Story highlights Sen. Rand Paul challenged Sen. Bernie Sanders on Thursday to a one-on-one debate on the merits of capitalism versus socialism

Paul is an avowed libertarian, while Sanders is a committed democratic socialist

Washington (CNN) Sen. Rand Paul challenged Sen. Bernie Sanders on Thursday to a one-on-one debate on the merits of capitalism versus socialism, describing himself and Sanders as "really the diametric opposites of viewpoints in our country."

"We've been saying what a fun, dramatic, and informative debate it would be if Bernie Sanders and I could have an hour-long debate," said Paul during an interview with Iowa radio station WHO NewsRadio 1040.

"Can you imagine," he continued, "debating over what rights are versus what obligations are, and debating socialism versus capitalism?"

The two presidential candidates represent the ideological extremes of today's Republican and Democratic parties -- Paul, on the Republican side, is an avowed libertarian, while Sanders, running for the Democratic nomination, is a self-described democratic socialist -- and have premised their presidential bids on the need for a shift in their respective parties' philosophies.

Besides staking claims to ideas outside the political mainstream and serving as colleagues in the Senate, however, the two have very little in common.