I am wondering if there is a term for sentences that describe what the sentence accomplishes. For example, the phrase "I'm warning you." The sentence simultaneously does the warning and says it is warning.
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They are performative utterances (sentences which do something in the world, rather than describing something about it). A few more examples...
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).
This could be considered a type of meta-sentence, or self-referential sentence.
The archetype would be:
or similar contrivances such as:
In ‘The Study of Language', George Yule writes: