The Twitter fight between Carl Icahn and Pacific Investment Management Co.’s Bill Gross has sunk to a new low. Now both billionaires have brandished philanthropy as a weapon in their public exchange of insults.

This morning Icahn tweeted: “To Bill Gross @PIMCO: If you really want to do good, why not join givingpledge.org like Gates, I and many others have?” The clear implication: If Gross doesn’t do what Icahn says, then Gross must not want to do good.

Icahn’s broadside violates the Giving Pledge’s spirit. It isn’t supposed to be used as a cudgel to browbeat one’s critics. As described on the organization’s website, “the idea of the Giving Pledge came from the ideas and input generated in many great conversations that Bill and Melinda Gates and Warren Buffett had with other philanthropists in the U.S. and abroad.” It is “an effort to help address society’s most pressing problems by inviting the world’s wealthiest individuals and families to commit to giving more than half of their wealth to philanthropy or charitable causes either during their lifetime or in their will.”

Note the word “inviting” in that statement. Icahn didn’t invite the famed Pimco money manager to make such a commitment. Icahn dared him to, as a way to one-up him in a stupid argument that Gross started. (Michael Bloomberg, founder and majority owner of Bloomberg News parent Bloomberg LP, is among those who have joined the Giving Pledge, according to the organization’s website.)

Last week Gross tweeted that “Icahn should leave #Apple alone & spend more time like Bill Gates. If #Icahn’s so smart, use it to help people not yourself.” The next day, Gross wrote: “By the way, I should spend more TIME like Bill Gates too -– we all should. He and Melinda are great paragons.”

Icahn, the corporate raider turned activist investor, has received much criticism over his campaign to pressure Apple Inc. into buying back $150 billion of stock. (Twitter has been one his weapons of choice with Apple, too.) However, Gross’s initial attack on Icahn came across as personal and petty. It’s understandable why Icahn got upset.

Yet the sort of challenge Icahn issued back is out of order. It simply isn’t productive to have billionaires using the Giving Pledge as a claim to moral superiority over each other. If Icahn genuinely was interested in persuading Gross to join, why not call him on the phone or send him a nice, private note rather than flame him back on Twitter?

The Giving Pledge website also shows this quote from Icahn under his profile: “Until Bill, Melinda and Warren started this project, I never considered going public with my intentions. However, I certainly see the value of a project that encourages wealthy individuals to step forward and commit to use their wealth for the common good. I hope that by adding my voice with those who are supporting this project, we will all encourage others to participate.”

What Icahn said today wasn’t encouragement. It was a taunt.

For what it’s worth, as Alexis Leondis of Bloomberg News reported today, Gross’s personal wealth is estimated at $2 billion; he has endowed a foundation with $293 million in assets and raised money for Doctors Without Borders, a medical charity, by selling parts of his stamp collection. Maybe that’s a small part of his philanthropy. Maybe he plans to do more. Maybe he still is considering whether to go public with his intentions, like Icahn was not long ago. I have no idea, and neither does Icahn.

Here’s hoping we never see another nasty tweet from these two about each other again. They both need to get out of each other’s faces.

(Jonathan Weil is a Bloomberg View columnist. Follow him on Twitter.)