I've been avoiding jumping into these discussions lately, but I wanted to make the point that "irreducible complexity" is not a term of art and that its use in practice is mathematically self-inconsistent. The use of this notion to "prove" anything betrays a fundamental non-understanding of the principles that nominally are behind it.
First, all biological systems must be reducible, since the laws of thermodynamics have not been repealed. And even if no person ever figures out a reduction, such a reduction does exist (see: Solomonoff, 1978). Furthermore, in the general case such reductions are intractable i.e. if you can not observe the transition path then it will generally be impossible to discern the reduction in most non-toy systems (see: Hutter, 2000). Though we can make really good guesses for some classes of system and under certain conditions (see: Feder et al, 1992), which is what we limit ourselves to in practice.
The second problem is that "irreducibly complex" sounds very suspiciously like an actual term of art, particularly in algorithmic information theory: Minimum Description Length (MDL) (see: Kolmogorov). The only obvious reason that they invented a new term for ID purposes rather than using a standard term that had been around for almost a half century in the field they were nominally borrowing from is that properties are ascribed to "irreducible complexity" that can trivially be shown to be nonsense when you call it MDL. This is the "mathematically self-inconsistent" part I mentioned above. It is pretty much literally as if I decided that "1+2=3" is convenient for my theory but I really need "2+1=4" for everything to work out, and so I redefine mathematics to support this notion. You can do it but it will be completely broken, which irreducible complexity is in fact. You can make the mathematics support it, but not any mathematics that actual mathematicians generally use.
BTW, the papers referenced have nothing to do with evolution or ID, but are actually seminal and fundamental mathematical papers (all relating to the broader field of information theory) that prove the general point that references them. It is sad that "information theory" ID theorists like Dembski actually have some type of pseudo-credibility with ID proponents when most of what they write is grossly inconsistent or outright disprovable with the core theorems of the field nominally being used to prove the point. (Dembski is one of the worst offenders of this and therefore attracts much ire from me.)
None of this speaks to whether or not there is a Designer, but most current ID theory that I'm familiar with is trivially disprovable with the standard theorem set of algorithmic information theory. Which is fine -- you just need to develop a better theory for ID -- but it does not exactly speak to the credibility of the people currently working on ID theory.
First, all biological systems must be reducible, since the laws of thermodynamics have not been repealed.
Huh?
Yes, everything is reducible in the sense that you're saying it (well, until you get to the Planck length, but that's another discussion), but not everything is reducible while still sustaining the life of an organism and the usefulness of the organ in question. The point of the irreducible complexity argument is that there are many systems that would require either "hopeful monster" leaps of many major mutations all working together at once to create them. If you try to put them together piecemail (as in one mutated gene at a time), you have to go through multiple unviable stages--which would violate the whole natural selection argument.
The rest of your post is so obtusely written that, given the monstrous error exhibited in your first argument, it's not worth the effort it would take to try to pull it together into something coherant enough to debate.
And on that note, I'm off to bed. If it's a slow news day and work day tomorrow, I'll pop back in. Goodnight, and thanks to all for the spirited debate.