The ubiquitous argument for intelligent design is the hypothesis of irreducible complexity: some mechanism or item appears exquisitely designed in such a way that the following hold: the mechanism or item could not have arisen through gradual steps; and that mechanism or item is prohibitively improbable. The common analogy is with a mousetrap or a ticking watch; the common example is the bacterial flagellum. The conclusion that a mechanism or item is irreducibly complex strikes a death knell for evolution, as Darwin himself noted in On the Origin of Species.

To begin with, let's reexamine how science works. A scientists will propose a theory -- that is, a hypothesis which derives its descriptive power from a proposed mechanism -- and will then attempt to falsify it. If, time and time again, the theory is not falsified (and presuming that it can be falsified), it is established as an accurate approximation of reality.

To establish the existence of irreducible complexity would effectively falsify neo-Darwinism. Establishing the existence irreducible complexity, however, is far more difficult than it may appear at first sight: prohibitive improbability alone is casually and effectively explained by neo-Darwinism, so the important, and troublesome, assertion is that there exists no evolutionary pathway whatsoever. This claim is often confused with scientific ignorance -- i.e., because no pathway has been presented means that no pathway exists. The distinction is a subtle, but common, error in logic: confusing an implication with its converse.

More pertinently, lack of knowledge does not falsify evolution. It tells us nothing about whether or not the mechanism or item evolved. If a plausible evolutionary pathway can be advanced, it follows as a confirmation of evolution -- i.e., yet another prediction that was not disproven. However, the inability to advance a plausible pathway does not mean that no explanation exists.

To drive the point home, consider the analogy of a trip. Suppose you saw me at my home in Muncie at 1:00 pm, and now you see me arriving in Evansville (presumably for the first time) at 7:00 the next morning. You advance the theory that I drove from Muncie to Evansville, leaving my home at 1:00 pm. This is, of course, analogous to the evolution of our "irreducibly complex" item. Among other things, the theory predicts that I will arrive sometime after 5:00 pm, that I will be in the same car, and that I will take some route to get there. Calling the item irreducibly complex is simply the assertion that I couldn't have taken any route to get there.

Since you see me arrive at 7:00 the next morning, your theory has already passed its first test: since it's not possible to drive into Evansville in less than an hour, that prediction was certainly falsifiable. You are, however, unable to describe the route I took to get to Evansville. This does not mean no route exists; it simply means that you are unable to confirm or falsify your theory's prediction in that area. There are many other ways to falsify your theory that I drove to Evansville; instead of harping on the fact that nobody knows how I drove there, you could, for instance, note that the color and make of the car I drove into Evansville was different than the one that I drove out of Muncie. This handily disproves your theory without having to examine the practically infinite possible routes between Muncie and Evansville.

The same holds true for evolution. There are many, many ways to falsify evolution beyond the practically impossible task of demonstrating there is no possible evolutionary pathway: a species out of place; a fossil showing up in the wrong strata of the geological record; the list goes on and on. In fact, the reason evolution is such a strongly accepted theory is that there are so many ways for it to go wrong; even a single fossil out of place, even a single species which does not fit into the evolutionary pattern, will call the theory into question. Out of all of the discoveries in biology in the past century and a half, not one has contradicted the modern evolutionary synthesis. This is why evolution is so accepted: the probability of it being wrong and no disproof showing up, out of all of the possible ways for evolution to be disproven, is astronomically small.