Rupert Murdoch has spent the better half of a week apologizing for his News of the World tabloid’s phone-hacking scandal.

“We are sorry for the serious wrongdoing that occurred,” he said in a full-paged newspaper ad last weekend, and then, during this week’s Parliamentary hearing, the “humbled” media mogul insisted, “What happened at News was wrong. We have apologized profusely.”

Murdoch’s admissions are only one of the high-profile apologies we’ve seen in recent days. Footballer DeSean Jackson earlier this month offered contrition for using a gay slur during a radio show, and Tracy Morgan offered similar atonement after his homophobic rant in Nashville.

Anthony Weiner, meanwhile, held a career-ending press conference to apologize for tweeting pictures of his penis, the most recent example of all-too-common political apologies.

It’s clear then that apologies permeate every corner of our culture, from the pop to the political; so how do you know which ones matter and which ones are hogwash? That, of course, is the eternal question.

Philosophers have pondered the meaning of apologies for centuries. Plato, we know, wrote extensively about beloved mentor Socrates’ apology for “corrupting” Greece’s youth by questioning the status quo.

In that era and context, however, apologies had a very different definition: they were self-defenses, rather than a plea for forgiveness. The apology we speak of today didn’t emerge until the late 1500s, when it came to mean “frank expression of regret for a wrong done,” according to the Online Etymology Dictionary’s rudimentary definition.

The apology’s evolution from self-defense to inter-person exchange only complicates our understanding of it.

My girl Hannah Arendt spent a large portion of her storied career studying apologies, and in her seminal book ‘The Human Condition,’ the political theorist writes that man can only overcome the “predicament of irreversibility” — “of being unable to undo what one has done” — by achieving the apology’s ideal end: forgiveness.

“Without being forgiven, released from the consequences of what we have done, our capacity to act would, as it were, be confined to one single deed from which we could never recover,” she says.

Apologies and forgiveness, like yin and yang, must come together to right the wrongs of the past, which means that apologies are only effective if they involve both the offender and the victim.

“No one can forgive himself,” says Arendt. “[Forgiving] enacted in solitude or isolation remain[s] without reality and can signify no more than a role played before one’s self.”

For Murdoch and others’ apologies to “work”—to be as personal and powerful as possible—the offended party or parties must forgive the error. There must be, to use Arendt’s term, “mutual release.”

Contemporary philosopher Nick Smith argues out in his 2008 book, “I Was Wrong: The Meaning of Apologies,” that an ideal apology must meet a few prerequisites before it can be “maximally meaningful.”

In addition to the offender and offended agreeing on what in fact happened and the offender offering sincere regret, he or she must also take absolute responsibility for a misdeed.

Murdoch’s “apology” at Parliament falls flat in this regard — he refused to take responsibility, saying, “I feel that people I trusted let me down, and I think they betrayed the company, and me, and it’s for them to pay. I think I’m the best person to clean this up.”

Some may argue that Murdoch himself didn’t do the hacking, but he was in charge at the time, and it’s logical that the businessman knew how far his most successful paper went to compete with rivals.

This brings us to another question: Do we trust Murdoch’s moral compass?

As with Kwame Anthony Appiah’s definition of honor codes, apologies only “work” when both parties use the same sense of right and wrong, the same morality. One can’t apologize for something in which one doesn’t believe, Smith argues, using the example of not apologizing for bringing a black person to a racist’s party, because you don’t think integration is wrong.

“The victim and offender thus declare that they share moral values,” he writes in his essay ‘The Categorical Apology.’ “The offender will understand the victim’s claims as legitimate, her own behavior as wrong and will offer the most meaningful words in an apology: ‘I was wrong.’” This means, Smith argues, that the offender must also have the best intentions.

“It matters why [the offender] apologizes,” says Smith in one of his essay’s most forceful moments. “We want an apology from a person who agrees with our sense of right and wrong, not from a machine or animal mimicking moral agency.”

Was Murdoch apologizing because he feels actual, human regret, or to save his company? We may never know.

But both Smith and Arendt argue that an apology is not just words; it is a promise to alter future behavior and, as Smith writes, “entails a promise that the offender will not repeat the offense even under the same conditions and with the same incentives.” The apology is an ongoing act.

Murdoch indeed told Parliament that his company would change its ways, writing in a closing statement, “We will come to understand the wrongs of the past, prevent them from happening again and, in the years ahead, restore the nation’s trust in our company and in all British journalism.” Now he has to prove his word.

Even for a man as powerful as Rupert Murdoch, an apology is made of more than just words; like a piece of art, the most nuanced, meaningful and powerful apologies have some heart.