How the experience of the X comes to our mind. How thoughts get initiated in the mind. One can say because one wanted(intentional) to think about X. but why one wanted to think about X at a particular time, say t. I think that the activities (both in the brain and the environment) before time t(t-dt) determines what is going to come next in the mind(if exist). I claim that the want (intentionality) of thinking about the X is probabilistic. for e.g. if one is in the maths class, the chances that the want to think about X(intentionality) and X will come to the mind is more compared to when one is in the in a movie theater (influence of the environment). Suppose there are two person, one mathematician and another say musician, the probability of X to come in the mind of a mathematician is higher than musician due to the previous experiences. Even the though environment created just before the want of thought of X will also contribute to the creation of want ( the influence of the internal environment). If we know all the factors affecting the initiation of thought X with its probability, we can predict (by Bayesian integration) what want we are going to have at the next moment.
in this model of want (intentional), can someone predict what one will want after say 5 minutes? Nobody can ever predict, because the variables that affects the want has still not unfolded. Our system will be only able to predict the evolution of a want only when it has the current values(or some values just before it if it is leaky integrator Bayesian model) of variables affecting the thoughts of X.
To me, it seems that we humans have illusion that we do things or we want to think about something and it comes to our mind, whereas even our want itself is determined by many external and internal variables (many unknown of course). Illusions like rubber hand syndrome, we erroneously attribute it to us. The intetionality is an illusion.