Many people were appalled at comments made by Kentucky U.S. Senate candidate Rand Paul, son of Ron Paul, a 2008 Republican candidate for president. Both Pauls lean toward the libertarian end of the spectrum. Shortly after Rand Paul won the Kentucky GOP primary, he was asked if he would have voted for the Civil Rights Act of 1964. He said he liked that it put an end to discrimination in public domains, but was less enthusiastic about it dictating that private businesses not discriminate.

The idea of turning the clock back to the days of Jim Crow, when people of African-American descent had to use different drinking fountains, sit in the back of the bus and be banned from some hotels and restaurants is worthy of the outrage that has been expressed. But Mr. Paul’s views suggest something more troubling, which is a deep misunderstanding of the social contract as it exists in 21st century America, a contract that has been hard-won and which provides the underpinning for much of what we enjoy living here.

After Mr. Paul’s comments, Fox News commentator John Stossel said more clearly what the candidate attempted to explain: “Private businesses ought to get to discriminate. And I won’t ever go to a place that’s racist and I will tell everybody else not to and I’ll speak against them. But it should be their right to be racist.” Mr. Stossel also suggested the public accommodations section of the Civil Rights Act be repealed, which would allow restaurants, stores and hotels to ban customers based on skin color, religion and so on.

There is something appealing about libertarianism. One of its basic tenets is its call for local, state and the federal government to take big steps back to allow the individual and private business more freedom. Rather than draw stark lines in the sand, the libertarian philosophy trusts social and market forces to create good behavior. Mr. Paul implies that a restaurant that refused to serve left-handed redheads would earn a bad reputation in the community and eventually go out of business. Except it may not, because so few would be affected; that effect may be described as the tyranny of the majority.

While such concepts may make sense in the abstract, they do not work in real life. And we know they don’t work because they have been tested. Mr. Paul and Mr. Stossel should view film of young African-American men and women being battered with high-pressure fire hoses — and worse — when they tried to reverse Jim Crow.

It has taken centuries, but Americans have settled on the rules of the public square. If an entrepreneur wants to open an ice cream stand, he knows that he must follow certain rules, including not discriminating against certain groups of people.

And they include not serving week-old ice cream that has been left out in the sun. Under Mr. Paul’s rules, when word got out that the ice cream stand made customers sick, it would close for lack of patronage. That’s not good enough. And this debate has been had and settled. Such libertarian utopias may exist in the minds of Rand Paul and John Stossel, but they have no place in public policy.