Georgina,
"Does assigning boundary conditions mean specifying or at least deciding what will and will not be considered as part of the problem, the limit of the particular investigation?"
No. It means arbitrarily limiting a continuous function to an interval of analysis that does not result in infinities or singularities.
"If so then I agree we do do that. Though we could have open ended investigations where gradually more and more parameters and variables are added to the boundary of the investigation, giving further complexity to the answer."
That's the problem, though. One cannot extend boundaries with sufficient ad hoc parameters (adjustable variables) to assure a unique solution. Consider the various climate change models in this context -- there's a raft of parameters that produce a great number of predictions; however, the outcomes are all dependent on which variables are physically manifest. Information doesn't increase knowledge -- (the source of Einstein's aphorism "Imagination is more important than knowledge") -- knowledge is realized in the correspondence of theory (what we imagine) to physical result (what happens).
"Gaps could also be filled at different scales and linked, until theoretically everything is causally linked to everything else."
We already know that everything is causally linked to everything else -- at least, we assume so. If there are uncaused effects, the implication is that some force external to nature ("God of the gaps" argument) tinkers with creation at either random or unknown intervals. We can't treat such a case by scientific method, even if it should happen to be true. Science depends on replication of results in an objective way.
Suppose I have a pain in my stomach, and a physician determines that a signal from my brain is causing the sensation. She gives me a chemical to block the signal. No pain -- yet can we assign the cause of the pain to a random brain impulse? Probably not -- suppose an infection has created pressure on nerve endings in my gut -- the pain is a symptom, created by positive feedback between nerve endings and brain. The brain is not controlling the activity causing the pain; it is relaying information that compels the body to create a negative feedback loop, bringing into play a range of responses that release various chemicals and white cells to attack the infection and restore normal function. Any treatment intervention is only an extension of this negative feedback. If the body's reponses and treatment fails, a unbroken positive feedback loop leads to extinction of the organism.
Locally, positive feedback is always disagreeable. Consider the "squeal" of a positive feedback loop between a microphone and amplifier. We cannot identify the cause of the squeal (microphone or amplifier) though we know the effect is not uncaused.
By top-down causation, I think George Ellis implies that any ultimate cause must result in negative feedback -- i.e., there exists a universal control mechanism that accounts for the coherence and comprehensibility of the universe as we experience it. (I suggested in my ICCS 2007 paper, "Time, change and self organization" that gravity itself qualifies as such a mechanism, because it operates in but one direction, toward the center of mass.) The subsystems of the universe (such as we creatures) therefore must be endowed a priori with the means of cognitively choosing a direction that escapes the positive feedback loop that leads to extinction. As George says explicitly, "... life would not be possible without a well-established local arrow of time." The property of consciousness cannot be separated from all of the properties of life itself, whether organic or inorganic.
Tom