His town hall meeting is in an auditorium at the Figge Art Museum, which an audience of some 100 people has filled on a sunny fall afternoon. Other candidates may arrive to thumping music, but Paul gets a simple introduction as "the Thomas Jefferson of our day."
Others may affect shirtsleeves or cowboy boots to show their connection to ordinary folks, but the 76-year-old Paul wears a business suit. He doesn't tell jokes or pay homage to local politicians. When he is done, he leaves without stopping to shake hands or pose for photos.
Paul is the only Republican contender who can speak for more than an hour without attacking President Barack Obama by name or invoking Ronald Reagan. His rivals are running political campaigns. Paul has bigger fish to fry.
"I've had a strong message for a long time, and I've been talking about it for many, many years if not decades, but it seems like the message of liberty is more appropriate now than it has been in a long, long time," he says.
Style is the least of the ways in which the candidate departs from convention. Paul delights in two principal habits: taking un-conservative positions that are anathema to the other candidates, and taking conservative positions further than the other candidates would dare.
Today, he is intent more on the latter, criticizing the federal government for bailing out financial institutions, running up debt and meddling in the economy. "It's time to change policies and quit spending so much money," he says, to hearty applause.
Paul has unassailable credibility on the issue, having earned an "A" from the National Taxpayers Union every year he's been in Congress going back to 1997. While other Republican members of Congress were approving swollen budgets under President George W. Bush, the retired obstetrician was validating his nickname: "Doctor No."
He has released a plan to slash federal spending by $1 trillion -- not over four years or 10 years, but in one year. He would reach that goal by, among other steps, abolishing five Cabinet departments. Total number of departments abolished by the past two Republican presidents? Zero.
Rick Perry may utter ominous warnings to Ben Bernanke, but no one is more critical of the Federal Reserve than Paul. He objects not just to its recent conduct but to its existence.
Central banks, in his view, are shadowy institutions that exist to enrich the powerful and debase the currency. He said earlier this year, "We need to stop allowing secretive banking cartels to endlessly enslave us through monetary policy trickery."
That's the sort of alarmism that causes many people philosophically compatible with Paul to roll their eyes. His fetish for the gold standard finds few allies even among economists who favor free markets and low inflation.
But his views on monetary matters don't evoke fierce disagreement from his fellow GOP candidates. What makes them recoil is his rejection of military intervention in places like Iraq and Afghanistan, which he blames for squandering money and provoking anti-American terrorism.
But again, Paul laces useful insights with irrational paranoia. In Libya, President Obama might get points for insisting that NATO take the lead role. Not from Paul, who denounces the multilateral approach as "a victory for one world government" -- one of his curious obsessions. He has previously accused both Obama and George W. Bush of favoring one world government.
Paul often makes such detours into the strange or indefensible. The newsletters he put out in the 1980s and 1990s showed a penchant for crude bigotry against blacks ("animals") and gays. Paul disavowed the offending passages, claiming he never saw or approved most of them -- an implausible excuse for a publication carrying his name.
But his appeal in this campaign lies elsewhere, in his longstanding opposition to inflation, excessive spending and endless war. On those issues, Paul has not moved toward the Republican mainstream since 2008; the Republican mainstream has moved toward him. As he hurries off to his next event, he leaves the crowd behind him, but he seems to be pulling the party in his wake.