Capital letters are markers of positions that are used more than positions marked by small letters.
Thereby, there is no principal structural difference between languages of American type and Altaic type, difference is in degree of manifestation of certain parameters and so, in order to our conclusion will not be speculative, we should speak about degree of prefixation producing ability / prefixation ability degree / prefixation ability index, i.e.: of certain measure of prefixation.
I suppose that each language has its own ability to produce prefixation and that this ability doesn’t change seriously during all stages of its history.
Also I suppose that prefixation ability demonstrates itself in any circumstances, i.e.: it is manifested by any means: by means of original morphemes existing in a certain language or by borrowed morphemes.
If a language has certain prefixation ability it is shown anyway. That’s why I don’t make difference between original and borrowed affixes.
Also for current consideration is not principal whether this or that affix is derivative or relative: if we take into account relative affixes only, then, for instance, Japanese is a language without prefixes.
That’s why we should define prefixes not by its derivative or by its relative role but by its positions inside word form, prefix is any morpheme that meets the following requirements:
1) it can be placed only left from nuclear position;
2) it never can be placed upon nuclear position;
3) between this morpheme and nuclear can’t be placed any meaningful morpheme with its clitics (i.e.: between nuclear root and prefix can’t be placed a meaningful morpheme with its auxiliary morphemes).
I am specially to note that there are no so called semi-prefixes. If a morpheme can be placed in nuclear position it is meaningful morpheme and any combinations with it should be considered as compounds.
Thus can be resumed the following:
1) Each language has its own ability to produce prefixation and this ability doesn’t change seriously during all stages of its history.
2) Prefixation ability is manifested by any means: by means of original morphemes existing in a certain language or by borrowed morphemes. That’s why the method doesn’t suppose distinction between original and loaned affixes.
3) Genetically related languages are supposed to have rather close values of Prefixation Ability Index.
2.1.3. PAI calculation algorithm
How Prefixation Ability Index (here and further in this text abbreviation PAI is used) can be measured?
Value of PAI is portion of prefixes among affixes of a language.
Hence, in order to estimate portion/percentage of prefixes of a certain language we should do the following:
1) Count total number of prefixes;
2) Count total number of affixes;
3) Calculate the ratio of total number of prefixes to the total number of affixes.
Why is it important to count total number of prefixes and then calculate the ratio to the total number of affixes but not to estimate PAI by frequency of prefix forms in a random text?
A certain language can have quite high value of PAI but in a particular text word forms with prefixes can be of low frequency. Our task is to estimate portion of prefixes in grammar but not portion of prefix forms in a random text. Prefixes/World index estimated by Greenberg was exactly that estimation of prefix forms frequency in a text (Greenberg 1960).
Of course, that index also can give some general notion of prefixation ability of a language, though it is extremely rough and inaccurate since in a randomly chosen text can be very little amount of words with prefixes: the longer text is the more precision is the conclusion but anyway error of such estimation still remains very high; while when we count all exiting affixes of a certain language potential error is extremely low and even if we occasionally forget some affixes it doesn’t influence seriously on our results.
Moreover I am to note that despite Greenberg made great work on the field of typology he didn’t actually use those results in his research; he was an adept of megalocomparison and made his conclusions basing on “mass comparison” of lexis but not on structural correlations; his interest in typology was a “glass beads game” and was separated from his actual field of studies.
To those who think, that it’s impossible to estimate number of morphemes since living language always changes, I am to tell that living language doesn’t invent new morphemes every day, especially auxiliary morphemes. The fact that learning a language we can use descriptions of its grammar written some decades ago is the best proof that grammar is a very conservative level of any language.
Hence, we can estimate total number of affixes of a living language as far as we can get its description where all stable forms are represented. And there is no need to care of what can be in a certain language in future, i.e.: we consider current stage of living language and don’t care of possible future stages since they simply don’t exist yet.
