Dear Donald,
thank you for taking the time of reading and commenting on my essay. Regarding intentionality, I agree that the concept is treated somewhat vaguely in much philosophical literature, but I'd say my level of rigor is par for the course, at least---compare my definition: "Mental content exhibits the curious property of intentionality--of being directed at, concerned with, or simply about entities external to itself.", and that of the Stanford Encyclopedia of Philosophy: "Intentionality is the power of minds to be about, to represent, or to stand for, things, properties and states of affairs." Both essentially follow Brentano, who introduced the concept into modern discourse (saving it from the old scholastics).
Again, I can understand---and to some degree, sympathize with---wanting a more thorough definition, but sometimes one also risks getting embroiled in petty turf wars when trying to clarify every last definitional issue ('rigour mortis'). So rather than spending most of the allocated room on such definitions, I chose to introduce my model instead, hoping that this would help clarify lingering issues---apologies if it didn't.
Regarding Richard's paradox, the ordering itself isn't really so important; one merely needs an unambiguous way of referring to certain elements (either of English phrases corresponding to natural numbers, or of behaviors of a given automaton). Any association between these elements and natural numbers will do fine, since then, you can refer to the nth element, which picks out a unique one; then, you can use the diagonalization trick by creating a new element that wasn't part of the original association.
But since that was claimed to be complete (a list of all the English sentences describing real numbers/a theory of all behaviors of the automaton), we arrive at a contradiction.
Regarding self-replication, you raise a good point---natural replication is indeed never exact. This doesn't necessarily address the infinite regress, though: if the parent needs to have access to a plan of the child in order to construct the next generation, we still get a regress, even if all of the plans are allowed to differ. Furthermore, when replication is inexact, we start getting into issues of vagueness: when is a construct a 'child'? How similar do parent and child-generation have to be in order to constitute an example of self-replication? If a stone, rolling down a hill, breaks off another, is that an example of self-replication?
Lastly, you're dead-on regarding perception: it's indeed a far more active process than my caricature gives it credit. But whether the outside world is just faithfully projected onto an internal screen, or whether a sort of virtual internal reality, perhaps only loosely 'inspired by actual events', is created, doesn't make a difference for the conceptual point: both implicitly presume some central meaner (as Dennett calls the homunculus) using the internal representation as pertaining to the outside world. And with that, we're already off the rails as far as a theory of representation goes.
Again, thanks for your thoughtful comments!
Cheers,
Jochen