This article today at The Intercept includes a video of a 2013 interview with Gen. Mattis. I had previously accepted all the hype about him being a mad dog, but he sounds reasonable here. I would recommend watching at least part of the video in order to see his demeanor. He argues against the no-fly zone concept, including whether it even would make sense in Syria:

https://theintercept.com/2017/04/07/donald-trumps-own-defense-secretary-...

DONALD TRUMP’S OWN DEFENSE SECRETARY WARNED IN 2013 AGAINST RUSHING TO WAR AGAINST SYRIA
Zaid Jilani
April 7 2017

… This is exactly what Trump’s defense secretary, Jim Mattis, warned about in remarks he made in 2013.

Mattis had just retired from his role as the commander of U.S. Central Command, and agreed to be interviewed by CNN’s Wolf Blitzer about U.S. policy in the Middle East.

When Blitzer asked Mattis about his views on military intervention against Syria’s government, the former general sounded a stern note of caution. He stressed that the United States should not intervene without a serious and well thought-out plan, and that it would be an enormous commitment.

“On Syria, ladies and gentlemen, we are going to have to determine what is the end state we want. This war needs to be ended as rapidly as possible. That’s the bottom line,” Mattis began. “But if the Americans go in, if the Americans take leadership, if the Americans take ownership of this, it’s going to be a full-throated, very, very serious war. And anyone who says this is going to be easy, that we can do a no-fly zone and it’ll be cheap, I would discount that on the outset.”

He then drew an analogy to the war in Iraq.

“We need to be very clear about our military end state, contributing to what political end state,” said Mattis. “Otherwise, you’re liable to invade a country, pull down a statue, and then say, ‘Now what do we do?'” Hearing this, the audience burst into laughter.

… Mattis also offered some skepticism to Blitzer when asked about a so-called no-fly zone, wherein the United States would militarily prohibit Syrian aircraft from flying over a certain territory to shield civilians.

“Why do you want to take out their air support? Is it because they’re using aircraft to kill most of the people on the ground? No, they’re not. They’re using artillery, machine guns, and mortars and snipers. So let’s have a reason for what we’re going to do,” he noted.

… There are indeed serious considerations about the possible results if American bombardment aimed at the Syrian government continues.

As former Secretary of State Hillary Clinton noted in one of her paid speeches, most of Syria’s air defense systems are in populated areas — meaning that if the U.S. were to strike them while creating a no-fly zone, it would “kill a lot of civilians.”