Stems and affixes

Both inflection and derivation are formed by concatenating stems and affixes. Inflections are formed by means of concatenating stems with an affix pattern of fixed, finite length: only one affix occurs in the pattern in English, but three occur in German, as in bau#+t+e+st, and more than this occur in agglutinative languages like Finnish, Turkish, Japanese. Given a fixed number of simple stems, only a finite number of inflected word forms can be formed. In German, the inventory of inflected forms is about five times as large as the inventory of ininflected simple stems.

Derivation is adding affixes to stems. Stems can be simple (sometimes called roots, bases, lexical morphemes), or compound. Unlike inflection, derivation is defined recursively and not in terms of an affix pattern of fixed length:

1. Basic term: A lexical morpheme is a derivational stem.
2. Recursive term: A derivational stem concateneted with a derivational affix is a derivational stem.
3. Exclusive term: Nothing else is a derivational stem.

For example, note the occurrences of ise in

as illustrated in Table 1.

 
Table 1: Suffix iteration. 

Is there a limit to the length of derivations? If not, then the definition is indeed recursive. If there is, then there might not strictly be a need for recursive rules, but their use could make the description much simpler.