I’ve criticized irreducible complexity and specified complexity as design inferences, so I think I should put forth a positive case for a proper design inference. The design inference I favor is based on background knowledge of intentions.
Consider Dennett’s examples of a laying hen, Pekingese dog, a barn swallow, and a cheetah. The first two were designed by human artificial selection, while the latter two were not. Without background knowledge of human intentions, we wouldn’t be able to tell which were designed and which weren’t. The basic point is that we infer design based on our background knowledge of intentions. But, of course, this inference is fallible, that is, we could have false positives.
Obviously when someone designs something they have an intention or a goal to create something. When Paley sees a watch on the heath, he probably is relying on his background knowledge that humans make such devices and that such devices do not naturally occur. When I see a small hole in my lawn, I infer it was designed by a rodent because of my background knowledge about the intentions of rodents in addition to my belief that holes like that are unlikely to occur naturally.
When archeologists find arrowheads, they infer it was designed because of background knowledge that humans design tools for hunting. In all these cases it’s also true that our background knowledge holds that watches, certain holes, and arrowheads are surprising assuming mindless natural causes, but that knowledge is not enough to infer design, we also need intentions. A snowflake’s structure was also once surprising, but we don’t infer design. As far as humans being designed, we have no background knowledge about intentions of creatures whose goal is to create humans. Regardless of that point, any design theory would have to beat out our current evolutionary theory; and as far as abiogenesis, the past success of naturalistic research programs give us inductive justification over any supernaturalistic research program.