT? It is generally accepted that voiceless aspirates in Sanskrit, and some instances of aspirated stops in Greek, come from voiceless stops followed by a laryngeal, but with the breathy-voiced ("voiced aspirated") stops, your claim is not borne out by the facts. There are no alternations between *dh and *d(e/o)H anywhere in PIE. It seems like you are just misinterpreting Grassmann's Law, which is a parallel development in Old Indic and Greek.
– No Grassmann's Law is different, of course. Already the Neogrammarians knew of alternations D : Dh (cf. Brugmann, Grundr2 1:633-4). This and the series Dh in general is treated in my dissertation §4.6. (Mediae Aspirate) which you'll find informative.
- Also in PIE Lexicon you can find several examples of D—h : dh. There are more or less hundreds of examples of this, because in principle every instance of Dh can be traced back to a root t—h, d—h or both.

It is clear, however, that, if Indo-Uralic is real (we don't know yet), one of the two language families must have innovated regarding manners of articulation of the stops. Either Uralic has lost voicing and aspiration distinctions, or IE has innovated them. As long as we cannot reconstruct conditions which determine which stop ends up in which grade in PIE, we must assume the former. If such a change happened in Tocharian (where it certainly did), why couldn't it have happened in Proto-Uralic as well?

- I admit that this is possible, but I am really not competent in Finno-Ugric except of few pieces of data I can figure out on the basis of Finnish my mother tongue. Therefore I usually abstain of discussing Uralic (or Indo-Uralic). My experience is that amateurs are more a burden than helpful for the research and I do not want to be one of those...

[JounaPyysalo]

If you want to bring in Indo-Uralic, might a system of consonant gradation account for some of the complexity of the PIE consonants?

Already mastering and working with 100+ ancient IE languages is a suitable challenge for myself at the moment. Bringing Uralic in would enforce me to learn some 30 more languages, a process that could easily take five years or even more, so this is currently not in the menu.

Well clearly nobody can be an expert in every detail of everything, that's why science is a collaborative venture. I assume there are experts in Uralic, not least in your part of the world. It's interesting that you feel you would need to "reinvent the wheel" from scratch, rather than simply check out any points that looked doubtful in the existing reconstructions of Proto-Uralic. For example, few of the people who have worked on PIE would claim to have "mastered 100+ languages" and I really wonder exactly what you mean by that. Making such apparently outrageous claims does nothing for you general credibility.
– I did first a MA in classical Greek, then another in IE linguistics. With this strong basis I was able to learn the most ancient IE languages one by one. I, of course, keep forgetting, but it all usually comes back to me when dealing again with the language, especially because I have been compiling and etymological dictionary basically throughout my university time – and keep seeing the same words there over and over again.
Often the challenge in Indo-European linguistics is that there are so many languages that one has to learn and equally many suggested sound laws, but I feel that it is the actual capability in the languages that allows one to distinguish between the right and the wrong.

Btw. my original remark was mainly directed at WeepingElf, not an attempt to wind you up.

- Yes, I noticed this immediately after I had posted, just didn't see WeepingElf's comment before I had responded.

[JounaPyysalo]

Jouna :
Saying "it's like that because that's how it is" is simply restating the data, it is not an explanation of anything.

I am a natural scientist. Therefore everything reconstructed is simply inductively restated data for me.

Yes, but if the explanation is more complex and confusing than the data it's supposed to 'explain', what is the point?
- The story of the Indo-European languages is that of losses, changes and mergers, in general of entropy, i.e. PIE was by definition more complex than the data, i.e. the Indo-European languages – and so is the reconstruction and the theory. The point is that when reconstructed right we are also able to generate/predict the IE data with the sound laws.

