Socrates proposes a new theory to Menexenus: the "friend of the good" is neither the good nor the bad, but that which is neither good nor bad. This puzzles Menexenus, and Socrates claims to have come upon the notion partly because he is "dizzy with thinking." He conjectures that the beautiful, that quality which is "smooth and slippery" and which sneaks-in to fill our souls, is the friend ("as the old proverb says"), and further that the good is the beautiful.
What is neither good nor evil, Socrates continues, is the friend of both the beautiful and the good. He claims this based on the notion that there are three fundamental principles: the good, the bad, and the neutral. Since it has already been concluded that the good can be the friend neither of the good nor of the bad, and that the bad cannot be the friend of anything, and further that like cannot be the friend of like, there is only one other possibility: the good is the friend of the neutral.
Socrates uses a medical example in support of this claim. The sick body is the friend of medicine (which is good), because the sick body is a neutral thing in which evil is present. By way of showing how it can be that the body in which an evil (a disease) is present is itself still neutral, Socrates recalls that color applied to a substance (such as Menexenus's auburn hair) does not change the true color of that substance. Of course it is sometimes the case that evil does corrupt the neutral entity to which it is "applied," and this is precisely when the good no longer is desired by the neutral as a friend.
Thus, Socrates arrives at the following formula: the good is a friend to the neutral when that neutral is "in the presence of evil" but not yet corrupted by it. On this model, neither the wise nor the willfully ignorant (those who believe they know what they do not) are lovers of wisdom. Only those who are accidentally ignorant—and, therefore, who are neither good nor bad—love the good of wisdom. Further, this would mean that the good don't love the good anymore than the bad.
With this, Socrates tells the boys, "we have discovered the nature of friendship: there can be no doubt of that." For a moment Socrates is satisfied, "like a huntsman whose prey is within his grasp," but he soon feels an "unaccountable suspicion" that the argument is amiss. Socrates tells this to the boys.
The arguments presented here are quite messy. As in much of the dialogue, we will get much less out of them by interrogating their logic—for there isn't much logic to them—than by looking at them in terms of metaphor, rhetoric, theme, and clusters of ideas. An argument like the one Socrates uses to defend his notion that good is the friend of the neutral (the argument about the body and medicine), for example, has a pretty flimsy analytical structure, but it is quite poetic and original.
In the last section, we saw that much of the Lysis is particularly flexible in its aims and methods; in short, it has an improvisational feel to it. In this section, Socrates makes a statement concerning precisely this improvisational feel. His introduction, from out of nowhere, of the thesis about the good and the neutral confuses Menexenus, who asks, "how do you mean?" Socrates responds, "the truth is that I don't know; but my head is dizzy with thinking of the argument, and therefore I hazard the conjecture "
This remarkable admission is accompanied by a few jumbled assertions about beauty (it is "the friend," it is "a soft, smooth, slippery thing"), which are immediately dropped as the argument about the good and the neutral gets underway. The beginning of this section of the argument, then, is a moment of dizziness and poetic description (how amazing to say that beauty is "slippery"), a moment at which Socrates is so intoxicated by the argument that he proposes a thesis that at first he doesn't even understand.
Our gut reaction might be to take this as yet another playful, disingenuous piece of rhetoric on Socrates's part. But this notion is partly countered by the equally remarkable moment at the end of the section, where Socrates tells us (but not the boys) that he really thought, at the time, that they had reached the true solution to the problem of friendship, which they hadn't, of course. This admission suggests that we read Socrates as much less of a conscious manipulator of rhetoric than he might be: if he really thinks, at least for a moment, that each of the proposed "solutions" is true, it seems likely that he really doesn't know just what he means when he dizzily proposes this new one.
We must keep in mind, of course, that even if we read Socrates as an "honest" debater and narrator, that still leaves plenty of room for Plato to manipulate Socrates as a character. Thus, the real question is not so much whether Socrates tells the truth about this moment of dizziness and poetry, but rather why Plato makes it happen. A provisional answer, again, is that this dialogue depends to an unusual degree on the mingling of philosophical argument and various kinds of inspiration (divine, poetic, and, above all, erotic).
With that tool for thinking about the "messy" parts of this section, the overall argument stands out more clearly. In essence, it is quite simple: given the previous rejection of likeness, non-likeness, and goodness as foundations for friendship, Socrates simply creates a new category that is neither like nor unlike the good: the neutral. Thus, the good can be the friend to the neutral. Evil comes in naturally as an extra motivating factor, though technically it shouldn't be necessary.
This solution, too, is destined to fail, and it goes out in a manner similar to the way it came in: not by logic, but by a kind of emotional insight. The thesis is born in dizziness and dies in "fancy": "a suspicion came across me, and I fancied unaccountably that the conclusion was untrue."