Fred buys a used car in terrible shape. Off the top of his head, he can see a dozen problems with it: the window is cracked, the engine doesn't start, the window washer liquid line is leaking, the steering is gone, etc. He knows little about how cars work, but some things are obvious. He takes a roll of duct tape, and immediately fixes three problems: puts lots of tape on the window to keep the glass in place, patches the window washer liquid line, etc. With a bit more thought, he can find three more of the twelve problems that, with some ingenuity, he can fix with duct tape. While doing this, he discovers two new problems with the car. He then struggles and struggles, and with a great deal of cleverness manages to fix a steering shaft broken in half with just duct tape. He is really proud of his solution--it involved stretching the duct tape very, very thin, then put down many thin layers of duct tape over the break, and finally melt the layers together, with that the resulting shaft having almost the strength of unbroken steel.
So now Fred knows of 14 problems with his car, of which he's fixed seven with duct tape. Question: How much reason does Fred have to think that he can fix all the remaining problem--the seven he knows of plus whatever ones he would discover while fixing those--with duct tape as his only material? Answer: Very little (particularly if he notices that the reason the engine doesn't start is because there is no spark plug). One might try an inductive argument: all of these particular seven problems were solvable with duct tape, and hence so are the others. But this argument fails due to an egregious bias in sampling: the seven problems just are the problems that Fred found himself capable of solving with duct tape. They were selected for their solvability. The other problems are ones that Fred couldn't see how to solve with duct tape.
Likewise, if we ask whether Fred has much reason to think that of the remaining solvable car problems, the solutions all involve only duct tape, the answer is negative, for exactly the same sampling bias problem. We may, however, have some inductive data that of the remaining car problems solvable by Fred, the solutions will all be based on duct tape, since it seems that Fred doesn't know any other way to solve problems.
ApplicationConsider this argument for naturalism: We've been able to solve many, many explanatory problems naturalistically. Hence, the many remaining explanatory problems which we do not at this point know the answer to are also solvable naturalistically if they are solvable at all, and naturalism is true.
The same reason that the argument for Fred's ability to solve the other problems with duct tape was bad shows that this is a bad argument. The set of problems that we've solved naturalistically is not a random sampling of the explanatory problems. Rather, it just is the set of problems that we've solved naturalistically.
One might try to strengthen the argument for naturalism by adding that no explanatory problems we know of have non-naturalistic solutions, and concluding, inductively, that all the explanatory problems that have solutions have naturalistic solutions, which could be enough to make naturalism plausible. But this argument becomes question-begging against typical non-naturalists who claim that they have non-naturalistic solutions to a number of vexing problems (intentionality, free will, normativity, the origin of life, the origin of consciousness, the origin of space-time, the origin of mass-energy, the origin of contingent things, etc.) Moreover, even if all of those can be argued not to work, it could well be the case that the problems that have non-naturalistic solutions are much harder to solve, perhaps even are not solvable by humans; nor is this some ad hoc posit, but simply comes from the that fact non-naturalistic things are not amenable to empirical study. Thus even if it were true that all the explanatory problems that we have solved have naturalistic solutions, it would not give us much reason to believe that all explanatory questions that have answers--including those that have answers that are beyond our capabilities--have naturalistic answers.