A regretful acknowledgment of an offense or failure, or a formal defense or justification of one's beliefs or actions.
From Greek apologia meaning 'a speech in defense' (apo- away + logos speech). Originally meant a formal defense or justification, as in Plato's 'Apology of Socrates', but evolved to mean expressing regret for wrongdoing.
The original meaning of 'apology' was actually the opposite of saying sorry - it meant a vigorous defense of one's actions! Socrates' 'Apology' wasn't him apologizing for his philosophy, but defending it. The shift to meaning 'expression of regret' didn't occur until the 16th century.
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