Appeal to mystery

Oh dear — your cult's belief system is patently nutty. Not only do you have little in the way of argument for it, there also seems to be a great deal of evidence against it. If you want, nevertheless, to get lots of people to believe it, what do you do?

Why not appeal to mystery? By appealing to mystery, you can portray your critics as arrogant, unspiritual know-it-alls who think they have the answers to everything. You will appear humble and spiritual by acknowledging that, when it comes to the deepest questions, we must acknowledge our powers of reason have their limits. You can neutralize your opponent's […] reason, and make yourself look good and them look bad all […] at the same time!

See, the water, the tide comes in and it goes out, Mr. [David] Silverman. It always comes in, and always goes out. You can't explain that.

An appeal to mystery is a logical fallacy which argues, as an explanation for something, that there can be no explanation.

The fallacy is a an appeal to ignorance and an informal fallacy.

Explanation
There are more things in heaven and Earth than are dream't of in your philosophy, Horatio. If something is unexplainable (unknowable, etc.), then it functionally cannot be asserted to be true, because the evidence necessary to prove its truth is also unknown. (Consider attempting to prove that "Xydlgrp" is true, without knowing anything about it.)

The fallacy is appealing not least because "mystery" is interesting and because, as noted below, epistemic doubt is a reality. However, lack of knowledge cannot prove anything to be true.

Examples

 * Common words used to express this fallacy are "mysterious," "inscrutable," "ineffable," etc.
 * Invoking "the romance of the unknowable": "What a dull world it would be if everything were known!"

Theology

 * Are you above God? Do you pretend to understand God? etc.
 * We cannot know why God allows suffering. Who can fathom the ways of the creator?
 * Theists often claim that God is unknowable, which somehow exempts God from logical disproof. This, however, prevents asserting that God exists at all.
 * Other aspects of religion are often relegated to the realm of faith, because they are "beyond reason".

Distinction from legitimate doubt
Few philosophers claim to know anything with certainty. The more one inquires into any subject, the more one is inclined to accept the wisdom of Socrates: I know only that I do not know. There is good reason, then, that the language of doubt and uncertainty strikes us as wise and reasonable. The fallacy of Appeal to Mystery is often persuasive because it mimics epistemological modesty.

However, there is a difference. A good hypothesis is understood to be provisional. We understand that errors are possible. When any scientist offers any real hypothesis to explain some phenomenon, he would be wise to add, "Of course, I might be wrong," but no such apology is really necessary. We already know he might be wrong. But he might also be right. If he is wrong, we hope his theory will eventually be replaced by a better theory. Real epistemological modesty is an invitation to further inquiry. It is an admission that a better theory may be possible. The Appeal to Mystery, by contrast, is used, not to invite further inquiry, but to shut down further inquiry by claiming that truth (in this matter) is unattainable. No better theory is possible because no theory could possibly be adequate. It says, "This might be wrong," not in order to replace one theory with a better theory, but in order to replace one theory with no theory at all.