There is something of a paradox at the heart of skepticism. On the one hand, we are told that we can have no certainty with respect to a certain subject matter (the external world, other minds, etc.), no adequate justification, and no knowledge—that all such epistemic claims are false. On the other hand, we are assured that with respect to some things we can be certain, justified, and knowledgeable, even when skepticism has been extended to beliefs about one’s own mind. For we can be certain, justified, and knowledgeable about skepticism itself: that is, skepticism is skepticism-proof. I can be certain that I don’t know there is an external world, say. There is no room for doubt that I am deficient in this respect. I can know of a certain object that it has a certain property, i.e. the property of not knowing there is an external world. I can’t know of other objects that they have properties of the kind normally attributed to them, but I can know that I have this property—the ignorance property. I can also know with certainty that you have this property, since for everyone the external world is dubitable. So the skeptic actually makes a strong epistemic claim: he has cast-iron certainty that skepticism is true, based on the classic skeptical argument. He knows that we can’t know certain things.
You might wonder whether he can weaken his position: but by his own arguments that is not possible, because any weakening makes the position incapable of assertion. He can’t claim that skepticism is probably true without opening up this possibility for beliefs about the external world; nor do skeptics ever attempt any such maneuver. They tacitly assume that their position is unassailable, not susceptible to rational doubt. Whether that is so is questionable: maybe there has been a mistake in the reasoning; maybe our memory of the argument from day to day is fallible; maybe we are all insane. There are forms of skepticism that can be made to apply to skepticism itself. But the position of the skeptic is that there is a radical asymmetry between his epistemic claims and ours: his are indubitably true and ours are demonstrably false. He is not a skeptic about his own skeptical beliefs; in fact, he is a diehard believer. We might wonder whether his arguments are as impregnable as he supposes, but he has no doubts—or else he would allow that our epistemic claims might be true. His position is not that we should be agnostic about our epistemic claims; his claim is that we should outright reject them. Nor is he agnostic about the truth of his own epistemic claims: he is fully committed to their truth. He is not a skeptic at all when it comes to his own epistemic credentials. He regards skepticism as an established certainty.
That is why I say there is a kind of paradox at the heart of skepticism: the skeptic is curiously prone to denying some epistemic claims but asserting others. He might even reject the Cogito as unjustified but still insist that he is certain that we lack the epistemic attributes that we commonly assume we possess. Oughtn’t a principled skeptic to concede that he has no certainty about whether we lack knowledge of the external world, but then he wouldn’t be a skeptic in the sense that he denies that we have such knowledge. The committed skeptic can’t be a consistent skeptic. He must always make an exception for himself, as part of the logic of the position. It isn’t that he denies knowledge tout court; rather, he limits it to his own beliefs (rightly or wrongly). He thinks human beings are perfectly capable of knowledge, but it is confined to the attribution (or non-attribution) of epistemic properties: he knows perfectly well that other people don’t know what they think they know, and he is certain that he knows what he thinks he knows. Even Socrates was quite certain that his interlocutors lacked knowledge. The skeptic isn’t someone who discourages attitudes of certainty; he indulges such attitudes freely—but selectively. He is not remotely skeptical about his own beliefs, just yours. He is, in fact, a complete dogmatist—just by being a convinced skeptic. He is absolutely certain that no one has knowledge of the external world, other minds, etc. If he were not, he would keep his mouth shut, or simply say that he doesn’t know whether people have knowledge. But in fact the skeptic is the most opinionated of men: he is sure beyond any possibility of doubt that other men are ignorant and misguided, while he is in possession of the incontrovertible truth. So let’s not give him credit for humility or self-criticism: the skeptic isn’t skeptical about himself—he doesn’t think he might be wrong. And it isn’t as if his beliefs are widely shared, natural to mankind, or conducive to happiness; his beliefs are eccentric and disturbing. Yet he persists in holding them with complete confidence (rightly or wrongly). To be a skeptic is to be a true believer. 
 To be a true doubter, by contrast, one would need to have a questioning attitude towards the standard skeptical arguments—but that is not the position of the skeptic. A true doubter would point out that skeptical arguments are like other philosophical arguments, i.e. endlessly debatable and fallible. Are those arguments any better than philosophical arguments against free will, or in favor of dualism, or for moral relativism? Skepticism is philosophy and as open to question as all philosophy.