Although the sophists did not form a single philosophical school, they did have commonalities among themselves. They were itinerant teachers who charged for their teachings. Most of them taught rhetoric, and they seemed to have been particularly interested in argumentation. In Athens, where citizens actively deliberated in the Assembly and in courts, rhetorical skills would have meant increased political influence. This could explain the demand for such instructors in cities like Athens.
For instance, Protagoras thought about the nature of argumentation and logic. Diogenes Laertius records that "Protagoras was the first to declare that there are two mutually opposed arguments on any subject" (Curd, 146). If it is possible to say A, then it is also possible to say not-A. Of course, these two statements contradict each other, but that can in fact be helpful in developing an argument. For a rhetorician, it could be useful to know both sides of an argument. Practically, this could prepare him for counter-arguments, but it could also contribute to his own argument. However, in unscrupulous hands, a subtle argument from a contradiction could be used to prove anything. But these were the sorts of teaching that the sophists could sell.
Gorgias warns about the power of words in his Praise of Helen. He says that logos is a powerful master, and argues that Paris could have overpowered her with his words. He asks, "What, then, keeps us from supposing that Helen too, against her will, came under the influence of logoi just as if she had been taken by the force of might men?" (Curd, 149). Because everyone must judge words for himself, and judgment is fallible, for someone to persuade with misleading words. Gorgias himself wrote an argument which supposedly proves that nothing exists. Because it seems obvious that Gorgias must have at least thought himself to exist, his argument is most likely an exercise in rhetorical skill. He demonstrates the power of words by proving something obviously false.
Such approaches are certainly different from those taken by previous philosophers, but they do present a problem for philosophers. Philosophers construct arguments using words, but words can charm and mislead. If a philosopher creates an argument from an equivocation, it may not be immediately obvious how he is able to prove an apparent false conclusion. If a philosopher writes so beautifully that the meaning of the words is overshadowed by their aesthetic properties, he can lead you anywhere.
Thus the sophists present a concern that philosophers must take into account. In the pursuit of truth, it is important to use words carefully. Protagoras writes that "A person is the measure of all things - of things that are, that they are, and of things that are not, that they are not" (Curd, 146). Unfortunately, as Gorgias states, man is fallible. We must use reason, but should also recognize that we may judge that things are not as the truly are. The sophists show us a need for epistemic humility and for the wise use of words.