Irreducible Complexity (IC) has been theorized centuries ago. For example, Cuvier in the 1830's clearly described IC. Now, Behe proposes that if there IC therefore there is Intelligent Design (ID). That is one of the main lines of force in his writings. Notice however that even Behe is aware that IC is not proof of ID as stated in his 1996 conference:
Behe said:
Demonstration that a system is irreducibly complex is not a proof that there is absolutely no gradual route to its production. Although an irreducibly complex system can't be produced directly, one can't definitively rule out the possibility of an indirect, circuitous route.
To circumvent the limitations of IC -> ID reasoning, Behe uses the simple example of a mouse trap. Now let's put Behe's mouse trap example in relation to his own definition of IC:
Behe said:
A single system composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning
The mouse trap fits the definition well: it is a single system (independent from other systems) and it performs one single basic function (killing mice). Plus each part performs one single sub-function while they interact with each other in a sequential/linear way.
Now, are living systems single systems? Are living systems only performing one single basic function? Do we know for sure the function(s) served by the system?
To answer those questions one should be able to know to what extant a system interacts with its environment, to what extant it's connected to other system and also what the
intent of the designer was (if there is a designer). Indeed the observer only assumes the presumed function(s) of a system through his limited observation. For example the Egyptians ascribed, wrongly, a tombstone function to the pre-existing pyramids.
Nowadays, cars are equipped with EGR (exhaust gaz recirculation) that reduces emissions. If one observers is not equipped with emission sensors, he might consider wrongly that the EGR is a useless part, or worse it is a detrimental part because EGR do reduce car performance.
The observer's mistakes were due to his inability to measure some variables (emissions) and to the wrong assessment of the car's functions. He might think that the sole function is performance while the designers had a multitude of functions in mind, some of these functions (performance VS emissions) being quite antinomic.
There is a bone of contention between Behe and his (neodarwinian) opponents. Behe claimed that the clotting system was IC and scientists discovered that it was not since the lampreys have a functional clotting system although three agents are missing from the clotting cascade found in most mammals.
Interestingly Behe's opponents use the non-IC of the clotting system of lamprey to disprove ID. This is a logical fallacy, Behe claims that IC implies ID. the logical consequence of IC -> ID is not non IC -> non-ID but non-ID -> non-IC. For example the following statement: "if you're Congolese, therefore you're Black" doesn't lead to "if you're not Congolese, therefore you're not Black" but to the logical consequence that "if you're not Black, therefore you're not Congolese".
So basically, to disprove Behe's points "If you're Congolese, therefore you're Black", his opponents found, say, a Mexican (non-Congolese) who is non-Black, et voilà!
One important question remains: is the clotting system really non-IC? I think here Behe became the victim of his own IC concept. While it works well for a mouse trap, it is more iffy when applied to non-linear interrelated and multipurpose biological "system" where the intent of the "designer" are not exactly known.
Behe followed many scientists by arbitrarily isolating a biochemical cascade involving a dozen different molecules and labeling it "clotting system" (one single system, one basic function). By doing so, Behe made some important (and probably wrong) assumptions:
a/ this dozens of molecules are exclusively involved in the blood clotting function
b/ this biochemical cascade is dedicated to only clotting
c/ No other system/cascade plays a role in clotting
d/ the clotting cascade does not interact in any way with other cascades or systems
Maybe the clotting system of the lamprey is different (three "missing molecules") from most mammals by design. Maybe those three missing molecules would be detrimental due to the lamprey specifics, maybe those three missing molecules do not stop the clotting but modulate it, there are so many ignored possibilities here.
Removing parts while keeping the assumed function intact is not proof of non-IC. For example a mechanics might take a production car and transform it in a race car. To do so he will strip down the car (remove the AC, remove the radio, etc.) in order to reduce weight and therefore increase performance.
If one considers the function of the car solely as to drive from point A to point B, then the function is intact despite the removal of weighty parts.
The mechanics designed the sport car, like the engineers who designed the initial production cars. The difference is not in terms of designing but in terms of functions, for the production car the functions are a complex mix of performance, luxury, reliability, cost, etc. for the race car, the functions are a different set of goals that is more focus on performance. In both cases there is design, parts are removed/added. What changed is the functions, i.e. the intent of the designer.
To falsify Behe's proposition according to which IC -> ID, his opponents brought up the lamprey controversy, an example according to them of non-IC and concluded that therefore there is no ID. As shown above it is a logical fallacy. To falsify Behe's proposition on should find an example of non-ID that is IC. Does such examples exist?
Now, let's imagine a conglomerate of various rocks partly fused together and then rolled in a river for years. It becomes a nicely cylindrical rock conglomerate. Humans use it as a rolling pin to spread and thin bread doe (here, humans have arbitrarily ascribed a function to the conglomerate).
Now, if you remove one part (one rock) from the system (the cylindrical rock conglomerate) it stops performing its basic function (rolling pin). So is it really IC?
The problem here is the function assessment and its intrinsic arbitrariness. It is humans who assigned a rolling pin function to the mineral cylinder, but what was the intent, if any, of the forces behind its creation?
According to official science this cylinder was the result of "random" fusing and erosion, therefore is it really non-ID, right?
The problem here comes from random chance, a concept actually foreign to science though abundantly used by darwinians and others. Random chance is usually a convenient term for things we don't understand. The fusing of the rock, the water erosion followed some physical laws (thermodynamics, phase transitions, fluids mechanics, etc.), so its final shape is the result of physical laws acting on it, where is then the randomness?
If it is physical laws that shaped this item, were these laws created? Is the shape therefore the (undirect) result of ID?
In the end, I think that IC while being an interesting didactic tool will never prove or disprove ID for the simple reason that at the core of the IC there is the notion of function, which is closely related to the intent of the designer. If the designer is 4D or 6D, it will be very difficult for 3D humans to decipher the exact intent behind this or that creation because it involves a level of complexity and intelligence that is simply behind our reach. If one can't for sure assess the intent behind a creation, IC becomes of the little demonstrative value.
For the above mentioned reasons proving ID might be trickier than expected. Disproving Darwinism seems more possible. In my opinion, Bryan Schiller in his book titled "the 5th option" did a briliant work proving the inanity of Darwinism by using their very own argument: random mutations.