More than most Republican contenders for the presidency, Wisconsin Gov. Scott Walker, who made his official entrance into the campaign Monday, is known for his style of politics — combative — rather than the substance of his views. He regales conservative audiences with his success in defeating public unions in his home state and surviving three tough elections.

Winning elections takes political skill, and no president can succeed without that. Toughness, though, is variable, and more complex. In an era of stagnant middle-class wages, declining unionization and soft labor markets, it’s not clear that unions posed the toughest threat to prosperity in Wisconsin.

It’s also unclear how Walker’s brand of toughness applies to the presidency. He has claimed that when President Ronald Reagan broke an air traffic controllers’ strike in 1981, it marked “the beginning of the end of the Cold War.” And he has equated his own defeat of public unions in Wisconsin with his capacity to defeat the Islamic State.

It is difficult to overstate how dubious such claims are.

Now that he’s officially in the contest, Walker should assume he’s already made his case on style: Granted, he’s tough. It’s time to move on to substance.

His first effort should be to clarify his stand on immigration, which he has muddled by saying different things to different people at different times. A candidate for county executive might get away with that. A leading candidate for the Republican presidential nomination cannot. The same applies to Walker’s position on education standards.

Walker has ample time and opportunity to make his views clear in the months ahead. For the moment, he seems intent on wooing Iowa conservatives in hopes of triumphing in the first presidential contest. As he surveys the crowded field of well-funded challengers, it may seem expedient to curry favor with archconservative Iowans. The danger is that he will back himself into an ideological corner. And that would be the opposite of tough.

FROM AN EDITORIAL ON BLOOMBERG VIEW

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Washington doesn’t lack for “fighters.” It has a shortage of leaders with the maturity to choose battles carefully and win them without setting bridges ablaze. If Mr. Walker made it to the general election, he would have to explain why his confrontational style would help in Washington.

He would also have to explain why his agenda should be the nation’s. Here, too, he would have a challenge. Mr. Walker’s signature struggle against Wisconsin’s public-sector unions was understandable, given how many states have seen unaffordable pension commitments steer them into budgetary disaster. His drive to reform public schools against the status-quo opposition was broadly worthy. But his flip to the far right on immigration — he has even made noises about reducing legal immigration — was not sensible. Nor was his decision to remove a 48-hour waiting period to buy guns in Wisconsin, or his desire to amend the Constitution to allow states to deny marriage licenses to same-sex couples.

It would be a big mistake to underestimate Mr. Walker, who has already shaken Wisconsin politics to its core and has a plausible path to the GOP nomination. He still has to show, however, that his supporters aren’t overestimating him.

FROM AN EDITORIAL IN THE WASHINGTON POST