Thanks to the Boston Herald, we now have our fullest sense yet of how the Boston mayor's race is shaking out. A new Herald-Suffolk University poll puts Boston City Councilor John Connolly and State Representative Marty Walsh atop the crowded preliminary-election field, with support from 12 and 11 percent of Boston voters, respectively. Next up: Suffolk County DA Dan Conley and Boston City Councilor Rob Consalvo, with 9 and 8 percent support.

Interesting stuff in its own right -- but the Herald had a bigger takeaway. "The surprise in this poll," the Herald argued, "is that no minority or so-called 'progressive' candidate has been able to cobble together enough support to get into the top tier of candidates."

It's true that there's no minority candidate in the Herald's top four. But the statement that there's no "progressive" in the race seems more dubious. Thanks in no small part to Menino, whose early advocacy of issues like gay rights has made him a favorite of left-leaning voters for years, the term "progressive" has become almost a badge of honor for Boston politicians.

Given that, it seemed likely that at least a couple of the Herald's top four would take issue with the suggestion that they're not progressive. So I asked them--and they all did:

@reillyadam @marty_walsh @DanFConley @RobConsalvo yes, definitely.

@reillyadam I'm a Menino Progressive. I believe government's role is to help people and Boston should be a leader in equality and fairness

@reillyadam I run one of the most progressive DA offices in the country. I am a practical progressive.

@reillyadam Yes, and anyone looking at my legislative record would agree.

Now, what defines a "progressive" is certainly up for debate -- and some voters who thrill to that label will likely conclude that one of the Herald's top four doesn't really fit the bill. Still, the implication that there's no appetite for a "progressive" candidate for Boston mayor seems off base. Judging from what Connolly, Walsh, Conley, and Consalvo had to say, the opposite may be true.