Appearing Sunday on CNN's State of the Union, Kentucky Senator and presidential candidate Rand Paul explained how his opposition to gay marriage does not contradict his libertarian ideology.

In an interview with Dana Bash, Paul was asked about the apparent contradiction.

“In New Hampshire, you said, 'I will fight for your right to be left alone.' I realize that you believe gay marriage is a state issue, but why do you believe, just as a core principle, as a libertarian, that people should be left alone but not when it comes to their right to marry somebody they love?”

“I do believe people ought to be left alone,” Paul answered. “I don't care who you are, what you do at home or who your friends are, where you hang out, what kind of music you listen to. What you do in your home is your own business. That's always been who I am. I am a leave-me-alone kind of guy.”

“But not when it comes to marriage,” Bash said.

“I think there's a religious connotation to this. I also believe people ought to be treated fairly under the law. I see why if the marriage contract conveys certain things, that if you want to marry another woman, you can do that and have a contract. But the thing is that the religious connotation of marriage that has been going on for thousands of years, I still want to preserve that,” Paul said.

Paul went on to say that gay couples could “have contracts.”

“You could have both the traditional marriage, which I believe in and then you could also have the neutrality of the law that allows people to have contracts with another,” he said.

Lawsuits challenging state gay marriage laws, however, are not asking for church recognition. A civil marriage is a neutral contract which applies only to the government, and no contract between private individuals can impose the responsibilities on third parties – including the government – that marriage does.