As for possibility of count, I am to tell that even set of words is countable set while set of morphemes and especially auxiliary morphemes is not just countable set but also is finite set.
2.1.4. PAI method testing: from a hypothesis toward a theory
In order to test PAI hypothesis I paid attention to some languages of firmly assembled stocks: Austronesian, Indo-European and Afroasiatic.
2.1.4.1. PAI of languages of Austronesian stock
Polynesian group
Eastern Polynesian Subgroup
Hawaiian 0.82 (calculated after Krupa 1979)
Maori 0.88 (calculated fater Krupa 1967)
Tahitian 0.66 (calculated after Arakin 1981)
Samoan-Tokelauan subgroup
Samoan 0.5 (calculated after Arakin 1973)
Tongic subgroup
Niuean 0.8 (calculated after Polinskaya 1995)
Tongan 0.78 (calculated after Fell 1918)
Philippine group
South Mindanao subgroup
T’boli 0.72 (calculated after Porter 1977)
Northern Luzon subgroup
Pangasinan 0.6 (calculated after Rayner 1923)
Malayo-Sumbawan group
Malay subgroup
Indonesian 0.53 (calculated after Ogloblin 2008)
Pic. 2. Map representing location of Austronesian languages mentioned in current chapter: languages are marked by red, place names are maked by black.
Chamic subgroup
Cham 0.6 (calculated after Aymonier 1889; Alieva, Bùi 1999)
Formosan group
Bunun 0.8 (calculated after De Busser 2009)
Eastern Barito group
Malagasy 0.74 (calculated after Arakin 1963)
2.1.4.2. PAI of languages Indo-European stock
German group
Dutch 0.49 (calculated after Donaldson 1997)
German 0.51 (calculated after Donaldson 2007)
English 0.61 (calculated after Barhkhudarov et al. 2000)
Icelandic 0.63 (calculated after Einarsson 1949)
Slavonic group
Czech 0.52 (calculated after Harkins 1952)
Polish 0.57 (calculated after Swan 2002)
Celtic group
Irish 0.67 (McGonage 2005)
Welsh 0.35 (calculated after King 2015)
Roman group
Latin 0.26 (calculated after Bennet 1913)
Spanish 0.34 (calculated after Kattán-Ibarra, Pountain 2003)
2.1.4.3. PAI of languages of Afroasiatic stock
Semitic group
Central Semitic subgroup
Arabic (Classical) 0.26 (calculated after Yushmanov 2008)
Phoenician 0.26 (calculated after Shiftman 2010)
Eastern Semitic subgroup
Akkadian (Old Babylonian dialect) 0.2 (calculated after Kaplan 2006)
Egypt group
Coptic (Sahidic dialect) 0.87 (calculated after Elanskaya 2010)
Pic. 3. Diagram representing PAI values of some firmly assembled stocks
2.1.5. PAI of a group/stock
PAI of a group or a stock can be calculated as arithmetical mean and it’s quite precise for rough estimation.
One can probably say that just arithmetic mean is quite rough estimation and in order to estimate PAI in a more precise way it would be better to take values of PAI of particular languages with coefficients that show proximity of particular languages to the ancestor language of the stock. Coefficient of proximity is degree of correlation of grammar systems.
Let’s test this hypothesis and see whether it so.
For instance, in the case of Austronesian it would be somehow like the following:
Malagasy^PAN9 ≈ 0.5;
Bunun^PAN ≈ 0.8;
Philippine group^PAN ≈ 0.7;
Indonesian^PAN ≈ 0.6;
Cham^PAN ≈ 0.4;
Polynesian languages^PAN ≈ 0.5.
Indexes show degree of proximity of languages (grammatical systems). In current case these indexes are not results of any calculations but just approximate speculative estimation of degrees of proximity of modern Austronesian languages with Proto-Austronesian; it is supposed that Formosan languages and so called languages of Philippines type are the closest relatives of PAN among modern Austronesian.
