In the Apology, at 38a5, Plato famously reports Socrates as saying that the unexamined life is not worth living. At least, that is the standard English translation. But every now and then, someone contests the claim. Why should a life be worthless if it is wholly outward-looking, devoid of introspection? (We may note in passing that "not worth living" may be too strong a translation. "Not the sort of life one should live" would be a possible reading.)
Sometimes, when I have seen this view, or some related view, I have wondered out loud about the translation. (Examples where I have commented are Brian Leiter's blog on 17 January 2012, and Stephen Law's blog on 12 September 2013 - original post dated 7 September.)
I put my thoughts here now, in the hope that some expert in Plato's Greek may have a view. I am not such an expert, so my own thoughts are mere speculation.
My concern is the word "anexetastos". This is the word that is standardly translated as "unexamined", with the implication that it is one's own life that needs examining. Liddell and Scott (the big one, colloquially known as the Great Scott) gives two meanings:
(a) not searched out, not inquired into or examined;
(b) without inquiry or investigation.
This dictionary refers to Apology 38a5 in giving the latter meaning.
An Intermediate Greek-English Lexicon (the Middle Liddell) reinforces the point by giving (a) not inquired into or examined, (b) uninquiring, and again links Plato to the latter meaning, although without a reference to the Apology.
On the scope for a verbal adjective to have both active and passive meanings, see Smyth's Greek Grammar, page 157, paragraph 472.
Liddell and Scott's decision to link Plato to (b) and not (a) does not in itself prove anything. I assume that they simply followed the opinion of Plato scholars as to the translation. But if (b) were the meaning to adopt, Socrates' prescription would look rather different. It would amount to saying that you should enquire into things and strive to find out the truth about the world. You might yourself be a main object of your enquiry, or you might turn your gaze outwards, making enquiries in physics, natural history, geography, philosophy, or whatever else was of interest. The prescription would amount to an injunction not to be slothful intellectually, but to pursue knowledge and understanding.