There are a few erroneous assumptions about systems, and a logical flaw in the models you all use. Your logical methodology is that of verbal mathemetics. Your statements can all be rewritten as formulas. Your conditions are all controlled. 
There is no such thing as a closed system, first off. There is no system that is completely free of external influence, even so much as you can say that rules of quantum interaction are universal and therefore internal reactions of any system are governed by the external rules of quantum phenomenon. 
Since the majority of phenomenon, are quantum phenonmenon, you can actually assume that most systems are going to behave like any other system, as the presence of emergent behaviour/structure is dictated by the number of participants within the system. External interactions (my ass in this chair, for example) have little effect on the quantum make-up of either system (ass or chair) and only serve to relocate or direct the location of each sub-system within the total system.
I will now say that j03j03 is technically.. if you want to draw it out, correct in his statements about infinity and causality. But what is really being argued is semantics. Semantically, infinity supercedes everything. That has no practical application, as it was already stated that large enough numbers do a damn good job of explaining 99% of everything. Quantum mechanics is based upon renormalization. the field couldn't exist without it, without a way to "get rid of those pesky infinities." 
Causality would, of course, be technically true, if you believe in a first event at the start of creation. But you really have to admit.. that after the 13+ billions years that the known universe has existed, the number of interactions, (and really causality only applies to quantum phenomenon) would be so great, and the system so complex as to be rendered immeasurable. 
If you cannot measure causality, then why is knowing whether or not it is a product of reality in any way important? This has been a battle of semantics, which is what intellectuals do when they know that none of them has a fucking clue as to what's going on.

Chaos theory assumes random participants, or that each is acting in an independant fashion. 
The reality is that there is no such thing as an individual participant. The notion of a closed system is the perception of a system that is partially self propogating. A system cannot exist outside of its environment, the environment is a necessary condition for the system to exist in the first place. Thus the environment is part of the system, and has to be taken into consideration. If you want to expand further and take the immediate environment's environment into consideration.. and draw that out as far as you can, you realize that everything in existence is a necessary condition for everything else. 
Well.. if you expand it out to the scale of quantum phenomenon, you realize that all the atoms and electrons are beaming out energy, and effectively governing the location of thier surrounding quanta with that energy. And so you can say that in a very, very literal and impractical sense that the location of every quanta in the sphere of the planet earth would be slightly different, if you were to remove even one atom from the earths' core, and that on a timeline of a few billion years, you may just have rain in central park when they predicted sunshine.
There's your proof of causality.. but is it really that important to my life?
Emergent behaviour, and hence the predictability of emergent behaviouor can be explained in another way, and still retain the sanctity of free will.
As already stated there is no such thing as an individual anything, or a closed system. It's all part of the same system, and there's no escaping that. But there is an overlooked quality about our systems; they all have form and function, and that could not happen if every part of reality was "off, randomly doing its own thing." 
What this tells us is that reality must allign with itself in some way, and it's not that difficult to understand. It's easier to do things in groups. And that's just common sense. Every chemical is trying to do its own thing, when pitted against another chemical, it forms a reaction. Nature may randomly mix an acid and a base, but what is not random is the outcome of that reaction. 
The same can be said of all interactions: where the scale of causality is such that it is effectively random. (i'm absolutely positive, i'm the only one sitting here at this exact second doing exactly this.. that's pretty damned random) The outcome of a causal interaction is predictable. I know what sort of responses i'll get from this. I know what happens when i drink too much liquor.

And this notion of individualism.. what the fuck is that anyway? You are not an individual. You do not have only one personality. You do not have any thought the exact same way twice. You are more than you think you are. Your brain is an instant by instant snapshot, represesnting the sum total of trillions of individual and distinct organisms each being stimulated in different ways, and reacting with predictable and consitent outcomes for each varying form of stimulus. If it were not for this reliability (reliability in this case being a product of scale) you could not exist. If it were not for the fact that you will have consistent, reliable, and predictable reactions, there could be no thought at all. 
You would also not have the depth of information available to you, if you were a single intelligence, it is because of the scale of the system that you are comprised of that you think. 
A virus is a single intelligence: it contains one single piece of genetic information, coded with the information to allow it to become self-propogating, and self replicant when met with favourable conditions.
Key wording there: favourable conditions. You can determine the world as partially causal on one scale, in that you can identify one reaction that is not occurring, identify the necessary conditions to elicit this reaction, introduce them and make it happen. This is cause and effect. 
I think my points been made: that whether you view the wold as causal, or non-causal simply depends upon the scale at which you view it.

More on emergence:
Complex systems should not be viewed as random systems, but rather as the relationship between the cyclical actions of its participants. In gradeschool science, we learned that if you see three cars stopped with thier turn signals on, that as you watched, they would eventually line up, blink at the same time for a few seconds and then appear to blink randomly again. This is an example of emergent behaviour.
It is easier for actions to be completed when there is a unification in behavior of the participants. Think of three trucks pulling on a boulder from 3 directions.. the boulder isn't likely to move. It will if the unify direction. This is because there is only so much entropy available to a system for consumption. Two groups participating in the same system will divide entropy amongst thier participants. The group with the highest sum total of entropy will gain dominance of the system. It is easier to store entropy in large groups.
So really, what we see as causality is the behaviour of multi-participant groups, usually partially self replicant*, as they respond to favourable conditions as they become more or less favourable. 
 *(meaning to have the ability to direct entropy from other systems, into the current system. think of giving 110%..) 

feel free to contact me for further discussion on systems theory.