Dear Conrad,
Thanks for taking the time to read my essay and for your thoughtful questions.
Since I'm not a philosopher, what I meant by "intentionality" is the first definition you'll find in a dictionary, namely "the fact of being deliberate or purposive", and likewise "intended" and "intended outcomes" etc. have their usual meaning.
I guess Eq.1 in my essay,
[math]
|\Psi\rangle_{world} = |Intention_1\rangle_{mind} |Intended Outcome_1\rangle_{env} the.rest
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can be best explained by looking at the simplest kind of entanglement, namely that of EPR/Bell state:
[math]
|\Psi \rangle ={\frac {1}{\sqrt {2}}}(|\rangle _{A}\otimes |-\rangle _{B}|-\rangle _{A}\otimes |\rangle _{B}
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when this entangled state collapses, either |>A and |->B happen together, or |->A and |>B would. (is there a way to type inline LaTeX equations??)
Similarly for Eq.1 above from my essay, we're entangling the mind state |...>mind with the environmental state |...>env in the specific way shown, such that when the entangled state collapses the states |Intention1>mind and |IntendedOutcome1>env should happen together.
As an example, |Intention1>mind may stand for "my mind wanting to grab an apple with my right hand", then |IntendedOutcome1>env may stand for "my body muscles are coordinated so that my right hand reaches out to grab the apple".
As for how exactly this kind of entanglement can occur in reality, it's the million dollar question I guess :). I offered a rather hand-waving example of how simple entanglements at the level of neurons may be combined into more complicated ones, though it's more an illustration than anything else. But Nature is surely more clever than us and I'm sure she has worked out exactly how to build the entanglement in question through billions of years of evolution.
What I mean by "intentionality" in Section 4.1 of my essay is a more generalized concept, where we started from identifying quantum entanglement of the proper type between mind and environmental states with intentionality at the macro scale, and then we infer that as we break down the macro entanglement state into its simpler constituents, we may still refer to these simpler kinds of entanglements as "intentions" at the simpler level ,and probably all the way down to the microscopic scale. In this sense, even the simple Bell state we mentioned above can be imbued with some rudiments of intentionality, though of a much more primitive variety.
Hope this answers some of your questions. I'll be checking out your essay shortly.
Ming.