Any given data set could in principle be accounted for by an infinity of hypotheses. Most however would be neither plausible nor helpful.
- In OS PIE Lexicon there is no an infinity of hypotheses, but on the contrary a finite (and minimal) set of sound laws, which is precisely why the digital application is called "finite-state technology". You can easily confirm this by checking out, e.g., the rules (sound laws) of Hittite as written for Foma so far:
http://pielexicon.hum.helsinki.fi/?showrule=21

If I leave a piece of fish unattended in my kitchen, and return to find it gone, a likely hypothesis is that my cat has eaten it. A very unlikely hypothesis is that it's been beamed up to an alien spacecraft. And there are any number of possibilities in between, some may be testable, others not. But the cat hypothesis will be favoured because it is well known that cats eat fish, this has frequently been observed, whereas alien intervention has not been reliably recorded. In the same way if we propose a model of PIE and its development that uses processes and structures commonly observed in real languages, that is more likely to be correct than a theory involving rare or entirely hypothetical constructs. They are not of course impossible in an absolute sense, but should only be given serious consideration after more probable models have been eliminated.

- The model underlying OS PIE Lexicon is exclusively based on comparison of the IE languages for every detail. No hypothetical constructs are allowed, but every single feature must be (and is) postulated on the basis of the PRINCIPLE of POSTULATION, "Durch zweier Zeugen Mund wird alle Wahrheit kund" or (August) Fick's rule.

Quite generally I feel that hypothetic constructions – if not inductive hypotheses proper – should be trashed and banned forever, only causing confusion and disarray...

[JounaPyysalo]

There are quite a few criticisms I could levy against System PIE, but if I had to pick a couple top problems, I'd go with these basic methodological issues:

1. The overloading of ablaut as a "black box" that is used to explain, almost as a deus ex machina, a number of embarrassing vowel reflexes that are normally explained using regular sound laws within the mainstream laryngeal theory of reconstruction. It should be a clear fact that a theory that allows unlimited alternation between five entities is greatly weaker than theories that seek to set constraints on where, how, and when different ablaut grades could occur.

We are quite unconcerned of that, since the five vowels are those that actually existed. No claim of unlimited alternation is made as such, but we simply allow the vowels of the cognates to be what they are.

"Allowing vowels to be what they are" is, I dare say, a failure to understand the comparative method. It does not consist of just pooling together cognates and saying that they all "existed as variants" in the proto-language.
- I agree with this, but also note that PIE Lexicon is inductive in character and a very complex effort. Due to this we have begun with providing the PIE photo-forms with the attested vocalisations and the plan is that when with sufficient data we will turn into internal comparison between the reconstructed roots and vocalisms and derive inductively on the basis of the attested vocalisations the empiric theory of Indo-European ablaut.

One reconstruction idea of yours that seems particularly terrible is that for standard CVh₁C roots and stems, long ē-grades should be reconstructed instead of compensatory lengthening thru the loss of the laryngeal. If ē-grade variants of any PIE words could exist, how come it is only certain roots where such "long grades" appear in a wide number of reflexes?
- Here I would separately discuss two different issues
First I would discuss about Saussure's original postulation of the compensatory lengthening rule, which he paralleled with the ablaut pattern *ei : i, *em : m, eA : A, the last one equated by him with the Neogrammarian schemata *ā : ǝ. Although I consider de Saussure's idea of the existence of a common factor *A underlying the schemata *ā : ǝ as his lasting (and main) contribution to the PIE reconstruction, I don't think he got the ablaut right, because the Indo-European ablaut patterns do not consists of only two, but three terms in terms of quantity. The ablaut of the quantity schemata for PIE *i, for instance, is therefore not †ei : i, but PIE *ēi : ei : i (as, e.g., in

PIE *ēi RV. raikṣ- (s.ao.) ‘einräumen’ (WbRV. 1165, āraik)
PIE *ei Gr. λείπω (pr.) ‘lassen, verlassen, zurücklassen’ (GEW 2:99,. λείπω)
PIE *i Li. lìk- (vb.) ‘(übrig, zurück) bleiben’ (LiEtWb. 372, lìkti)

Similarly, the correct outcome of the ablaut pattern for *A is *ēA : eA : A – or in the notation of PIE Lexicon PIE *ēɑḫ : eɑḫ : ɑḫ, which would be Neogr. ā : a : ǝ in the notation of Brugmann and his colleagues. What happened was that Saussure didn't master the Indo-European ablaut well enough at the time to have recognised the "Wackernagel-ablaut" Neogr. ā : a or "Pedersen-ablaut" a : ǝ which put together yield the schemata Neogr. ā : a : ǝ.

