DURING Mayor Nutter's budget address last week, he devoted the end of his speech to challenging the next mayor of the city, outlining the issues that he believes the next mayor must tackle.

They included chipping away at the pervasive problem of poverty, addressing violence among young men and boys of color, pushing for higher high-school graduation and college attainment rates, fostering integrity and ethical culture and encouraging business and development. Basically, Nutter challenged the next mayor to carry on the work of the Nutter administration.

Anyone who spends eight years doing a job surely wants to see his work continue, but we doubt that any of the current mayoral candidates will be interested in carrying on Nutter's legacy. In fact, the political reality demands that they set themselves apart and promise their own vision for the city.

Right now, the city is on an upswing. Not only is there momentum on increased development and employment, lower poverty and crime, and increased attention on ethics, but big events like the pope's visit and the selection of Philadelphia as the site for the Democratic National Convention are wins for the city's overall outlook.

All that momentum must continue, but "maintaining momentum" should be a minimum requirement for the job of mayor.

We want more.

A mayoral election is not just a process to elect the next leader of the city. It's a process of helping a city define who we are and what we want to be.

We theorize that one of the reasons Nutter prevailed in 2007 was that his focus on ethics, sustainability and "a new way" gave people enough of a glimmer, and promise, of what the city might become. Other candidates - Fattah on poverty, Brady on keeping the old machine intact, Evans and Knox with unclear visions - missed the boat.

So far in the current race, it's hard to discern a big vision from any candidate.

With 10 weeks to go until the primary, two candidates have no policy papers on their website but are essentially home pages to generate donations. Others have limited information on issues, with few detailed strategies for action. One has no website at all.

And that's troubling: We're a big city, worthy of big ideas. And despite Nutter's accomplishments, there is still much at stake.

In 2007, the Philadelphia Workforce Investment Board issued a report detailing how Philadelphia is a tale of two cities: a city of working people, and a city looking for work. A city of prosperity, and a city of disparity. A city of higher learning, and a city struggling to learn.

Eight years later, despite progress, these observations are still true.

No candidate has so far described his view of what the city is at this moment, and where he wants to take it. This city - like any other - is a story being constantly revised and refined. The mayor is an author of that story. The current mayoral candidates are vague on how their temporary authorship might shape that story.

Maybe this lack of vision means the strong-mayor form of government is morphing into something else. Maybe the city's momentum will take care of itself, and no longer depends on a leader to push it. But we don't really believe that.

There's 10 weeks left, candidates. Time to take a stand. Show us what you have.