First, all biological systems must be reducible, since the laws of thermodynamics have not been repealed.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.
Never mind, it went completely over your head. Not a flame, just a fact. This response itself is so out of context that you clearly do not understand the terms of the discussion. Not only did you not refute my point, your response was not even relevant to my point.
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.
Actually, it would seem you are in over your head, theoretically. My points are not new to veterans of these threads, and the mathematics have been well-vetted here before. Was my argument esoteric? Yes. Was it relevant? Very.
Let me rephrase, and let you work from there:
All biological systems are as a class reducible per mathematics. In the general case, there are an astronomical number of possible reductions and one can neither prove nor solve for the actual reduction that occurred in the system in practice. In other words, we can prove that a solution exists and also that proving the solution is generally impossible and finding a solution is generally quite intractable. Therefore, any argument premised on the notion of "irreducible complexity" is fallacious ipso facto.
This has been argued very successfully in the past against people who had more relevant mathematics background than you seem to possess. Hell, I even provided references for really basic math, something I do not normally do in these threads. I largely made the comment for your benefit and for the benefit of the discussion; it does no one's credibility any good to use arguments that are trivially falsifiable by someone competent in the art.
BTW, you need to work on your understanding of "reduction". To say that something is "irreducible" in this context means that there is no valid path between two state configurations given some arbitrary system model, which can easily include being a viable organism as a requirement. Either you do not understand this, or you do not understand the mathematical consequences of this.