Irony is one of those concepts that's a bit difficult to nail down in some cases, and double irony even more so. Irony is generally defined as a statement or event that is the opposite of what's expected or intended, sort of like sarcasm, and often with a tragic or darkly humorous bend to it. Double irony, then, should reflect a further compounding of the reality contradicting the intention.
The text introduces us to the ruins of the statue of Ozymandias, but also to the evidence that its sculptor was so skillful that their own impressions of Ozymandias were incorporated into the carving; the sculptor seems to have thought that Ozymandias was a tyrant and blow-hard, considering how he depicts the king with a "sneer of cold command." We can envision the king directing his sculptor to create the statue, and the sculptor petulantly leaving subtle traces of his displeasure in the carving.
The irony works as follows;
- The king's original message, "look on my works, ye Mighty, and despair!" were intended as a boast and challenge to any who thought themselves powerful, that they might see how much greater Ozymandias is by virtue of his creations.
- Of course, there's nothing to see, and the statue itself is ruined, thus making the "despair!" command ironic. There is nothing impressive about the ruins of a statue. Part of this irony lies in the fact that we may, indeed, despair, but not for the reasons Ozymandias intended; we despair that all of his accomplishments have been reduced to a few ruined stones in a desert.
- Likewise, the sculptor's intended mockery falls flat, and yet resurrects itself. He intended to make Ozymandias look foolish, but within his lifetime and within the context of his original orders. Ultimately the sculptor succeeded, but for the wrong reasons and in the wrong context.
So, the double irony is the fact that the sculptor wanted his contemporaries to see the statue and smirk at how arrogant and conceited Ozymandias was depicted, and "despair" at his vaunted accomplishments; yet we do despair because Ozymandias and all that he created has been reduced to dust, leaving us to ponder the meaning of human life itself.