Irreducible complexity is the argument that certain biological systems cannot have evolved by successive small modifications to pre-existing functional systems through natural selection, because no less complex system would function.
An example of this is the bacterial flagellum, which relies on a system of intricately-arranged mechanical parts. If you remove just one part, you would lose the function of that system. This can be likened to a mouse trap, which comprised five basic components. Remove any one and it ceases to have the function of a mouse trap. Evolution cannot explain how the bacterial flagellum can be built gradually when you have no function until all the parts are in place.
In the video below, Ken Miller tries to refute the concept of irreducible complexity. However, he makes the following fundamental flaws in his argument.
Miller brings up the analogy of the mouse trap. The mouse trap consists of five individual parts and all the parts have to be in place before it can trap mouse. Miller understands irreducible complexity to mean that the mouse trap is completely useless unless all the parts are in place. He then went on to prove that that is not true. By taking out two of the parts – the base plate and the spring – he can create a tie pin that serves a function. That to him is proof that irreducible complexity is untrue.
The flaw of this reasoning is that while it is true that the individual parts even by itself can serve a function, e.g. a spring can bounce objects, none of the individual parts can perform the function of trapping mouse. Therefore, how did the mouse-trapping function evolve? Something must have a function for natural selection to take place. So evolution would say that the spring has a function and evolves to a better spring. The base plate has a function and evolves to a better base plate. But none of them have the function of even a poorly-functioning mouse-trapping so they can’t evolve to a normal-functioning mouse trap.
In this next video, Miller extends the same reasoning to the bacterial flagellum and he points out that one of the parts of the bacterial flagellum, the Type III Secretory System, has a function. The same mistake in reasoning as above. Even though the Type III Secretory System has a function, it is not a sluggish propeller that later evolved into an efficient propeller of the bacterial flagellum. At best it will evolve into a more sophisticated secretory system. In other words, you still need all the parts of the bacterial flagellum to come together. How did this happen?
The parts of a mouse trap must come together first to form the most basic mouse trap before this mouse trap can evolve to become a more sophisticated mouse trap. The question is how do they come together to form a mouse trap. In the video below, Behe explains that the parts of the bacterial flagellum are not “nice little boxes” that align themselves when they happen to come together.
Even if you have a universe of all available parts for every object, like maybe a junk yard. You toss the parts at random and after few billion years the five parts required for a mouse trap come together in one place. Now what? Does a mouse trap appear? No, you still need the gluing, screwing, etc. Like a flagellum that is intricately joined correctly at the right place. If the simple mouse trap with five parts needs an intelligent agent to put it together, can the bacterial flagellum come about spontaneously?
Genes for building the Type III Secretory System are older than the genes for building the bacterial flagellum suggesting that if both are related, it is the bacterial flagellum degenerated into the Type III Secretory System and not the bacterial flagellum being built from the Type III Secretory System.