"I don't understand how this could happen so therefore it couldn't have."
An argument from incredulity (also known as argument from personal belief or argument from personal conviction) which is that one's personal incredulity or credulity towards a premise is a logical reason for acceptance or rejection.
This incredulity can stem from ignorance (defined as a lack of knowledge and experience) or from willful ignorance (defined as a flat out refusal to gain the knowledge). The concept of irreducible complexity is based entirely around this idea of personal incredulity. One person (Michael Behe) cannot see how something evolved naturally, therefore it can't possibly evolve naturally.
Your Ignorance
What Good Is Half An Eye?
100 years ago, this was go-to argument for Creationists.
But many organisms have been found with very primitive eyes - a 100th of an eye in our terms.
Even an eye that can do little more than distinguish between light and dark gives the owner an advantage over one with no sight. It can better find food, avoid predators, and find a mate, all of which increases its chance of finding a mate.
Irreducible Complexity
The argument from irreducible complexity is a descendant of the teleological argument for God (the argument from design or from complexity). This states that because certain things in nature are very complicated, they must have been designed. William Paley famously argued, in his 1802 watchmaker analogy, that complexity in nature implies a God for the same reason that the existence of a watch implies the existence of a watchmaker.
The term "irreducible complexity" was coined by Michael Behe, who defined it as applying to: A single system which is composed of several interacting parts that contribute to the basic function, and where the removal of any one of the parts causes the system to effectively cease functioning.
The argument is supposed to go that something like the eye is so complex and intricate, that it could not possibly have evolved through natural selection. Each part is useless without the other parts, and it either works as a complete unit, or not at all.
In the 2005 Kitzmiller v. Dover Area School District trial, Behe gave testimony on the subject of irreducible complexity. The court found that "Professor Behe's claim for irreducible complexity has been refuted in peer-reviewed research papers and has been rejected by the scientific community at large."[2] In fact, there are plenty of examples documented through comparative genomics showing that complex molecular systems are formed by the addition of components as revealed by different temporal origins of their proteins.
Behe's Mousetrap
Behe uses the mousetrap as an illustrative example of this concept. A mousetrap consists of five interacting pieces - the base, the catch, the spring, the hammer and the hold-down bar. All of these must be in place for the mousetrap to work, as the removal of any one piece destroys the function of the mousetrap. Likewise, he asserts that biological systems require multiple parts working together in order to function. Intelligent design advocates claim that natural selection could not create from scratch those systems for which science is currently unable to find a viable evolutionary pathway of successive, slight modifications, because the selectable function is only present when all parts are assembled.
In his 2008 book Only A Theory, biologist Kenneth R. Miller challenges Behe's claim that the mousetrap is irreducibly complex. Miller observes that various subsets of the five components can be devised to form cooperative units, ones that have different functions from the mousetrap and so, in biological terms, could form functional spandrels before being adapted to the new function of catching mice. In an example taken from his high school experience, Miller recalls that one of his classmates
...struck upon the brilliant idea of using an old, broken mousetrap as a spitball catapult, and it worked brilliantly....It had worked perfectly as something other than a mousetrap....my rowdy friend had pulled a couple of parts --probably the hold-down bar and catch-- off the trap to make it easier to conceal and more effective as a catapult...[leaving] the base, the spring, and the hammer. Not much of a mousetrap, but a helluva spitball launcher....I realized why [Behe's] mousetrap analogy had bothered me. It was wrong. The mousetrap is not irreducibly complex after all.
Other systems identified by Miller that include mousetrap components include the following:
use the spitball launcher as a tie clip (same three-part system with different function)
remove the spring from the spitball launcher/tie clip to create a two-part key chain (base + hammer)
glue the spitball launcher/tie clip to a sheet of wood to create a clipboard (launcher + glue + wood)
remove the hold-down bar for use as a toothpick (single element system)
The point of the reduction is that - in biology - most or all of the components were already at hand, by the time it became necessary to build a mousetrap. As such it required far fewer steps to develop a mousetrap than to design all the components from scratch.
Thus the development of the mousetrap, said to consist of five different parts which had no function on their own, has been reduced to one step: the assembly from parts that are already present, performing other functions.
The Intelligent Design argument focusses on the functionality to catch mice. It skips over the case that many, if not all, parts are already available in their own right, at the time that the need for a mousetrap arises.
Behe's Examples of Irreducible Complexity
Supporters of intelligent design argue that anything less than the complete form of such a system or organ would not work at all, or would in fact be a detriment to the organism, and would therefore never survive the process of natural selection. Although they accept that some complex systems and organs can be explained by evolution, they claim that organs and biological features which are irreducibly complex cannot be explained by current models, and that an intelligent designer must have created life or guided its evolution. Accordingly, the debate on irreducible complexity concerns two questions: whether irreducible complexity can be found in nature, and what significance it would have if it did exist in nature.
Behe's original examples of irreducibly complex mechanisms included the bacterial flagellum of E. coli, the blood clotting cascade, cilia, and the adaptive immune system.
Behe argues that organs and biological features which are irreducibly complex cannot be wholly explained by current models of evolution. In explicating his definition of "irreducible complexity" he notes that:
An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modifications of a precursor system, because any precursor to an irreducibly complex system that is missing a part is by definition nonfunctional.
Irreducible complexity is not an argument that evolution does not occur, but rather an argument that it is "incomplete". In the last chapter of Darwin's Black Box, Behe goes on to explain his view that irreducible complexity is evidence for intelligent design. Mainstream critics, however, argue that irreducible complexity, as defined by Behe, can be generated by known evolutionary mechanisms.
Behe's claim that no scientific literature adequately modeled the origins of biochemical systems through evolutionary mechanisms was challenged at the Dover trial, in quite an amusing way. Behe is a very small guy, and as he was sitting in the witness stand, the prosecutor produced book after book, each one containing a study which supported the evolutionary explanation, which he stacked on the shelf surrounding the witness box. By the end, Behe had completely disappeared behind the wall of published evidence refuting his claim. At that point, he was asked if he could produce any scientific publications supporting his view. Behe was obliged to admit that not one existed.
The judge in the Dover trial wrote "...on cross-examination, Professor Behe was questioned concerning his 1996 claim that science would never find an evolutionary explanation for the immune system. He was presented with fifty-eight peer-reviewed publications, nine books, and several immunology textbook chapters about the evolution of the immune system; however, he simply insisted that this was still not sufficient evidence of evolution, and that it was not "good enough." "We therefore find that Professor Behe’s claim for irreducible complexity has been refuted in peer-reviewed research papers and has been rejected by the scientific community at large.
He went on to rule that "In fact, the theory of evolution proffers exaptation as a well-recognized, well-documented explanation for how systems with multiple parts could have evolved through natural means .... By defining irreducible complexity in the way that he has, Professor Behe attempts to exclude the phenomenon of exaptation by definitional fiat, ignoring as he does so abundant evidence which refutes his argument. Notably, the National Academy of Science has rejected Professor Behe’s claim for irreducible complexity..."