In response to Miles's first post, I want to say a little about so-called essentialism (we can say more in class). The historical Socrates was prone, apparently, to ask what something is on the whole (kata holon -- later combined by Aristotle into a word for something like 'universal concept' -- katholou). For example, if two sticks are equal to each other in length, and we can correctly judge whether this is true, and if two rather different kinds of things are ALSO equal to each other (say, two runners are equally fast), then it would seem that there must be something both pairs of things, sticks and runners, have in common. That would be equality. But if both claims of equality are true, and we're using the word properly, then we must in some sense know in advance what equality is before we start in with the comparisons. Raising questions like this seems to be about as far as Socrates the man got.
Others later developed this into something like a theory of universal meanings, and it got turned into some kind of dogma (hence the oft-attributed "theory of forms," to which Plato may, or may not, have subscribed at some point or other in his life). But to project this back onto Socrates and call him essentialist is anachronistic and extravagant. This is so not least because the term itself, 'essence,' was coined in the late middle ages by the Arabic scholars Ibn Sena and Ibn Rushd (known as Avicenna and Averroes among Europeans). Reading Aristotle more closely than anyone else (they are largely responsible for restoring much of the Aristotelian corpus to European attention), they noticed that Aristotle uses the one Greek term 'ousia' in two distinct ways: first as being (in the sense of the bare existence of something), and then as being (in the sense of what is unique or singular about the kind of thing it is). The first they called Existence (from an Arabic phrase for 'that something is,' or that-it) and the second Essence (the 'what-it-ia' of the thing). This was of course about a millennium and a half after Socrates died.
So while it's fair to say that Socrates was interested in finding the truth about things, and thought there must be some important and difficult truth to be learned about general concepts such as piety, it is a stretch to saddle him with essentialism.