Historically, much of philosophy has involved philosophers trying in vain to answer the challenge of skepticism. Basically, philosophical skepticism asserts that if it is possible for some assertion to be false, then one can never "know" that that assertion is true.
For example, inductive skepticism claims that induction does not bestow true knowledge. They claim that if you have seen 100 sheep, and they all had ears, you are unjustified in claiming "All sheep have ears" because somewhere out there might be a sheep without ears. Even if you have analyzed all sheep that you can find, there might be another somewhere. Skeptics will claim that only knowledge gained through deduction from known facts is knowledge. (See the philosophers deduction fallacy.)
Another major skeptical argument is that we can't know that our senses are valid. It is possible that we may all be brains in vats, with some sort of computer program simulating what we think is reality. Because it is impossible to prove this vision false, the skeptics claim that our senses are unreliable and we can't claim any knowledge derived from our perceptions. The doubt that even the world around us exists is called Metaphysical Skepticism.
Essentially the skeptics claim that nothing can ever be certain and that we can't truly know anything. And philosophers throughout history have been trying to refute this assertion while granting the flawed premises at its core.
First, deduction is no more "certain" than induction. This is the case because the rules of deduction are not magically bestowed upon us a priori. They are inductively discovered and tested and accepted like all the rest of our knowledge.
Second, the skeptics notion of "certainty" is meaningless. By their definition, nothing is certain. It's a useless concept. A concept is only meaningful when it subsumes some things and not others. If every human ever born were right-handed, we would have no concept or phrase of "right-handed". It would be meaningless. Properly, certainty should mean belief without any reason to doubt.
Which brings is to the third point to consider regarding skepticism. Skepticism is doubt without reason, or arbitrary doubt. An arbitrary doubt of an assertion is just as useless and unfounded as an arbitrary assertion. When an armchair philosopher comes up, trying to sound deep, and claims "You might just be a brain in a vat", the correct response is "And Martians might have extensive underground cities and are planning an invasion this very moment!" (Or any equally arbitrary statement.)
"We know that we know nothing," they chatter, blanking out the fact that they are claiming knowledge -- "There are no absolutes," they chatter, blanking out the fact that they are uttering an absolute -- "You cannot prove that you exist or that you're conscious," they chatter, blanking out the fact that proof presupposes existence, consciousness and a complex chain of knowledge: the existence of something to know, or a consciousness able to know it, and of a knowledge that has learned to distinguish between such concepts as the proved and the unproved.