These are some passages from Plato's writing about the general character of Socratic reasoning, how it feels from the point of view of one practicing it.
These passage are important because they show that Socratic reasoning should not be an argument between two people, each arguing his or her own side. Even when it is done in conversation between two people, it must be an examination of a single person's ideas and perceptions - the other conversation partner must just help this single person articulate and critically examine his or her own ideas and perceptions. This means also that it is possible for one person to engage in this kind of discussion by herself, as a kind of self-critical self-exploration.
Richard Robinson, calling Socratic inquiry by its Greek name elenchus, describes this key feature as follows:
The Socratic elenchus is a very personal affair... If the ulterior end of the elenchus is to be attained, it is essential that the answerer himself be convinced, and quite indifferent whether anyone else is... The art of elenchus is to find premises believed by the answerer and yet entailing the contrary of his thesis.
Whereas in law-courts you have to convince a third party, namely the judges, in the Socratic elenchus you have to convince your opponent himself. Hence the witnesses who are so effective at trials are useless here. The only true witness and authority is the answerer himself; and if he does not admit the fact it is irrelevant how many others do. The result depends not on a majority of votes, but on the single vote of the answerer...
The whole essence of the elenchus lies in making visible to the answerer the link between certain of his actual beliefs and the contradictory of his present thesis.
("Elenchus" by Richard Robinson, in The Philosophy of Socrates, ed. G. Vlastos. NY: Doubleday. 1971, p. 88-89.)
[Theaetetus 167e]
Socrates: Do not conduct your questioning unfairly. Unfairness here consists in not observing the distinction between a debate and a conversation. A debate need not be taken seriously and one may trip up an opponent to the best of one's power, but a conversation should be undertaken seriously. One should help out the other party, and bring home to him only those slips and fallacies that are due to himself or to his earlier instructors. If you follow this rule, your associates will lay the blame for their confusions and perplexities on themselves and not on you. They will like you and want your company. Disgusted with themselves, they will turn to philosophy, hoping to escape from their former selves and become different men. But if, like so many, you take the opposite course, you will reach the opposite result. Instead of turning your companions to philosophy, you will make them hate the whole business.
[148e]
Theaetetus: I have often set my myself to study that problem... but I cannot persuade myself that I can give any satisfactory solution or that anyone has ever stated in my hearing the sort of answer you require. And yet I cannot get the question out of my mind.
Socrates: That is because your mind is not empty or barren. You are suffering the pains of childbirth...Have you never heard that I am the son of a midwife...and that I practice the same trade? It is not known that I possess this skill, so the ignorant world describes me in other terms: As an eccentric person who reduces people to hopeless perplexity...
The only difference [between my trade and that of midwives] is that my patients are men, not women, and my concern is not with the body but with the soul that is experiencing birth pangs. And the highest achievement of my art is the power to try by every test to decide whether the offspring of a young man's thought is a false phantom or is something imbued with life and truth.
I am like the midwife, in that I cannot myself give birth to wisdom. The common reproach is true, that, though I question others, I can myself bring nothing to light because there is no wisdom in me...Of myself I have no sort of wisdom, nor has any discovery ever been born to me as the child of my soul. Those who frequent my company at first appear, some of them, quite unintelligent, but, as we go further with our discussions, [some] make progress at a rate that seems surprising to others as well as to themselves, although it is clear that they have never learned anything from me. The many admirable truths which they bring to birth have been discovered by themselves from within...
The proof of this is that many who have not been conscious of my assistance but have made light of me, thinking it was all their own doing, have left me sooner than they should...and then suffered miscarriage of their thoughts through falling into bad company. They lost the children of whom I had delivered them by bringing them up badly, caring more for false phantoms than for the true...
Those who seek my company have the same experience as a woman giving birth. They suffer labor pains and by night and day are full of distress. My art has power to bring on these pains or alleviate them.
.....
[Later in the discussion, Theaetetus 157c:]
Theaetetus: I cannot make out whether you are stating [some ideas] as something you believe, or merely testing me.
Socrates: You forget that I know nothing of such matters and cannot claim to be producing any offspring of my own. I am only trying to deliver yours, and to that end uttering charms over you and tempting your appetite with a variety of delicacies from the table of wisdom, until by my aid your own belief shall be brought to light. Once that is done, I shall see whether it proves to have some life in it or not. Meanwhile, have courage and patience, and answer my questions bravely in accordance with your convictions...