If we take each particular PAI value with corresponding coefficient of proximity we get that PAI of Austronesian is about 0.44.
If we take just arithmetical mean without proximity coefficients we get 0.6.
0.6 is obviously closer to real values of PAI of Austronesian languages than 0.44. Hence thereby it’s possible to state that just arithmetical mean is completely sufficient way to calculate PAI of a group/stock while PAI calculated with use of proximity coefficients gives results that differ seriously from reality.
2.1.6. PAI in diachrony
It can be supposed that PAI doesn’t change much in diachrony.
PAI of Late Classical Chinese is 0.5 (calculated after Pulleyblank 1995).
PAI of Contemporary Mandarin is 0.5. (calculated after Ross, Sheng Ma 2006).
PAI of Early Old Japanese is 0.13 (calculated after Syromyatnikov 2002).
PAI of contemporary Japanese is 0.13 (calculated after Lavrent’yev 2002).
Probably it should be also tested on other examples but even on the material of these examples we can see that PAI of a language is same in different stages of its history.
2.1.7. Summary of PAI method
One can probably say that Coptic has broken our hypothesis, but actually PAI just has shown us that group of Coptic language and Semitic group diverged very long ago, probably in Neolithic epoch yet.
However, the tests have shown that values of PAI of related languages are actually rather close, i.e.: they do not differ more than fourfold (pic. 3).
Thus, it is possible to say that PAI is something alike safety valve of comparative linguistics: if its values don’t differ more than fourfold then PAI has no distinction ability and actually there are no obstacles for further search for potential genetic relationship; but if values of PAI differ fourfold and more, then should be found absolutely ferroconcrete proves of genetic relationship.
Also I am specially to note that PAI method doesn’t require estimation of measurement error as far as PAI allows fourfold gap of values.
2.2. Why is it possible to prove that languages are not related?
2.2.1. Root of problem is changing of concepts
One can probably say that it is impossible to prove unrelatedness of two languages so I am to make some explanation on why it is possible.
In contemporary comparative linguistics there is a weird presupposition that it is impossible to prove that certain languages are not genetically related. As I can understand this point of view was inspired by Greenberg as well as some other obscurantist ideas of contemporary historical linguistics. It seems quite weird that it is possible to prove relatedness but it is not possible to prove unrelatedness. Let’s check whether it is so.
First of all, I am to note that statement about impossibility of proving unrelatedness is actually sophism based on changing of concepts, i.e.: when they speak about proves of relatedness then relatedness means “to belong to the same stock” and it is regular and normal meaning of the concept of relatedness in linguistics; however, when they speak about unrelatedness then meaning of relatedness suddenly changes: they start to suppose that actually all existing languages are related since they are supposed to be derivates of same proto-language that existed in a very distant epoch in past and due to this fact we can’t prove unrelatedness but can just state that a language doesn’t belong to a stock.
2.2.2. Concepts of relatedness and unrelatedness from the point of view of other sciences
In order to clear the meaning of the concept of relatedness it’s useful to pay some attention to other sciences where this concept also is used. If we take a look at, for instance: biology, physics or technical sciences we can see that many items are distributed by classes/classified despite they obviously have common origin; and considering them it is completely normal to speak about relatedness and unrelatedness. All being have common origin and so they all are relatives in a very deep level but this fact doesn’t mean they cannot be classified into kingdoms, phylums, classes, orders, suborders, families, subfamilies; the fact that ant, bear, pine tree, whale, sparrow have common ancestor doesn’t mean it is impossible to distinguish bear from whale and whale from pine tree.
However, as far as languages aren’t self replicating systems like biological systems and are closer to artifacts so any parallels between biological systems and language always should be made with certain degree of awareness since they are more allegories than analogies while correlations between languages and some artificial items are more precise, for instance: all existing cars are derivates of steam engine that existed in the middle of 19th century, but it doesn’t mean we can’t classify cars/engines and speak of relatedness and unrelatedness of certain types.