Suppose we consider the assertion "There is a ninja hiding in my bedroom." Ninjas are of course human beings who are experts at hiding; they are better at hiding than any finite person is at discovering them. This assertion is, at a purely semantic level, completely material: ninjas are physical human beings of meat and bone; they don't have any spooky or paranormal powers, they just have a particular material skill.
There is absolutely no logically possible empirical observation I could make from which I would conclude the falsity of this statement. We won't play any semantic games: even if I were to actually see a ninja in my bedroom, there could be another ninja who is successfully hiding. For the same reason, there is no empirical observation that could falsify the converse, that there are no ninjas hiding in my bedroom.
Our intuition about the world positively screams, however, that both statements really are truth-apt: It really is true, or it really is false that there's a person in black pajamas hiding under my bed right now, even if I'm completely incapable of ever knowing one way or the other. (If I were to actually look under the bed, the ninja is skillful enough to move somewhere where I'm not looking, and sneak back under the bed when I stand up.)
In philosobabble, we would say that the assertion that there's a ninja hiding in my bedroom is ontologically meaningful — it is a statement about the world that all competent English speakers would understand and consistently describe — but it is, on empiricism, epistemically unavailable: we cannot know the truth or falsity of this meaningful assertion.
This assertion captures the essential "limits" of scientific naturalism, such as it is. The ninja who is hiding and doing nothing more has removed herself from my experience.
(Note that a ninja could, if she chose, convince me that she was hiding without being discovered. She could, for example, leave a note on my desk: "Hey doofus! I'm a ninja, and I'm hiding in your bedroom! Mwahahahahaha!" Under obvious circumstances I could very easily be persuaded by this evidence that there really was a ninja hiding in my bedroom, without actually discovering her. But for me to have positive evidence of her existence, she has to at least in some way re-enter my experience.)
We can come up with infinitely many statements about the real world, about objects as prosaic and non-spooky as our stealthy ninja, none of which can even in principle be empirically known. It is indeed the case that our 21st century Earth might be full of unicorns and leprechauns, all shy and easily able to hide from us clumsy and inattentive humans.
There's no choice for the scientific naturalist but to bite the philosophical bullet. Yes, indeed, there are infinitely many meaningful statements about the world we can't ever in principle know the truth or falsity of.
I can't even say I'm agnostic or apathetic. I'm both agnostic and apathetic about whether President Obama wears boxers or briefs. My attitude about a ninja in my bedroom is so qualitatively different from my attitude towards Obama's underwear that to use the same words to qualify both seems like a grievous offense against the English language. One might just as well call a big hole a mountain of nothing. It is at least conceivable that I could be persuaded to care about and discover the truth about Obama's underwear. It is, however, absolutely inconceivable and logically impossible for me not just know about but to care about a ninja hiding in my bedroom, at least until she somehow obtrudes on my experience.
So I'm complete unimpressed by theists talking about the "limits" of scientific naturalism. Yes, scientific naturalism has limits, and those limits precisely conform by definition to the limits about what I can possibly care about. Theism does in some sense "transcend" the limits of scientific naturalism, but only by suspending principles by which we can ever agree on any statements about reality.
I say, "There really is no God; if there were, She would love everyone regardless their sexual orientation and give them all eternal life in Heaven."
A theist might reply, "There really is a God, and He hates fags, and He'll punish fags for all eternity."
I can then say, "Excellent! We are in complete agreement!" Such a theist would fail not just to demonstrate he was correct and I was mistaken, he would fail to show that we actually disagree! Wait, what!?
If we transcend the limits of scientific naturalism, if we admit that one can actually have a relevant opinion about the truth of empirically unknowable statements, then we must conclude that both statements are known to be true. If they mean mutually inconsistent things, then we have a contradiction; to preserve logic we must therefore conclude that the statements both mean the same thing, and therefore we agree.
It doesn't matter how deep you go. At some point you'll assert the truth of a freely controvertible proposition. A theist might say, "The Bible says that God exists and He hates fags, every empirically unknowable statement in the Bible is true, therefore God hates fags."
Again, I would reply, "Excellent! We agree completely! The Bible says that God exists and hates fags, the Bible is false in these respects, therefore God does not exist and if she did, She would love all people, including homosexuals." Both statements are true, therefore they must be saying the same thing.
The fault lies in our ontological intuition. There are statements about the world we don't happen to know that we believe are true or false regardless of our knowledge or lack thereof. In general, our best scientific model to explain our experience is, in general, a real world where statements about that world are indeed true or false without regard to the knowledge we happen to have at the time. But it is an unwarranted generalization — despite our linguistic and cognitive habits — to actually believe there is truth or falsity to statements about the world that cannot be known, however prosaic such statements appear to be. Our belief that unknowable statements can be true or false is simply an artifact of the shortcuts we take to efficiently process language, not any truth about the real world.