Socrates held that some things could be defined, but not others. Aristotle thought that a definition was a statement of the essence of something but found it hard work proposing a satisfactory definition of essence. Both were living in a society where dictionaries were unknown.
It is sometimes argued that definitions must ultimately rest on undefined terms; otherwise definition risks either circularity or infinite regress. If lexicographers worried about that, few of them would ever have set up in business. Dictionaries came into existence by public demand, and sometimes with government support. In modern society they fulfilled a need that was simultaneously practical, political and psychological.
In a dictionary culture there exists - for better or for worse - an authoritative account of what words mean. That authority can be questioned in minor details. It is always possible to quibble with dictionary entries, and lexicographers often quibble with one another. But what no one calls in to question in a dictionary culture is the founding principle of the dictionary itself - namely, that every word does have a publicly ascertainable meaning or meanings, and that meanings can be stated clearly in other words. The dictionary functions as an institutionalised court of appeal. Without it, there are many whose work would every day be in danger of losing its way.
That is why it is rare for dictionaries to be subject to a great deal of critical scrutiny. The community is too thankful just for their existence, in the same way as it is thankful for having a government, however much individuals may complain about this or that government policy. Even if we do not often have occasion to look a word up in a dictionary, any more than we have occasion to call in the police, it is comforting to know in both cases that there is someone out there keeping order. Language, people feel, needs policing, too.
Humpty-Dumpty's bolshie decision to define the word "glory" as "a nice knock-down argument" was calculated to amuse and scandalise Lewis Carroll's Victorian readership, probably the most dictionary-minded generation the world has ever seen. Only the Victorians could have contemplated the impossible enterprise of defining every word in the English language. But perhaps it did not seem at all impossible to those who believed they were running an empire on which the sun never set. It is a supremely bureaucratic concept.
No one, of course, believes in it any longer, even as an ideal (except perhaps a few of those still compiling the latest edition of the Oxford English Dictionary). The ideal was always based on an authoritarian view of "the English language". It excluded words not "approved" by the Establishment. James Murray, the Oxford English Dictionary's first editor, was in his way quite progressive. He fought, and eventually won, a battle against those who objected to including words whose sole claim to authenticity was their appearance in newspapers of the day. But he would never have dreamt of consulting his own domestic servants in quest of a definition of the words they used. Murray's intellectual world was still a million miles away from accepting the anarchist mantra "the meaning is the use".
The collapse of that world has left lexicographers with a definitional problem they have not so far succeeded in resolving. Not just lexicographers - legislators, lawyers, everyone else, too. Postmodernists rejoice in its insolubility. (That might be as good a "definition" of postmodernism as you are likely to find.) Recognition of the indeterminacy of meaning has become a pervasive feature of the current cultural scene. It underwrites everything from scepticism about primary school "targets" to rejecting the official "reasons" given for the war in Iraq.
Anthropologists once proposed a "great divide" between literate and pre-literate cultures. Arguably, however, there is an even greater divide between dictionary cultures and pre-dictionary cultures. How the way we think is moulded by the taken-for-granted existence of the dictionary (even when, intellectually, we reject it) is a subject that has so far been shirked by both linguists and psychologists. But until its importance is recognised, the self-understanding of modern societies will be far from complete.