No need to keep readers in suspense – the fallacy is to aim for certainty beyond the shadow of doubt! It is very costly because by holding on to the belief that if one lacks such certainty, it's OK to believe this or that and to do this or that, one is wasting enormous resources. And this is the basis of much public policy – especially, since the funds to engage in such fruitless pursuits can be obtained via the extortionist methods of taxation which creates the illusion of no limits. It is no accident that President Obama, for example, has linked his own public philosophy to the idea of hope – as seen in the title and theme of his famous book, The Audacity of Hope (Canongate, 2007). Pursuing what one can only hope for, mostly against all reason, is just how one produces enormous debts, especially when one doesn't need to worry about who will have to foot the expense of such pursuits.
In the sciences, too, this is a major fallacy. For centuries, for example, there has been a debate about whether one can know if other people are conscious. It goes something like this: "No one can enter another person's mind and all one can do is observe behavior, so isn't it possible that everyone who superficially seems to be conscious like oneself is, in fact, mindless? Isn't this possible? Can it be ruled out? Is it certainly so beyond a shadow of doubt? If not, well go for it!"
Well, if the standard of what can be ruled out is that it must be
certain beyond a shadow of doubt that it could be, then most of what one
imagines cannot be ruled out. Are we certain like that of anything at
all? Isn't it conceivable, imaginable, that I am dreaming that I am
sitting at my computer now typing away? Can I be sure beyond a shadow of
doubt that I am not? Sure, but what of it? Such doubtfulness is utterly
pointless, irrational. It is why in a court of law the goal is
certainty beyond a reasonable doubt, not a shadow of doubt.