This is a question that I’ve been trying to wrap my head around that can be best illustrated as an example. SETI is a project that tries to monitor radio signals to detect extraterrestrial intelligence. It tries to detect certain sequences of prime numbers for example.
If we did detect them, it may seem reasonable to postulate extraterrestrial intelligence. For otherwise, it would be a very lucky coincidence.
But I can think of other coincidences that do not make many people postulate designers. One popular example is fine tuning. As a refresher,
the universe’s fine-tuning for life: according to many physicists, the fact that the universe is able to support life depends delicately on various of its fundamental characteristics, notably on the form of the laws of nature, on the values of some constants of nature, and on aspects of the universe’s conditions in its very early stages. Various reactions to the universe’s fine-tuning for life have been proposed: that it is a lucky coincidence which we have to accept as a primitive given; that it will be avoided by future best theories of fundamental physics; that the universe was created by some divine designer who established life-friendly conditions; and that fine-tuning for life indicates the existence of multiple other universes with conditions very different from those in our own universe.
If, say, we take the route that there is no multiverse and this universe is all there is, then we have two theories we can compare: one that includes a supernatural designer and another that doesn’t.
Let’s compare the argument that fine tuning is a brute coincidence vs. the argument that the constants of the universe were fine tuned to create life by a designer. Suppose now that a theist argues this: “well, we don’t have examples of such spectacularly improbable meaningful coincidences happening for no reason. But we do have examples of spectacular meaningful coincidences at this sheer level of improbability being explained by humans (such as multiple lottery wins by the same person suggesting that the person cheated). This then gives us atleast a weak inductive reason to prefer the designer explanation than the non designer one.”
How sound would this reasoning be?