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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.