Silicon Valley is full of lore when it comes to how entrepreneurs really got started. When serial founder Jack Dorsey took the stage at TechCrunch Disrupt in San Francisco Monday, he wanted the audience to get a few things straight about his own founding story.

"I never wanted to be an entrepreneur," said Dorsey.

So what did he want to be? At one time or another, his list included the next Bruce Lee, a sailor, a tailor, and an artist--specifically, a surrealist. Of course, he went on to found two of the hottest start-ups in Silicon Valley: Twitter and mobile payments start-up Square.

But Dorsey was eager to explain that a start-up's "founding moment" often isn't what it appears to be.

"There's a lot of emphasis on the initial moments of a company, but that ignores the reality that companies exist and evolve over time," he said. "A company has multiple founding moments."

A company also has multiple founders, he said, including early employees who never wind up sharing the co-founder title. Dorsey said he considers business people like Starbucks's Howard Schultz and Marissa Mayer, employee No. 20 at Google and current CEO at Yahoo, to be founders even though both joined those companies later. 

In his own companies, he cited Twitter's current CEO Dick Costolo and Square's COO Keith Rabois as examples of employees who have made the kind of contributions that have changed the course of both companies. "A founder is not a job. It's an attitude, it's a role, it's an idea that can happen again and again and again," Dorsey said.

The hard part, many entrepreneurs might say, is coming up with that idea again and again. Despire Dorsey's track record, you might say it's easier said than done. 

But Dorsey offered some parting words of encouragement to the packed audience of aspiring tech titans:

"You don't have to start from scratch to do something interesting, to do something worthwhile in the world. Twitter was not started because we wanted to start a company. It started out of a failed company. Pick a movement, pick a revolution, and join it. Pick something you believe in, that you want to make an impact in, and then question everything inside those companies or movements."