Dr. Ben Carson says Muslims who claim to be faithful to the U.S. Constitution and Shariah law are "schizophrenic."

The Republican presidential hopeful appeared on Breitbart News Daily on SiriusXM on Tuesday and was asked whether devout Muslims can credibly claim they are loyal to America's founding principles.

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"Do you think that Muslims that are Shariah-adherent can ... integrate into a society where you have the rule of law and ... a federal system?" Carson was asked, Mediaite reported.

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"Only if they're schizophrenic," the retired neurosurgeon replied. "I don't see how they could do it otherwise, because you have two different philosophies warring at you. ... So, no. That would be very difficult. That's why Teddy Roosevelt said what he said. He said you're welcome to come here from any place and [practice] any religion as long as you accept our ways and want to be an American. If you don't, then stay where you are."

Carson was then asked to comment on former President George W. Bush's claim after the September 11, 2001, terror attacks that "Islam a religion of peace."

"If you accept all the components of Islam, including Shariah, it is not a religion of peace. It is a religion of domination," said Carson.

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The Republican presidential candidate has never been one to shy away from a question on radical Islam. A September appearance on "Meet the Press" with NBC's Chuck Todd enraged Muslim activists when Carson said he would not be in favor of having a Shariah-practicing American as the commander in chief.

“I would not advocate that we put a Muslim in charge of this nation," said Carson Sept. 20, WND reported.

The Council on American-Islamic Relations, or CAIR, immediately responded to Carson's comments.

"Mr. Carson clearly does not understand or care about the Constitution, which clearly states that ‘no religious test shall ever be required as a qualification to any office,'" said CAIR National Executive Director Nihad Awad. "We call on our nation’s political leaders – across the political spectrum – to repudiate these unconstitutional and un-American statements and for Mr. Carson to withdraw from the presidential race."

CAIR's supporters, ironically, are the kind of Americans Carson is worried about. The Department of Justice named the organization an unindicted co-conspirator in a terror-fundraising scheme that raised $12 million for the Palestinian terrorist group Hamas.

Former FBI agent Mike Rolf reported in the book, "Muslim Mafia," "CAIR has had a number of people in positions of power within the organization that have been directly connected to terrorism and have either been prosecuted or thrown out of the country."

A review of the public record, including federal criminal court documents, past IRS 990 tax records and Federal Election Commission records detailing donor occupations, reveals that CAIR has been associated with numerous convicted terrorists or felons in terrorism probes, as well as suspected terrorists and active targets of terrorism investigations.

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"The Department of State should designate the Muslim Brotherhood and other organizations that propagate or support Islamic terrorism as terrorist organizations, and fully investigate the Council on American-Islamic Relations as an offshoot of the Muslim Brotherhood and a supporter of terrorism," Carson said on his campaign website Dec. 14, WND reported.

Carson is hoping his message resonates with South Carolina voters, who are preparing to cast their Republican primary ballots Feb. 20.

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