In terms of research history Saussure's error was proven to be a costly one: First he lost his credibility due to the absence of Neogr. *a in his system, secondly it opened the way for additional laryngeals obtained from the elimination of quantity.

Secondly, there is not the slightest problem in positing PIE *ē (and *ō), because these are well attested as a part of the general PIE ablaut schema PIE *ē : e : Ø : o : ō). With this ablaut all the forms of the root PIE √tɑh- √dɑɦ- (vb.) ‘geben, schenken’ (CTRL+F this in PIE Lexicon) displaying PIE *dēɑɦ- : deɑɦ- : dɑɦ- : doɑɦ- : dōɑɦ- are regularly generated.

Moreover, are you aware that some cases of *h₁ are even directly attested in loanwords into Finnic? E.g.
*ǵenh₁- 'to beget' → √inhi- in Finnish inhimillinen 'humane', ihminen (< *inhiminen) 'human'
*bʰleh₁-t- 'leaf' → Finnish lehti 'id.'
*gʰroh₁-to- 'plant' → Finnish rohto 'medicine'
*dʰeh₁-to- 'doing' → Finnish tehdas 'workplace' (> modern Fi. 'factory')
- As I have mentioned a couple of times above I do not master the Finno-Ugric field except for a couple of issues that I can figure out and verify on the basis of Finnish. In this case I can tell you that /h/ in Fi. tehdas does not represent *h, but *k, because the root is Fi. √tek- (e.g. in teko ‘deed’). In oblique stem *k was lost in Fi. tee- (from *teke-) and in Fi. tehdas we have *tekta-.

Personally I suspect though that also mainstream IE studies has suffered from the same problem to some extent, and that some number of what is even normally explained as "ablaut variants" might be explainable through conditional sound changes. Of course, we'd need significantly better-organized data than what exists currently to be able to look into this. So for that purpose, pooling together different apparent vowel variants and looking for general patterns seems likely to be indeed useful.
-

There is a vast complementary distribution in the vocabularly which allows the scholars to attach the labiovelar roots to their non-labiovelar counterparts.

This would be interesting to see, but it seems that you've so far only asserted this, not quite demonstrated it.
- I replied to this already to another visitor, but why not CTRL+F PIE √kɑhu- √gɑɦu- in PIE Lexicon. More examples can be found in my dissertation – and of course in PIE Lexicon in the future.

For a simple example, what would be the 'non-labiovelar counterparts' of *nokʷts 'night' or *gʷōws 'cow'?

In fact unconditional or near-unconditional /a/ : /i/ correspondences are quite easy to attest and quite easy to derive from a single proto-segment, e.g. between Finnish and Northern Sami:
Finnish ilma = Northern Sami albmi 'air'
Finnish liki = Northern Sami lahka 'near'
Finnish nimi = Northern Sami namma 'name'
Finnish silmä = Northern Sami čalbmi 'eye'
(In addition to the regular correspondence F i : NS a that this ought to demonstrate, all other correspondences appearing here are actually regular as well, in particular including even the "inverse" correspondence F a : NS i in stem-final position as in 'air'.)

I can say only little about Finno-Ugrian, (…)

I'm not asking you to. What I am pointing out that one of your arguments for reconstructing *a behind instances of standard *ə — an unelaborated assertion that the former would imply phonetic developments that are "next to impossible" — completely fails to hold water.
- Perhaps you should consult my dissertation for the reasons of this (especially the criticism of Burrow towards *ə).

