The words ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ occur in a famous passage in the Apology. In this passage, Socrates explains why he will not abandon the practice that has gotten him into so much trouble and is about to cost him is life. His words are sometimes translated so that he says that "the unexamined life is not worth living," but this translation can be a little misleading. What he means is that a human being who goes through life without examining certain issues is making a terrible mistake in the way he lives his life.

"Someone might say, 'Socrates, can you not go away from us and live quietly, without talking?' Now this is the hardest thing to make some of you believe. For if I say that such conduct would be disobedience to the god and therefore I cannot keep quiet, you will think I am jesting and will not believe me; and if again I say that to talk every day about virtue (ἀρετῆς) and the other things about which you hear me talking and examining myself and others is the greatest good to man, and that the unexamined life is not worth living [or: the unexamined life is not to be lived by man (ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ)], you will believe me still less. This is as I say, gentlemen, but it is not easy to convince you" (Apology 37e-38a).

What Socrates had glimpsed about human beings in talking in this way about "virtue" (ἀρετή) is the principal issue that occupies Plato and subsequent ancient philosophers.

(Henry George Liddell, Robert Scott, A Greek-English Lexicon: ἀρετή)