Aporia - The state of uncertainty reached when one realizes one is ignorant of what one thought one knew. This is the goal of most early Platonic dialogues, and it is the state in which the Lysis closes. Again, the effect of the aporia here is somewhat weakened by the fact that Socrates's interlocutors are just boys, who don't pretend to know a great deal in the first place. The aporia with which the Lysis closes is interesting, however, in that it is caused largely by the interaction of problems of identity (likeness) with problems of desire. Thus, it is an aporia that both reflects and contrasts with the expertise that Socrates shows in wooing Lysis.
Beloved - The term applied to the woman (or, in the case of the Lysis, the boy) in the lover/beloved relationship. The Greek word for the beloved is eromenos. See the term Lover below for more details.
Elenchus - The elenchus is the primary method of Socratic philosophy. It proceeds by an intensive series of questions, and aims to lead the interviewee to conclude for himself that he does not know what he thought he knew (a state of uncertainty, or aporia, with regard to the topic at hand). The form of elenchus taken in the Lysis is fairly standard, though it is particularly lopsided since Socrates is speaking with two young boys. Thus, the boys hardly utter anything except terse statements of agreement with Socrates's propositions. In this sense, the effect of the elenchus is weakened, since the boys do not think they know all that much in the first place.
Friend - The Greek words most commonly used for "friend" or "friendship" in the Lysis are based on the root term philia, which denotes affection or fondness for something. This is to be distinguished to some extent from eros which denotes passionate love. It is eros that is at work, for example, in the love of Hippothales for Lysis (or in any passionate love between a man and a boy). Philia on the other hand describes the relationship between the two boys, Lysis and Menexenus. The terms are put into extremely close proximity in the Lysis, however, and it is often unclear in translation which of the two is being used. Part of the reason for this is the tension generated between the dialogue, which is primarily about friendship, and the context of the dialogue (the wooing of Lysis), which is primarily about eros.
Likeness - The Lysis advances its various arguments about friendship partly on the basis of considerations about likeness. Socrates suggests that friendship may be caused by two like things being drawn to each other (this suggestion emerges from the theory of older poets and philosophers that "like is drawn to like"). Socrates eventually rejects this idea on the grounds that, because two like things cannot get anything from each other that they do not already have, they cannot desire each other. Likeness, according to Socrates, cannot be the cause of friendship. The same argument applies to goodness as the cause of friendship: since the good cannot desire the good (because it already has it), goodness cannot be the cause of friendship. This proposition, which puts forth some of the earliest philosophical theorizing about identity, will cause problems in the Lysis right through to the end.
Lover - The Greek term for lover is erastes. The term is intimately bound up with relationships between older men and young boys in Athenian society, and this context infuses the Lysis to a great degree. Such relationships were both passionate and socially regulated. The older man generally courted the boy (usually a teenager), with the boy playing the passive, shy role. Both roles had strict limits: the men could be prosecuted for seducing youths if they were overly aggressive, and the boys could be censured for prostitution if they sold sex. Ideally, the relationship between a man and a boy eromenos was one of teaching as well as love, with the older man imbuing the boy with knowledge and virtue (literally, "making him pregnant with" these ideals). The Lysis is entirely framed in this context, with Socrates agreeing to demonstrate for Hippothales the proper way to woo a boy (Lysis). The term "lover" mingles and blends in this dialogue with the term "friend" (see Friend above).