Jouna :
Saying "it's like that because that's how it is" is simply restating the data, it is not an explanation of anything.

I am a natural scientist. Therefore everything reconstructed is simply inductively restated data for me.

This is a misinterpretation of "natural science", both of its methodology and of its scope.

The "axiomatizing" of historical phonology is in a sense certainly useful, but it can never output theorems; only theories. Sometimes competing ones. This is for one part because a proto-form for any given data can always be reconstructed in multiple ways, many of them homeomorphic with each other. Which reconstruction we should prefer within any such group (e.g. any of the formulations of the Glottalic Theory, versus standard PIE, which agree on three series of stops and disagree merely on their phonetic values) can never be decided on grounds of regularity, only on grounds of typological naturality of the reconstructed inventory and implied sound changes.
- I do not see how proto-forms could be reconstructed in multiple ways: The proto-forms are obtained – or re+constructed – from the preserved phonemes and features of the data (= re) put together (= constructed) to which noting is allowed to be added (natural science is exclusively data-based although its results can be, of course, pondered with typological evidence).

For another part this is because the input of historical phonology is etymological data, which is in itself the result of research and always risks containing mistakes (lookalikes, loanwords, etc.)

The vowel /a/ attached to PIE *h/ɦ is usually provable (see the example above).

No, an attested /a/ cannot "prove" an *a — unless, of course, you circularly assume that your own theory already is true and that *a is the sole source of later /a/.
- Note that in System PIE (2013) I had to use PIE *a (due to a font problem), but this is now replaced with PIE *ɑ (Neogr. *ə). And indeed, PIE *ɑ is considered as the sole source of "later /a/, the latter resulting from PIE *hɑe or PIE *eɑh.

(There is, of course, no such thing as proof in historical linguistics anyway, though I hope you are already aware of this and are merely in the bad habit of using "prove" for "demonstrate".)
- There is such thing as proof in the Comparative Method of Reconstruction which is called "complete induction": The theory is proven valid by demonstrating its completeness and soundness by means of generating the entire data with "axiomatised" set of sound laws. Which – needless to say – is exactly what we are for in PIE Lexicon.

[WeepingElf]

- There is such thing as proof in the Comparative Method of Reconstruction which is called "complete induction": The theory is proven valid by demonstrating its completeness and soundness by means of generating the entire data with "axiomatised" set of sound laws. Which – needless to say – is exactly what we are for in PIE Lexicon.

Are you sure you understood what you are talking about? I know what complete induction is, but I don't see how it can be applied to historical linguistics.

[KathTheDragon]

What happens if someone creates another hypothesis which also generates the entire dataset? They clearly can't both be right.

Edit: inb4 Jouna states that there can be no other hypothesis, as System PIE is necessarily correct, and this principle therefore excludes any other hypothesis from performing similarly.

[WeepingElf]

It is clear, however, that, if Indo-Uralic is real (we don't know yet), one of the two language families must have innovated regarding manners of articulation of the stops. Either Uralic has lost voicing and aspiration distinctions, or IE has innovated them. As long as we cannot reconstruct conditions which determine which stop ends up in which grade in PIE, we must assume the former. If such a change happened in Tocharian (where it certainly did), why couldn't it have happened in Proto-Uralic as well?

It seems that at least some instances of PIE fricatives correspond to Uralic stops as well, such as the plural *-s and the dual *-h1 (Uralic *-t and *-k, respectively). Maybe Uralic collapsed all PIU stops and non-sibilant fricatives (the antecedent of those IE *-s that correspond to U *-t may have been */θ/) into its single stop series. Hyllested lists some cognate pair candidates where PIE laryngeals seem to correspond to PU *k; also, the three flavours of PIE laryngeals seem to correspond largely, though not perfectly, to PU vowel colours. (Also, I still maintain that it is at least plausible that the PIE "voiced aspirated" stops actually were voiced fricatives, giving Early PIE, or perhaps PIU, a nice 2x2 system of voiceless stops, voiced stops, voiceless fricatives and voiced fricatives - which Uralic would have collapsed into a single row of stops.)

