Is there a term for a self-fulfilling sentence?

Solution 1:

They are performative utterances (sentences which do something in the world, rather than describing something about it). A few more examples...

• I do (take this woman to be my lawful wedded wife) - in a marriage ceremony.
• I name this ship the "Queen Elizabeth"
• I give and bequeath my watch to my brother - in a will
• I promise (anything, in the right context)

In something like This sentence contains five words, I suppose you could say that what the sentence does is introduce itself into the world, so it can be analysed (by itself, as it happens).

Solution 2:

This could be considered a type of meta-sentence, or self-referential sentence.

The archetype would be:

This is a sentence.

or similar contrivances such as:

In this sentence the letter 'e' appears ten times.

Solution 3:

In ‘The Study of Language', George Yule writes:

We use the term speech act to describe actions such as ‘requesting’, ‘commanding’, ‘questioning’ or ‘informing’. We can define a speech act as the action performed by a speaker with an utterance.