Manual of comparative linguistics - Alexander Akulov

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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.

      These examples evidently show us the following:

      1) When they say about an item that is related with another it means “they both belong to the same class”.

      2) It is possible to speak about relatedness and unrelatedness of certain items even though all classes of them have common origin.

      2.2.3. Concepts of relatedness and unrelatedness from point of view of set theory and abstract algebra

      Concept of relatedness is actually equivalence relation since it meets necessary and sufficient requirements for a binary relation to be considered as equivalence relation:

      1) Reflexivety: a ~ a: a is related with a;

      2) Symmetry: if a ~ b then b ~ a: if a is related with b then b is related with a;

      3) Transitivity: if a ~ b and b ~ c then a ~ c: if a is related with b and b is related with c then a is related with c.

      If an equivalence relation is defined on a set then it necessarily supposes grouping of elements of the set into equivalence classes and these classes aren’t intersected (Hrbacek, Jech: 1999).

      2.2.4.

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<p>9</p>

PAN means Proto-Austronesian; “^” is sign of grammar/structure correlation