We can derive a name of action with the minen suffix from almost any verb, e.g. puhuminen (speaking) from puhua (to speak). There are several ways to derive names of actions, such as puhe and puhunta, and the minen suffix is just a way to form a general, abstract name.
This is so regular that -minen nouns could even be treated as nominal forms of verbs. However, the tradition of Finnish grammars is to treat only a few uses of -minen words as infinitives. In Iso suomen kielioppi, this tradition is broken: -minen words are treated simply as derived nouns. Instead of speaking of the IV infinitive at all, it just describes that -minen nouns have certain idiomatic uses. However, here we present the traditional view.
The IV infinitive is formed with the suffix minen, appended to the inflection stem. Of all the possible case forms of such words, only two forms are regarded as infinitives: the nominative and the partitive, e.g. puhuminen and puhumista.
The uses of the IV infinitive are:
As mentioned above, all case forms of -minen derivations could be described as infinitives. The important thing is that their use is often similar to the use of infinitives, and they can be regarded as parts of clause equivalents.
For example, the expression omenan syöminen (eating an apple) can be regarded as corresponding to the subclause että syön/syöt/... omenaa (that I/you/... eat an apple). In such constructs, the logical target (logical object) is expressed with a genitive expression before the -minen word. This differs from the normal word order as in syön omenaa or syödessäni omenaa.
The -minen derivations are often used in contexts where English uses the infinitive of a verb. For example, “To err is human” can be translated as Erehtyminen on inhimillistä. Here we cannot used the I infinitive erehtyä (to err), unless we change the word order: On inhimillistä erehtyä, which would have a different structure and tone.