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[Further still, Theaetetus 160e]
Socrates: [Speaking of a conclusion Theaetetus has come to] May we say that this is your newborn child?...Here at last, after our somewhat painful labor, is the child we have brought to birth...We must now look at our offspring from every angle to make sure we are not taken in by a lifeless phantom...Can you bear to see him tested, and not be in a passion if your first_born shall be taken away?
Theodorus [the teacher of Theaetetus]: Theaetetus will bear it, Socrates, he is thoroughly good tempered. But do explain what is wrong with the conclusion.
Socrates: You take me for a sort of bag full of arguments, and imagine I can easily pull out a proof to show that our conclusion is wrong. You don't see what's happening. The arguments never come out of me; they always come out of the person I am talking with. I am only at a slight advantage in having the skill to get some account of the matter from another's wisdom and think of it with fairness. So I shall not give any explanation myself, but try to get it out of our friend.
.....
In Plato's Socratic dialogues, he very often pictures the person being questioned as becoming very frustrated. Psychologically speaking, it could be said that frustration is part of the process that must be tolerated and worked through in order to produce positive results. The frustration comes from realizing how difficult it is to find a definition of a virtue that will stand up in the face of Socratic questioning. People experiencing this frustration are tempted to give up and turn their frustration into a dislike for argument itself.
When we had heard them state their objections, we all felt were very much depressed... We had been convinced by the earlier part of the discussion, and now we felt that they had upset our convictions and destroyed our confidence... How can we believe in anything after this? Socrates' [earlier] argument was absolutely convincing, and now it is completely discredited....
[Socrates said] There is one danger that we must guard against... of becoming misologic... in the sense that people become misanthropic. No greater misfortune could happen to anyone than that of developing a dislike for argument. [Misos is "hatred" in Greek. Logos means here "rational argument".]
Misology and misanthropy arise in just the same way. Misanthropy is induced by believing in somebody quite uncritically. You assume that a person is absolutely truthful and sincere and reliable, and then a little later you find that he is shoddy and unreliable. Then the same thing happens again. After repeated disappointments at the hands of the very people who might be supposed to be your nearest and most intimate friends, constant irritation ends by making you dislike everybody and suppose that there is no sincerity to be found anywhere...
The resemblance between arguments and people lies...in what I said before, that when one believes that an argument is true without measuring it by good logic, and then a little later decides rightly or wrongly that it is false, and the same thing happens again and again – you know how it is, especially with those who spend their time in arguing both sides – they end by believing that they are wiser than anyone else, because they alone have discovered that there is nothing stable or dependable either in facts or in arguments, and that everything fluctuates just like the water in a tidal channel, and never stays at any point for any time...
Suppose that there is a path of reasoning which is true and valid and capable of being discovered, if anyone nevertheless, through his experience of these arguments which seem to the same people to be sometimes true and sometimes false, attached no responsibility to himself and his lack of the special skills needed, but was finally content, in exasperation, to shift the blame from himself to the arguments, and spend the rest of his life hating and criticizing them, and so missed the chance of knowing the truth about reality – would it not be a deplorable thing?
That is the first thing that we must guard against. We must not let it enter our minds that there may be no validity in argument. On the contrary we should recognize that we ourselves are still intellectual invalids, but that we must brace ourselves and do our best to become healthy...
That is the spirit in which I am prepared to approach discussion... If you will take my advice, you will think very little of me, Socrates, and much more of truth. If you think that anything I say is true, you must agree with; if not, oppose it with every argument that you have. You must not allow me, in my enthusiasm, to deceive both myself and you....
In the following passage from one of his letters, Plato says that it is possible to arrive at something like a knowledge of pure and perfect Goodness. But this is something that might require a long time. It is also something that each person must do for herself, since this is not the kind of knowledge that can be conveyed in words from one person to another.
The occasion for this passage is that someone claims to have written an essay on "Plato's Idea of the Good."
One statement... I can make in regard to all who have written... with a claim to knowledge of the subjects to which I devote myself... Such writers can in my opinion have no real acquaintance with the subject. I certainly have composed no work in regard to it nor shall I ever do so in future, for there is no way of putting it in words like other studies.
Acquaintance with it must come rather after a long period of attendance on instruction in the subject itself... when suddenly, like a blaze kindled by a leaping spark, it is generated in the soul and at once becomes self-sustaining...
The study of virtue and vice... must be carried on by constant practice over a long period... After practicing detailed comparisons of names and definitions and visual and other sense perceptions, after scrutinizing them... by the use of question and answer... at last in a flash an understanding... blazes up, and the mind, as it exerts all its powers to the limit of human capacity, is flooded with light...