[JounaPyysalo]

- There is such thing as proof in the Comparative Method of Reconstruction which is called "complete induction": The theory is proven valid by demonstrating its completeness and soundness by means of generating the entire data with "axiomatised" set of sound laws. Which – needless to say – is exactly what we are for in PIE Lexicon.

Are you sure you understood what you are talking about? I know what complete induction is, but I don't see how it can be applied to historical linguistics.

Sound laws are induction hypotheses and with a complete set of sound laws applied through the complete data the required proof can be obtained.

[JounaPyysalo]

What happens if someone creates another hypothesis which also generates the entire dataset? They clearly can't both be right.

Edit: inb4 Jouna states that there can be no other hypothesis, as System PIE is necessarily correct, and this principle therefore excludes any other hypothesis from performing similarly.

– Actually we do have several open problems, all marked with red in PIE Lexicon desktop. The most urgent is that of the postulation of the PIE accent/tone system in a manner that generates all Indo-European languages from a single unified theory. We haven't tried nor failed in this as of yet, but I can readily see that the problem is very challenging, perhaps the most difficult of all.

In addition we still encounter a dozen (or so) unsolved problems with the individual languages (or language groups). Thus, for instance, we''ve not been able to set forth comparatively provable rules for predicting the vowels /a/ and /ä/ both in Tocharian A and B (also the vowel TochB. /e/ causing difficulties). Similarly the change *u -> o in Germanic languages (except for Gothic) remains somewhat puzzling: Some of the instances can be predicted if the "a-umlaut"-rule is added, but this seems not to be sufficient.

With regard to the correctness of System PIE I would like to say that the issue why it was made in the first place was that I was not pleased with the huge number of irregularities in all traditional theories. Accordingly a course was taken towards fixing the bugs – not actually caused by analogy but the problems with the postulated rules and their formulation. Once fixed, secured in the data and confirmed regarding to their mutual compatibility (consistency) the outcome is somewhat acceptable as a starting point. As mentioned above errors remain, but we indicate these with red directly in the PIE Lexicon desktop in order to approach their solution as well.

Whether PIE Lexicon will be completely successful in generating the entire data in a regular manner or not remains to be seen, but even if that is not the case at least we have a very accurate distinction between regular and irregular (i.e. the residue in red).

[JounaPyysalo]

It is clear, however, that, if Indo-Uralic is real (we don't know yet), one of the two language families must have innovated regarding manners of articulation of the stops. Either Uralic has lost voicing and aspiration distinctions, or IE has innovated them. As long as we cannot reconstruct conditions which determine which stop ends up in which grade in PIE, we must assume the former. If such a change happened in Tocharian (where it certainly did), why couldn't it have happened in Proto-Uralic as well?

It seems that at least some instances of PIE fricatives correspond to Uralic stops as well, such as the plural *-s and the dual *-h1 (Uralic *-t and *-k, respectively). Maybe Uralic collapsed all PIU stops and non-sibilant fricatives (the antecedent of those IE *-s that correspond to U *-t may have been */θ/) into its single stop series. Hyllested lists some cognate pair candidates where PIE laryngeals seem to correspond to PU *k; also, the three flavours of PIE laryngeals seem to correspond largely, though not perfectly, to PU vowel colours. (Also, I still maintain that it is at least plausible that the PIE "voiced aspirated" stops actually were voiced fricatives, giving Early PIE, or perhaps PIU, a nice 2x2 system of voiceless stops, voiced stops, voiceless fricatives and voiced fricatives - which Uralic would have collapsed into a single row of stops.)

- As I said I cannot say much of Uralic, far beyond my competence, but I have seen many alleged comparisons between PIE *H : Ural. *k and I cannot say I'd be too hopeful in this sector.