Philosophy, it is often remarked by philosophers who wish to remark on it, is all just a footnote to Plato. Plato is widely known as the student of Socrates, teacher of Aristotle, and the chronicler of the various conversations Socrates had with the people of Athens.
Plato wrote in dialogue form. In the early writings, generally considered based on actual conversations Socrates had with people, the form is pretty consistent: Socrates encounters an Athenian, begins questioning his stated position with respect to some virtue or metaphysical fact, and then apparently nitpicks until his interlocutor gives up. How does this happen? Socrates deploys the elenchus.
The elenchus is a method of questioning that forces an interlocutor to confront a contradiction. The nitpicking that Socrates undertakes is a search for some foundational belief his interlocutor has. It’s not just pestering, it’s dissection. “So, you believe X. Well, let me ask, do you also believe Y?” Often portrayed as accommodating, Socrates’ interlocutor usually obliges with something like “Of course I believe Y.” And then Socrates attempts to convey, through questions, that Y commits the Athenian to not-X at some level. One assumption that carries through all of the dialogues is that contradictions are very very very bad. Another assumption is that the stated position Socrates is dealing with is more weakly held than the buried position. So, when presented with the arm-lock that is the elenchus the Athenian is supposed to want to give up the stated position rather than the extracted one. The elenchus in the Socratic dialogues is usually not only a method for determining what someone believes, but a way to apply pressure on them to give up one of those beliefs.
The elenchus is different from a more general method of argument in which you present your opponent’s views (or just some position) as being contradictory. That’s usually what goes on in philosophy. The elenchus is special because of its questioning nature: Through questions, often requiring a ‘yes’ answer, the interlocutor creates or reveals a deep and consistent philosophical position on what looks like an unrelated matter, and then is forced to try to put that position together with the stated, controversial one that was up for grabs in the first place. To his surprise, but not to Socrates’, the combination fails. And because the elenchus first forces the interlocutor to reveal and develop a thoughtful position on some apparently unrelated issue it is too hard for them to then give up that belief rather than the controversial one. The elenchus isn’t just an opposition of contradictory beliefs, but also a way to load one up first as being more certain.
There is a little controversy about the Early dialogues: Does Socrates actually have an opinion about the issues he confronts? In the later dialogues, in which Socrates is more character and mouthpiece for Plato than a philosopher in his own right, he is clearly offering up beliefs of his (Plato’s) own. But in the Early dialogues it seems like Socrates himself, the self-described gadfly, is just annoyed that people say they believe things they shouldn’t believe and so he uses the elenchus to make them believe consistently, but not necessarily to find the truth or reveal his own beliefs.
This is a professional hazard for the philosopher who interacts with non-philosophers. Often annoyed that people believe sloppily he will pursue a point for the sake of revealing contradictions rather than for the sake of stating his own beliefs. However, this dogged pursuit of assumption and contradiction is interpreted as taking a position on the issue rather than a position on the argument. So the reckless philosopher will find himself saddled with statements he never makes because most people don’t listen as carefully as a philosopher questions. Later denials of ever having held a position are seen as backpeddling, or splitting hairs, and leave the impression that somehow the philosopher has just performed a trick rather than contributed anything to the world.
Tricks make people angry. And then hemlock ends up on the table.