I am going to go ahead and end this one because even I have a difficult time seeing this fallacy. My brain wants to concentrate on the other fallacies. Just as I could not think of a way to demonstrate reductio as absurdum without ending in a strawman, I can not think of a way to set up this example that doesn't
seem to beg the question.
This fallacy is called The Cluster Illusion. When we are dealing with random data, or what we think is random data, our brains want to assign meaning to any cluster points. We see it as a pattern of cause and effect. The fallacy is committed when we use the very same data that made us suspect an effect to conclude the cause. This is also known as The Texas Sharpshooter fallacy. Imagine a gunman firing random shots at the side of a barn from a great distance. He finds the space where the bullet holes cluster and draws a bullseye around it, then declares himself a sharpshooter.
1) John is an investigative reporter researching rabies. While reviewing data, John notices a certain town has a much higher rate of rabies among it's animal population than chance calls for. John concludes this town is purposely spreading rabies among it's animals.
John notices a cluster of data, his brain see's it as an effect, and then he uses the very same data to conclude the cause. John ignores that it's possible for this to happen by chance, or to have some other cause, such as the data including test animals at the towns rabies research facility.
If this were stated as "I know the town is infecting it's animals because the town has a high rate of animal infections" then it is non validating, a non-argument. If it is stated as "I know the town is infecting it's animals because the town has a high rate of infecting it's animals", it is a validating argument, but begs the question. I believe John is saying the former, and so not begging the question.
I believe the reason this is not asserting the consequent is because the premise does not arise from propositional logic, but from a mistake of causation.
2) John is also a ghost hunter in his spare time. John believes electromagnetic anomalies are evidence of ghost activity. He searches all the abandoned houses in his neighborhood and finds one with a high level of electromagnetic activity as compared to the others. He buys this house and declares it the most haunted in the neighborhood.
John is working under the assumption that anomalies are evidence of ghosts, but beyond that, John sees a cluster of data points in what he considers random chance (any abandoned house has a chance of being haunted), and uses that cluster not only to suspect the house is haunted, but to conclude the house is the most haunted.
3) When we look at life we see incredible complexity arise from randomness. The chances of a protein, a cell, a frog, or even the universe forming randomly out of chaos is near nonexistent. We must have a designer.
Of course life did not become complex randomly. Life was shaped by rules and selective pressures. In the scope of this argument however, if we accept that reality is random chaos, we see complexity as cluster points among the randomness. We use these cluster points not only to suspect non-randomness, but to conclude that it's caused by a designer.
http://rationalwiki.org/wiki/Texas_sharpshooter_fallacy