Since Brentano, intentionality has been the mark of the mental: mental states are directed at an object, even a nonexistent one, as when one fears a ghost (Brentano, 1874/1995). It is not to be confused with intending to do something: a perception is intentional in this technical sense though it pursues no goal.
For AI, the question is whether a system can have intentionality of its own or only a borrowed one. Searle (1980) argued for the latter. We attribute "understanding" to automatic doors and thermostats by metaphor, because in artifacts "we extend our own intentionality" (1980, p. 419); a program, by contrast, has a syntax but no semantics, and such intentionality as it appears to have lies solely in the minds of those who program and use it (1980, p. 422). Real intentionality would require causal powers equivalent to the brain's (1980, p. 417). Haugeland (1985) named the background of this dispute the "mystery of original meaning": some meanings derive from others, but not all of them can be derivative (1985, p. 27).
The most influential alternative is Dennett (1987)'s intentional stance: treat a system as a rational agent, ascribe to it the beliefs and desires it ought to have given its place and purpose, and predict that it will act accordingly (1987, p. 17). If it predicts well, there is no further fact to look for. Shanahan (2024) accepts it as harmless shorthand ("My phone thinks we are in the car park"), but warns that with LLMs "things can get a little blurry": when telling a model to think step by step improves its reasoning, the temptation to see human-like traits in it is almost overwhelming (2024, p. 71).
Between the poles there are nuances. Millière & Buckner (2024a) separate reference, which an LLM might inherit from the linguistic community, from stable, hierarchical communicative intentions, which it seems to lack, although a model given a goal can form subgoals in context (GPT-4 feigning a visual impairment to get someone to solve a CAPTCHA for it) (2024a, sec. 3.3). The question remains open: is intentionality an inner fact, a successful attribution, or a status that others grant us within a practice?